9916 lines
243 KiB
Plaintext
9916 lines
243 KiB
Plaintext
PRINCIPAL ARCS OF THE MERIDIAN, THE PAR.ALLEL AND OBLIQUE ARCS.
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Frrmtisp;,.,., .
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MA .. ON MOLLW(.IOC"S tQUIVAL[NT Qfl HDMALDCflAPHIC PROJECTION.
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M[-'~URCD IN PftOCFICSS • f'RO.JC.:OTCD
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THE
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TRANSCONTINENTAL rfRii\.NGULATION
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.\:SD THE
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AIVIERICAN ARC OF THE PARALLEL.
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ERRATA. P. 18. Sentence beginning on the seventh line should read: "The work in Ii1dia11a and Illinois cost $1 r per square mile, where the average cost per point was $r, 725; while
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that in- tlte most mtmntainous part <!I Colorado, and in Utalt and Nevada, cost about $2,
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whe~e the cost of occupying each station was $6,131." P. 6;?3, fifth line, subscript .. should be**" Pp. 655 and 656, omit footnote.
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·- P. 867, first paragraph, last line, "oscillatory" should be "osculatory."
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-.q.~
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') 7(
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-
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l"IA
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~S/
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1)011
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11 DO
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As. TRE.ASURY DEP.ARTMENT COAST AND. GEODETIC -SURVEY .HENRY S. PRITCHETT, SUPERINTENDENT.
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GEODESY.
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THE TRANSCONTINENTAL TRIANGULATION
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//
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.\ND THE
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AMERICAN ARC OF THE PARALLEL.
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By Assistant CHAS. A. SCHOTT, Chief'of"tho,> Con~putini& l:livision..
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SPECIAL PUBLICATION No. 4.
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_____ -- :..:.:_._,
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. -·- .
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LIBRARY ·
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APR 1 0 2006 .
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WASHINGTON:
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Nc.Hi ..Jt 1Cij \..i~t;,:.u 11v & Atmospheric Adn:iinistratior: J ___JJ.S. Dept. of Commerce
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. -.····---·
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GOVERNlllENT PRINTING OFFICE.
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rqoo.
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3
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National Oceanic and Atmospheric Administration
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ERRATA NOTICE
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One or more conditions of the original document may affect the quality of the image, such as:
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Discolored pages Faded or light ink Binding intrudes into the text
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This has been a co-operative project between the NOAA Central Library and the Climate Database Modernization Program, National Climate Data Center (NCDC). To view the original document, please contact the NOAA Central Library in Silver Spring, MD at (301) 713-2607 xl24 or www.reference@nodc.noaa.gov.
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LASON Imaging Contractor 12200 Kiln Court Beltsville, MD 20704-1387 ·January 1, 2006
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TREASl'.RY DEPART~IEN.1:,
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DqcuriJ.ent No: 21i3.
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Coast a111l Oeoddia 81!1Teg. 4
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THE TRANSCONTINENTAL TRIANGULATION AND THE AMERICAN ARC OF THE PARALLEL.
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GENERAL DIVISIONS OF THE WORK
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PART I. UNIT OF LENGTH, BASE LINES. AND BASE NETS. II. DETERMINATION OF HEIGHTS OF STATIONS. III. THE MAIN TRIANGULATION AND ITS CONNECTION WITH THE BASE NETS. IV. THE RESULTS OF THE ASTRONOMIC DETERMINATIONS OF LATITUDE. V. THE RESULTS OF THE ASTRONOMIC DETERMINATIONS OF AZIMUTH. VI. THE RESULTS" OF THE ASTRONOMIC DETERMINATIONS OF LONGITUDE.
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VII. THE GEOGRAPHIC POSITIONS AND COMPARISON OF THE ASTRONOMIC AND GEODETIC RESULTS. PRELIMINARY COMBINATION OF AMERICAN ARCS FOR DETERMINING THE EARTH'S FIGURE.
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5
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Blank page retained for pagination
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TABLE OF CONTENTS:
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Page.
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FOREWORD •.....••......................... ··'·..................................... . . . .
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rs
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INTRODUCTION .................................... .". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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r7
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PRE;I.IMINARY STATEMENT •••.•..........•............... ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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( 1) Location, scope, and purpose of the transcontinental triangulation, with historical
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notes as to its inception and progress.......................................... 23
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· ( 2) Subdivisions of the chain of tria11gulation and their distfnguishing characteristics. . ::?S
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(3) General statement in regard to the astronomic measures . . . . . . . . . . . . . . . . . . . . . . . . . 2·5
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PART I.
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UNI';r OF LENGTH, B.A,SE LINES, AND BASE NETS.
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A. INTRODUCTION ................ ; ......................................... .- . . . . . . . . . . . . . 31
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B. UNIT OF LENGTH•.......................................................... ·...........
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31
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(I) History of the committee metre of 1799... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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( 2) Coefficient of expansion ............................................. ·.. . . . . . . . . . . 32
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(3) Length, in terms of the international prototype metre ........................... · 33
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c. LOCAi, OR STATION ADJUSTMENT. . . . . . . . . . . . . . . . . . • • • . • . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . .
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36
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( r) General discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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D. REDUCTION OF HORIZONTAL DIRECTIONS To SEA LEVEL... . . . • • • . • . . . . . . . . . . . . . . . . . . . . .
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47
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E. ADJUSTMENT OF BASE NETS OR OTHER TRIANGULATION....... . . . . . . . . . . . . . . . . . . . . . . . 47
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F. REMARKS ON WEIGHT COEFFICIENTS IN THE NET ADJUSTMENT . . . . . . . . . . .. : . . . . . . . . . .
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SO
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G. COMPUTATION OF SPHERICAL EXCESS....................................... . . . . . . . . .
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SI
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H. ACCOUNT OF THE BASE LINES.........................................................
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S4
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(I) General statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
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( 2) Measurement ................................................................. ·. SS
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(a) Kent Island base line .......... ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SS
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Location, measurement, and length .................·.... " . . . . . . . . . . . . . . SS Abstract of horizontal directions . . . . . . . . . . . .......... : . . . . . . . . . . . . . . . . . . s"3 Figure adjustment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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Triangles of the base net............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Probable errors......................................... . . . . . . . . . . . . . . . . 63
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Description of stations........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
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(b) American bottom base line . . . . . . . . . . . . . . . . . . . . . . . : ....... : . . . . . . . . . . . . . . . . 66·
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Location, measurement, and length ............... : . . . . . . . . . . . . . . . . . . . . . . . 66 A,bstract of horizontal directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
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Figure adjustment ..................................... : . . . . . . . . . . . . . . . 72
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Triangles of the base net......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Probable t!rrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7S
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Description of stations......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
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(c) Olney base line...................................... . . . . . . . . . . . . . . . . . . . . . 79
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Location, measurement, and length .......'. .........·. . . . . . . . . . . . . . . . . . . . . . 79 . Abstract of horizontal directions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
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Figure adjustment....................................................... 84
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Triangles of the base net. . . . . . .. . . . . .. . . . . .. .. . . .. .. .. .. . .. .. . .. .. .. . . .. . 93
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Probable errors....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Description of stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . 98
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.i
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s
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CONTENTS •.
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H. ACCOUNT OF THE BASE I,INES~Continued.
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Page.
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(2) Measurement-Continued.
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(d) El Paso base line ................................... , .....................·. IOI
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Location, measurement, and length. . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . IOI
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Abstract of horizontal directions:.................... . . . . . . . . . . . . . . . . . . . . . IOS
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Figure adjustment. .. : ................................ :. . . . . . . . . . . . . . . . . . no
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Triangles of the base net ............. , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II::?
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Probable errors ........................... ·.................. , . . . . . . . . . . . . l 14
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . I 14
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(e) Yolo base line ............................................... :. . . . . . . . . . . . . n6
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Location, measurement, and length ............................... ::...... n6
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Abstract of horizontal directions ............................ : : : .. : . . . . . . . . 121
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Figure adjustment ............................ :·. . . . . . . . . . . . . . . . . . . . . . . . . 124
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Triangles of the base net ............... : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127
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Probable errors : .... : . : : : ·...............................................•. 130
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Description of stations . . . . . . . . . . . . . . . . . . .. '. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
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(f) Holton base line ........................................................ : . . 133
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Location,measurement, and length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 133
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Abstract of horizontal directions... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
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Figure adjustment. .......... :.................... . . . . . . . . . . . . . . . . . . . . . . . 142
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Triangles of the base net . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . ... . . . . . . . . . . . 144
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Probable errors .......................... : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
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(g) St. Albans base line........................................................ 150
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Location, measurement, and length....................................... 150
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Abstract of horizontal directions ........... : . . . . . . . . . . . . . . . . . . . . . . . . ·. . . . . . 154
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Figure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
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Triangles of the base net ................... .". . . . . . .. . . . . . . . . . . . . . . . • . . . . . 166
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Probable errors... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
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Description of stations . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . 171
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(h) Salina base line ................................... : . . . . . . . . . . . . . . . . . . . . . . . 174
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Location, measurement, and length.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
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Abstract of horizontal directions .....·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18..?
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Figure adjustment ...................... .". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
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Triangles of the base net . . . ............................................ : 186
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Probable errors ..................·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
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(i) Salt Lake base line ................................................ ." . . . . . . . 190
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Location, measurement, and length....................................... 190
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Abstract of horizontal directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
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Figure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
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Triangles of the base net ........................................ , . . . . . . . . 215
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Probable errors ....................... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
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Description of stations .... ·.................... . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
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(j) Versailles base line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
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Location, measurement, and length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
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Abstract of horizontal directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
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l''igure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23,,
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Triangles of the base net . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • 240
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Probable errors.......................................................... 244
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
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(3) Synopsis of facts and results. . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . • . . . . . . . . . . . . . . . • • • . 247
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CONTENTS.
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9
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PART II.
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DETERMINATION OF HEIGHTS OF STATIONS.
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Page.
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A. GENERAL REMARKS •••..•.•.•..•........... · .• · · ••......•. · · ..........•.•. • ••. · • · . · • • • 253 ( 1 ) Hourly values of the coefficient of atmospheric refraction . . . . . . . . . . . . . . . . . : ..... . 255
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( 2) Diurnal variation of the coefficient of refraction ............... · .......... · · · · · · · 255 B. DETERMINATION OF HEIGHTS IN EASTERN COLORADO ...... ~ .......... • •••• • • • · · · · · · · · · 256
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( 1) Abstract of zenith distances .................................... · ............... . 257 ( 2 ) Determination of coefficient of refraction ...................................... .. 261
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(3) Determination of differences of height ......................................... . 263
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C. DETERMINATION OF HEIGHTS IN CENTRAL CALIFORNIA ........................ · · ... · ·
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267
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( 1) Introrluction .................................................... ·: . ............ . 267
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(2) Abstract 9f zenith distances . . . . . . . . . . ................ , ....................... . 269
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(3) Computation of coefficient of refraction: ..... ·................... , .............. . 276
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(4) Computation and adjustment of differenc.es of :\leight . . . . . . . ................... . 277
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D. HOURLY OBSERVATIONS OF ZENITH DISTANCES FOR ATMOSPHE;RIC. REFRACTION, JACKSON
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BUTTE AND ROUND TOP . . . . • . . . . . . . . . . . . . . . . . . • . . . . . . . . • • . . . . . . . . . . . . . . . ......... .
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(I) Introductory remarks ......................................................... .
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("2) Observations at Round Top .................................................... .
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(3) Observations at Jackson Butte ................................................. .
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(4) Resulting zenith dista11ces at Round Top ...................................... .
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( 5) Diurnal variation of zenith ·distances ... •.................................... : ... .
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( 6) Resulting hourly mea11s, Round Top ........................................... .
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(7) Resulting zenith distances, Jackson Butte....................................... .
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(S) Resulting hourly mea11s, Jackson Butte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :
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(9) Meteorological record in connection with ze11ith distances ....................... .
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E. DETERMINATION OF HEIGHTS SOUTH OF LATITUDE 38° ................................ .
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(I) Introduction .................................................................. .
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( 2) Abstract of reduced zenith distances ........................................... .
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(3) Coefficient of refraction ....................................................... .
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(4) Computation and adjustment of differences of heights .......................... .
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F. DETERMINATION OF HEIGHTS, SACRAMENTO AND SAN JOAQUIN VALLEYS ..............•
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(I) Introduction ........................................... : ...................... .
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(2) Abstract of reduced zenith distances ........................................... .
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(3.) Coefficient of refraction . . . . . . . . . . . . . . . . . . .................................... .
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(4) Differences of heights, and their adjustment .................................... .
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G. DETERMINATION OF HEIGHTS BETWEEN PIKES PF.AK AND ROUND TOP, CALIFORNIA ... .
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( r) Abstract of reduced zenith distances ........................................... .
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( 2 } Coefficient of refracti'ln ....................................................... .
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(3) Adjustment of heights ........................................................ .
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(4) Table of differences of heights ................................................ .
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!'ART III.
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. THE MAIN TRIANGULATION AND .ITS .CONNECTIO.N WITH THE BASE NETS.
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A. INTRODUCTION ............ ·......... · · · .... · · · · · · ....... · · · · · · · · · · · · · · ....... · . · . · · · · · · 347 B. DISTRIBUTION OF BASE LINF.S •...... ·...• -· • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 C. GENERAL METHOD OF TREATMENT ........... ."......................................... 348
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D. PRECISION OF ADJUSTED TRIANGULA't"ION ...... · · · . . .... · · · .. ·. · · · · ·. . . . . . . . . . . . . . . . . . • 349 E. LENGTH OF SIDES OF BASE NETS (LOGARITHMS). . • . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 F. THE; TRIANGULATION ... ·...••• . • . . . . . . . . . . . . • • . . . • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35I
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(I) Eastern Shore seri.::s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 (a) Introduction............................................................. 351 (b) Abstract of horizontal directions .................................. · . . . . . . . 353 (c) Figure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 (d} Adjusted triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . 364 (e) Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
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IO
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CONTENTS.
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F. THE TRIANGUI.ATION-Continued.
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Page.
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(2) Allegheny series·.: ......... ·........... ' ...·.....................·.............. .. :;68
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(a) Introduction ................................................ · · .......... . 368
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(b) Abstract· of horizontal ·directions:
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·
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Eastern part ....... : ......... ." .............. , .... , : .................... .
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\Vestern part .. , .............. : ...... :·......... ·...... .' ....·...... : ... , ..
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(c) Figure adjustment:
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Eastern part. .. : . . . . . . . . . . . . . . . . . ......... : . : . . . . . . . . . . . . . . . . . . . . . . .. . 374 Western part ............................... : ......................... . 383
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(d) Adjusted triangles ........................................·................ . 388
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(e) Precision ............................................. · .... ·.......·... · · · · 394 (3) Ohio series ................................................................... . 395
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(a) Introduction ............................................................. . 395 ( b) Abstract of horizontal directions ........... : ............ :· ·............... . 396
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(c) Figure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............. : ..... . 404_
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~ ~:·: ;~~~~:~:~1 ~~i~~.~1~~. 4II : : : : ·.: ·. : : . : ·. ·. : . : : : : ·. ·. : : : ·.. ": : ·. : : . ·. ·. : : : ·. :_ : : : ·. ·. : : : ·. ·. ·. : : ·. : 416
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(4) Indiana· series . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 (a) Introduction .................................... ·.......... ·.............. . 417 (b )' Abstract of horizontal directions ........................................ . 418
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(c) Figure adjustment . . . . . . . . . . . . ......................................... . 424
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(d) Adjusted triangles .................... , ... ." ............... ·. . . . . . . . . . . . . . 430
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(e) Precision . . . . . . . . . . . . . . . . . . . . . . . ............... ." .................... . 433
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(5) Illinois series ................................................................. . 434
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(a) Introduction. . . . . . . . . . . . . . . . . . . . . ...................................... . 43-1
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(h) Abstract of horizontal directions ......................................... . 435.
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( c) I<'igure adjustment . . . . . . . . . . . . . . . . . ................ ·......... : .......... . -140
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(d) Adjusted triangles . . . . . . . . ·.......................................... .
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446
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(e) Precision .................................................. · · · · ......... . 450
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(6) Missouri series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ .' ......... . 451
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(a) Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .' . . . . . . . . . . . . . . . . . . . .. 45I
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(b) Abstract of horizontal directions ................................ .': ....... . 453
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( c) Figure adjustinent ........ : ............................................. . 46r
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(d) Adjusted triangles . . . . . . . . . . . . . . ....................... ._ ............... . 473
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(7) Mi:~~~:~~=:~~~ ~~~l~s·::: '.: :·.:::: :··::::::::::::. ::·.::::::::::::::: ~:::::: :-: ::::
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4So 4Sr
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(a) Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48r
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(b) Abstract of horizontal directions ............. ·......... .".. . ............. . 48I
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(c) Figure adjustment ....................................... : .... .": . ....... . 493 (d) Adjusted triangles ..................................... : ....... ·..... : ... . 505 ( e) Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........·....•........ . 5r3 (S) Kansas-Colora<lo series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... . 514 (a) Introduction ........................................................... ". .. 514 (b) Abstract of horizontal directions ................................ .'........ ." 515 ( c) Figure adjustment ..................... , . : .... , , .................. : ..... . 526
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(d) Adjusted triangles . . . . . . . . . . . . . . . . . . . . ...... , ... : ................. : .... . 539 (e ) Precision . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ·. 550 (9) Rocky Mount;;iin series ............................ : ......................... : .. . 551 (a) Introduction ................... .'........................ : : ......... : .. ·.. . 551 (b) Abstract of horizontal directions .................................... : .... . 555 (c) Figure adjustment ................................... ·................... . 560
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(d) Adjusted tri:mgles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 l e) Precision ............................................ : .. ·................ . 566
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(f) Description of stations .............................. ·..; .................. . 567 (IO) Nevada series ... : ............................................... -.·.'............ . 571
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(a) Introduction ........................................ ' ....... .'... : ....... . 571 (b) Abstract of horizontal directions....... . . . . . . . . . . . . . . . .................. . 573
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CONTENTS.
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II
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F. THE TRIANGULATION-Continned.
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Page.
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( 10) Nevada: series-,-Continued.
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( c) Figure adjustment . . . . . . . . . . . . . . . .................................. ,. .. . 581
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( d) Adjusted triangles ...... ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 5SS
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(e) Precision ........ ." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . 592
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( f) Description of stations. . . . . . . . . . . . . . ....... : ............................. . .59.:?
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(II) W~=t1e~~~~~~~:~o::~~~ ~~~~s- .......... ·. ·..... >.: :.......... :·.: ·.::::: :·. '. ·. ·.:: '. ·. '.:: ·. ·. ·.:: ·. ·.: ·.. ·. ·.
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597 .597
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(b) Abstract of horizontal directions ................. .'., ..................... . .598
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( c") Figure adjustment . . . . . . . . . . . . . . . . . . . .................................. . 6o.:?
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(cl) Adjusted triangles .................. : .... ·......... : ..................... . l)o8
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~~. ~'_r~~~~i. .~::::::::::::::: 0
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G. s·r.-1.TrSTic!
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6II : : : : : : : : : : :- : . : : : : : : : : : : : : : : : : : : : : . : : _:::::: :.. : : : : 6II
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H. SUMMARY OF RESULTS ..................................... .
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613
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I. ACCORD OF BASE LINES .......................... .
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613
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PAR'r iv.
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THE RESULTS OF THE ASTRONOMIC DETERMINATIONS OF LATITUDE.
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A. GENERAL REMARKS .......·............................................................ .
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B. INSTRUMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . C. DETERMINATION OF THE MEAN PLACES OF STARS ..................................... . D. 'WEIGHTS AND PROBABLE ERRORS . . . . . . . . . . .......................................... .
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E. ABSTRACTS OF RESUT,TING LATITUDES .................................................. .
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( I ) Eastern Shore series ......................................................... . (2) Allegheny series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... . (3) Ohio series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ . (4) Indiana series......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......... . (5) Illinois series . .'. . . . . . . . . . . .................................................. . ( 6) Missouri series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ·. ( 7) Missouri-Kansas !'>eries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8) Kansas-Colorado series ....................................................... . ( 9) Rocky Mountain series....................................................... . ( IO) Nevada series ................................................................ . ( 1I) Western or coast range series ............................... , ................. . F. REDUCTION OF THE OBSERVED LATITUDES TO THE SEA LEVEL ........................... . G. CORRECTIONS TO OBSERVED LATITUDES, AZIMUTHS, AND LONGITUDES, FOR VARIATION OF POLE OF ROTATION ................... · · · · · .......... · · · · ...... · · · · · · · · · · ... · · · · · · . . . 733 H. SYNOPSIS OF. RESULTS FOR LATITUDE OF STATIONS DETERMINED AS'fRONOMICALLV........ 734
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PART V.
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THE RESULTS OF THE ASTRONOMIC DETERMINATIONS OF AZIMUTH ..
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A. INTRODUCTION .............................................. · · · · : · · · ........... · . . . . . . 743
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B. ABSTRACT OF RESULTING AZIMUTHS .............. :...................................... 744
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( I ) Eastern Shore series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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744
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(2) Allegheny series...................... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.j.S
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(3) Ohio series .............. ·...................................................... 758
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(4) Indiana series.................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760
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(5) Illinois series ..... ·.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
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(6) Missouri series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764
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( 7) Missouri-Kansas series ...................•...................... .". . . . . . . . . . . . . . . 767
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(8) Kansas-Colorado series...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769
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(9) Rocky Mountain series ........................................ ." ..... :......... 771
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( IO) Nevada series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
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(I I) ·western or coast range series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795
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C. SYNOPSIS OF RESULTS FOR AZIMUTH .... , . · · . · . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Soo
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12
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CONTENTS.
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PART VI.
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THE RESULTS OF THE ASTRONOMIC DETERMINATIONS OF LONGITUDE.
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A. INTRODUGTION . . . . . . • . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . • . . 807 B. ABSTRACTS OF RESULTS AT TELEGRAPHIC LONGITUD1'; STATIONS . . . . . . . . . . . . . . . . . • , . • . • . • 8o7
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C: SYNOPSIS OF OBSERVED DIFFERENCES OF LONGJTlTDE.................................... 823 D. ADJUSTM1'~N'£ OF SECONDARY· STATIONS AND REFERENCE TO STANDARD LONGITUDE NET. . • 823 E. RESULTING STANDARD LONGITUDES .......................................... .,......... 826
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PART VII.
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THE GEOGRAPHIC POSITIONS AND COMPARISON OF THE ASTRONOMIC AND GEODETIC RESULTS. PRELIMINARY COMBINATION OF Al\1ERICA.N ARCS FOR DETERMINING THE EARTH'S FIGURE.
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A. GEOGRAPHIC COORDINATES OF THE STATIONS COMPOSING THE TRANSCONTINENTAL TRIANGULATION AND THE Ml1ASURE OF THE ARC IN LATITUDE 39° .................... ,
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B. COMPARISON OF ASTRONOMIC AND PROVISIONAL GEODETIC MEASURES....................
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( I ) Latitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • (2) Azimuths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3 ) Longitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4) Preliminary examination of results .................. : . . . . . . . . . . . . . . . . . . . . . . . . . . .
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C. DETERMINATION OF STANDARD (GEODETIC) VALUES FOR LATITUDJ; AND LONGITUDE OF
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INil'IAL STATION HAYS, AND AZil\fU'£H OF LINE, HAYS TO LACROSSE..................
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D. COMPARISON OF ·ASTRONOMIC .4.ND STANDARD GEODETIC DATA ON THE SPHEROIDS OF
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Cl.ARKE AND BESSEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . .
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(I) Latitude...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2) Azimuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . (3 ) Longitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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E. REVIEW OF THE STATIONS EXHIBITING LAR(.E I.OCAL DEFLECTIONS OF 'tHE PLUMB-
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LINE IN THE PLANE OF THE PRil\IE VERTICAL, OR IN LONGITUDE . . . . . . . . . . . . . . . . . . .
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F. SYNOPSIS OF RESULTS OF THE ASTRONOl\IIC AND CORRESPONDING GEODETIC MEASURES
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ON THE PARTS OF THE ARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . .
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( I) Preliminary statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2) Comparison of astronomic and geodetic longitudes. Table A. . . . . . . . . . . . . . . . . . . . (3) Results of arc measurement. Table B ....... .'................................... G. RESULTING GEOGRAPHIC POSITIONS AND AZIMUTHS OF. THE. PRINCIPAL TRIGONOMETRIC
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STATIONS, INCLUDING THE BASE NE'rs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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H. ARC MEASUREMENT................................................................... ( 1) Relation of the arc of the parallel of 1871-1898 to other American arcs.. . . . . . . . . . . . (2) Arc of the meridian between Parkersburg, Illinois, and St.Ignace, Ontario......... (3) Arc of the parallel of 42° between Willowsprings, Illinois, and Mannsville, New York......................................................................
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I. PREl.IMINARV P.\RTIAL COMBINATION OF AMERICAN ARCS ••••••.••. , •............• , •
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831 832
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832
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834 836
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836
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838
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841
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84r
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844 846
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848
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851 85 I 85 I
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853
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S54 866 866 868
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868 . 869
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UST OF ILLUSTRATIONS.
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Page.
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1. ?rincip~l arcs of the meridian, the parallel, and obl_ique arcs ...................... Frontispiece. 2. Diagram............................................................................... 37 3. Kent Island base net .......... .-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4. American botton1 base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6t 5. Olney base net. .... ·.... ·....... ."...... ·.·.~ .......... _. ......... ·..................... .".... 81 6. Footnote sketches ................ : ..... ·....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7. El Paso base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 8. Yolo base net............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II7 9. Holton base net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
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10·1fst. Albans base net and extension....................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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l I.
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12. Salina base net ........................................................ ·............... 175 13. Salt Lake base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 14. Versailles base net : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 15. Diurnal variation of the coefficient of refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 16. Determination of heights between Pikes Peak and First View, Colorado.. . . . . . . . . . . . . . . • • • 256 17. Determination of heights between Point Arena and Mount Diablo........................ 268 18. Diurnal variation of zenith distances observed simultaneously at Round Top and Jackson
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Butte, in September anrl. October, 1879 .................·........................ . . . . ... . 287 19. Determination of heights in the vicinity of Mount Hamilton, California . . . . . . . . . . . . . . . . . . 299 20. Determination of heights across the Great Valley of California . . . . . . . . . . . . . . . . . . . . . . . . . 305 2r. Determination of heights between Pikes Peak, Colorado, an<l Round Top, California...... 312 22. Stations near Salt Lake, Ftah, at which zenith distances were observed.......... . . . . . . . . . 338 23. Round Top, California, looking east. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 24. Kent Island base net to Atlantic coast.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 25. Observing station, Still Pond, Maryland. Elevation of instrument above ground 36_~;
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metres; or 120 feet. Elevation of target 84 metres, or 275 feet . . . . . . . . . . . . . . . . . . . . . . . . . 352 26. Kent Island base net to St. Albans base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 27. St. Albans base net to Holton base net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 28. Holton base net to Olney base net........................... . . . ... . . . . . . . . . . .. . . . . . . . . . . . 417 29. Scaffolding at Station Green, Indiana. Elevation of instrument above ground, 46·3 metn:s,
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or 152 feet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 30. Olney base net to American Bottom .base' net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 3r. American Bottom base net to Versailles base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 32. Versaj.lles base net to Salina base net... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Sr 33. Salina base net to El Paso base net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 q 34. El Paso base net to Salt Lake base net ......................... ·...................... :.. 551
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View of Cimaroon Canyon, as seen from l,Tncompahgre Peak, looking north ............. . 552 Breaking camp on Uncompahgre Peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 Heliotropes of latest pattern ................................... ." ....................... . 552 The 50 cm. or 20-inch theodolite used at the primary stations in the Rocky Mountain region .. 552 Interior Station on Ogden Peak, showing mounting of instruinent on position stand. Alti-
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tude 2 924 metres, or 10 592 feet. . . . . . . . . . . . . . . . . . . ................................ ·.. 13
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14
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ILLUSTRATIONS.
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Page.
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40. Summit Station on Treasury Peak, looking east, showing perforations of wall tent for obser-
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vation with large theodolite. Altitude 4 098 metres, or 13 444 feet ..................... . 552 High Summit Station, Tushar Mountain, Utah, showing ring wall and double shelter tent
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against storms and radiation of heat. Altitude 3 702 metres. or 12 146 feet ............. . 55'.! 42. Rocky Mountain ridges, as seen from Treasury Mountain, Colorado, and showing upper
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camp, 107 metres, or 351 feet belo;.v summit ................. , ........................ . 556 43. View of Treasury Mountai~, Colorado, looking west; station at extreme right of summit .. 556 44. View of Summit Station on Uncompahgre Peak, Colorado. Altitude 4 355 metres, or 14 289
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feet ............................................................................... . 556 45· Interior of station 011 Uncompahgre Peak; observing heliotrope on Mount Ellen, distance
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294·1 kilometres, or 182~;i:· statute miles ........................ : ..................... . 566 Salt Lake base net to Yolo base net ................................................... . 571 Summit of Round Top, California, principal triangulation station on the Sierra Nevarla.
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Altitude 3 165,!~ metres, or IO 386 feet ................................................· 575 Station at Iqepah, Utah, showing protection of instrument. Altitude 3 688!-:3 metres, or
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12 IO~ feet .. ·....................................................... ·......... , , ..... . 5So 49· Yolo base net to Pacific coast .................................................•.. : .... . 597 50. The Great Caspar Signal, California.· Instrument mounted on main scaffolding, at a· height·
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above ground of 4rr metres, or 135 feet. Observer supported independently by the
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central tree trunk and small top scaffolds surmounting it ................... ·. : ....... .
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5r. Systematic errors in latitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .·... ·. :· ... . 52. Diagrani. ........................................................................... ·.. .
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5_;. Diagram .......................................................................... .
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54. Diagram. . . . . . . . . . . . . . . . . . . . . . . . ............ ·.. ·. . . ................................ : .. 55. Diagram ........................................................................... .
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MAPS.
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A. Area covered by the transcontinental arc ..........·................. :..... : ... ·......... (Pocket) B. Distribution of astronomical stations............................. ; ............... , .... (Pocket)
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FOREWORD.
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The volume which is here presented to the scientific world contains the results of
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the most extensive piece of geodetic work attempted by any nation, a geodetic triangu-
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lation across the continent and the resulting arc of the parallel. Thi~ work has been
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conducted with the greatest care, and many improvements in the means of observation·
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have marked its progress.
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In presenting this complete record of a great undertaking, carried through by a
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bureau of the Treasury Department, the executive officers of the Department feel that
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it will prove"a contribution to the science of the world worthvof the United States.
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TREASURY DEPARTMENT, llfay, I900.
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L. J. GAGE, SccrdmJ'.
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15
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Blank page retained for pagination
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INTRODUCTION.
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The. completion of the measure of an arc of the parallel across the Continent of
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North America marks an epoch not only in the scientific history of the United States
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but in the world's geodesy as well. The results of the work, not only to geography but
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to geodesy, are most important and far-reaching. In the present volume are brought
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together not only the observations themselves and a discussion of the results, but also a
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description of the instruments and methoc1s employed, and the improvements which have
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been brought about in the progress of the work. This progress has been coincident with
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that of the science of geodesy itself and, in a measure, the work has been a history of the
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science.
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The transcontinental triangulation, which was designed to connect the triangula-
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tion lines already executed on the Atlantic and on the Pacific coasts, began under my
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predecessor, Professor Benjamin Peirce, the third Superintendent of the Survey, and
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the work has been prosecuted under the succeeding superintendents-Patterson, Hilgard,
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Thorn. Mendenhall, and Duffield.
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Soon after the close of the Civil \Var it became evident that greater extension must
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be given to geodetic operations, in order to keep pace with the material development of
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our country. It was at that time that Superintendent Peirce asked Congress for $15 ooo
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to begin a triangulation connecting the Atlantic and the Pacific coasts. He characterized
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the sum as ''small in amount but of inestimable importance.'' So favorably was the
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project received in Congress that the necessary legislation was immediately enacted.
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The appropriations increased with each succeeding year until 1~74 1 when $50 ooo were
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allotted to the work.
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During the next decade no· specific amounts were set aside for this enterprise, but
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the work was carried on in connection with the general triangulation. Congress always
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authorized the expenditure of certain parts of the great items of appropriations for this
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particular ·purpose. The original idea was steadily kept in view, however, and in 1883
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it again found fqrmal expression in the sundry civil bill, by the appropriation of $30 ooo
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for "transcontinental geodetic work." From this date to the completion of the general
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field work, regular annual appropriations were made. The total cost, from 1871 to
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18732-No. 4--2
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17
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18
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UNITED ST:'\.TES COAST AND GEODETIC SURVEY.
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1897, exclusive of salaries of officers, was approximately $500 ooo, giving an average expenditure of about $20 ooo yearly.
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The cost per mile of progress was least in Maryland and Delaware, being $103, and greatest in California, where it was $463. The average expense of occupying one
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station was $598 in the former case and $9 031 in latter. The cost per square mile of
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territory, strangely enough, however, is greatest in a flat country, where short lines are necessary. The work in Indiana and Illinois cost $11 per square mile, where the .
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avernge cost per point 1'YaS $1 725, while that in Colorado cost about $2, where the cost
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of occupying each station was $6 r3r. The immediate results are these: Sixteen States are given fundamental and per-
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manent points on which all their subsequent surveys may be based. The longest arc of a parallel ever undertaken by any single governmt:nt ha_s been completed, and valuable material has been supplied for a more exact determination of the earth's size and shape. Precision in scientific work has been substantially increased during the period mentioned, and improvement in the field methods has been marked in the base measures, in t]1e triangulation, and in the astronomical determinations. In fact, the progress of this work has kept pace with the progress of geodesy. Since the inception of the work, and growing- out of its prosecution, great strides have been made in point of rapidity an~l accuracy. New methods have been introduced, consequent upon the gigantic scale of the operations. Astronomical results obtained at an altitude of q. ooo feet require special treatment on account of changed conditions in attractive and centrift~gal forces. Horizontal angles, if the stations are extremely elevated, are sensibly different from what they·wouldbe at the level of the seil. The ordinary formula for spherical excess must be extended to meet the demands of the great triangles from Pikes Peak to .the Sierra Nevada. The laws of refraction applicable at lower and equal elevations require modification when great inequalities exist in the heights of stations. The calculation of geographical positions enters a new phase when lines of sight 182 miles long are to be dealt with. · The adjustment of the triangulation-that refined operation by means of which incongruous observations are made to blend harmoniously according to the mathematical theory of probabilities-assumes greater significance in a chain of 2 600. miles of continuous geometrical figures. The nature of the country traversed has developed new·
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ideas in signals and tripods. The mounting of a!1 instrument 152 feet above the ground,
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and the erection of an observing pole ~o a height of 27 5 feet, are featur~s hitherto unknown in similar work. For the first time corrections have been introduced for the variations of latitude. The present volume, therefore, marks an epoch in the a1mals of the Coast" and Geodetic Survey, and the completion of this great arc may be fittingly called one of the historic events in the progress of geodesy.
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· The method of treatment and the general results may be briefly stated as follows: Each base net was first adjusted separately. This gave, at intervals along the arc, certain lines whose lengths depend more directly upon measurement, and which were regarded as absolute. The triangulation intervening between any. two adjacent figures thus established was treated by the method of least squares, so as to reconcile discrepa11cies between the fixed values and those resulting from the angular measurements
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TRANSCONTINENTAL TRIANGULATION-INTRODUCTION.
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19
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connecting them. The operation thus far gave a connected homogeneous system of
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figures throughout, and opened the way for the final computation of the individual
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geographical positions.
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·
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In order to determine standard data to which the entire arc should refer, a first
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preliminary reduction was made. This gave provisio:Q.al values, which were afterwards
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corrected so that the average discrepancies between the computed positions and those
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determined by astronomical observations should be as small as possible.
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Latitude was observed at 109 stations, azimuth at 73, anci longitude at 37. The
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average local deflection, irrespective of sign, in the plane of the meridian, from 51 lati-
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tude comparisons, was about ::i"·4, and those in the prime vertical may be assumed, in
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general, to be of equal magnitude. After rejecting values ·which were clearly inadmis-
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sible on account of local configuration, the following corrections were made to the posi-
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+ tions first adopted: In latitude - 0"·64 and in longitude 0'"37. No change was
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reqnii;-ed in the pt;ovisional azimuth.
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'l'he discrepancies between the positions deduced through triangulation and those
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determined astronomically may result from deflections of the plumb line or from the·
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fact that the geometrical figures are developed on a spheroid whose dini.ensions are dif-
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ferent from those of the actual earth. Moreover, the deflections may be local, as when
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caused b); mountains, valleys, etc., or they may extend over great areas, where a change
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of density in the earth's crm;t is the underlying cause. As far as the present measures.
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go, the curvature of the North American Continent along the 39th parallel seems to be·
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intermediate between that of the Bessel and the Clarke spheroids.. The accuracy of this
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deduction is evident from the fact that the probable error of the measured length of the
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total arc (+ 2::i4 kilometres) is only 26 metres, whereas the difference between the arc
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of a parallel in latitude 39° on the Clarke and on the Bessel spheroids is 6r5 metres.
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It would be well-nigh impossible to give credit, in exact proportion to the service
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rendered, to all persons who have contributed to the accomplishment of this task. Pre-
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eminent on the list stands the name of C. A. Schott, who has been in active service in
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this Bureau for more than fifty years. He has had charge of all the computations, and
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the present report on the work stands substantialiy as it came from his hands. Assist-
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ance in the computations was given, principally, by M. H. Doolittle, E. H. Courtenay,
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D. L. Hazard, and J. F. Hayford.· The volume was edited by E. D. Preston, assist.eel
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by A. F. Belitz. .
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Prominent among the officers who had charge of the field operations, and who are
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here arranged in the order of linear distance covered by their trigonometrical operations,
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appear the following: \V. Eimbeck, F. D. Granger, A. T. Mosman, G. A. Fairfield,
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F. \V. Perkins, G. Davidson, and 0. H. Tittmann.
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The following table is believed to contain the names in alphabetic order of all the
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officers in the regular service· who took part in the operations. The year in which the
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observations were made and the character of the work executed by each officer are also
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shown:
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20
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UNITED STATES COAST AND GEODETIC SURVEY.
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TABUI,AR STATEMENT OF DISTRIBUTION OF WORK.
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'"' '.'." ~"~~:::~ I'~' I'"' '"' :~ '.'.~ ''~t" '~ '~I:~, :~.:
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H. '''·Blair...................... . . . . . . !:::.
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•••••••••••• • •• • • • ••••••••••••
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~
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6 ................ ..
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...... ...... ...... ...... ······ ······
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........................ 6
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~··:.ri~!~·:1~~,:::::::::::::::::::::
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*I I
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::::::i::::::i::'.:::
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I •H
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:::::(::::
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::~·::.
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::~::!::::*::
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· •
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·:::::
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··~·····
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r *
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::::::
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::::::
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:o.
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::::::
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.......
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* I E.I'.Dickins ............................... '............ L ...... ,C,H !
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*H
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H ............ H
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W. Eimbeck.............. .. .. . . . .. . ...
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/.:o 6 6*H :i C::,H I L,H ,::,.*H 6*H 6 6* 6H 6
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~~}~~:••••·•>ti•••••tt•• • • • • • iri·••f: J·(:'\F:i~i:.;•
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].].Gilbert ........... ····'·....................... ..... ...... ...... ...... H *H ...... 1...................... ..
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F.D.Grang<:r ..........................·................................... :'.:,* 6*
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6 . 6 6 !:!.
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J. F. Ji::!yford..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
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W. C. H•Jdgkins ................................................................................................... .
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E. B. I.atham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ........................................ .
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* ............................. . J. S. 1.3. \\"S•.Jtl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . . . . • . . . • . . . . . . • . . .
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R.A. Marr..................... . ...... ...... ...... ...... ...... ...... ..
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H *H *H H H t:,.H Ii
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]. E. l\IcGrath....... ............ ...... ...... ...... ...... ...... ...... . ...
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H
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6 6 ...., ....... .
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:: ~~:,~~:~;,,~;; :::::::::::::::::::1. :: :_::: :: :: :·-~.. ·-~-~ ·: :: :: r:::: ··;.,.. ·:~· ···~; ···:~.. :::::: ..~; · : :.
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.. * ]. Nelson ............... ·............................................................................ : ............ .
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F. Ji. Parsons .................... ..................................................... .
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*
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l'. W. P~rkins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,::,. ...... ...... 6 ........... ..
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J. F. Pratt . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . ."..... . . . . . . c::,H H H ...... H* . . . . . . . . . . . . . . . . ..
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E. D. l're•ton... .. . . .. . . .. . . .. . . . . .... . . .. . . . . .... . . .. . . . . . . . .. . . .. . . . . . . . . . .. . . . . . . . ........................ 6H
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H~~f.P •t !/ ~ +• •••••1•••• ?1•••• 1>• IJ• • • •••··l·.•1:•••••••••r•••
|
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E. 51nith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * ...... ...... ...... ...... ...... ...... .....
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...... ...... ...... *
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H. L. Stidham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . ........................... .
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]. A. Sullh·an... .... .. . . .. .. .... . . .. .. . ... ... . .... . . .. .. . . .. ... ... .. . 6
|
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E. L. Taney ·1 ................................ ····.. .. .. ......................................................... .. * · ........... . C. ·rert")', jr .......... ·........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .G . . . . • . . . • • • .
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|
~-:.·.~:~:::';''.'.'.::::::::::::::::: :::::: :::::· :::::· :::::· :::::: :::::: .. ~.. -~-*-~. -~~- -~-*-~. :::::: :::::: :::::: ::::::
|
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C.H. Van Orden. .. .. .. .. . .. .. .. . L,.
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ti
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i:, .................. · ·· ·· · ........... · · ·· ·· · ..... · ··· ·· · ··· ·· · · ·· ··.
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D. B. 'Vaitl\Vl"ig11t . ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l:i,H • •• • . . . . . • . . ....... ·.· ...........••.
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J.B. Weir .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . .. . . . . . .. . . . . . . . . . . . . H 6H 6 L. ................ ..
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P.A. \Velker ....................... : . ........................................................................... ..
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F. Westdahl.............. . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . . .. . . . . . . . . . . . . . .. . . . . ................................ .
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::::::::::: : : . :·: : .:: : : I. Winston............... : ........ :. ........................ :. .......................................................
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~-·~: ~:~~:~~~r-~.
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::::::::::::I::::::_::::::::.::...~.. :::::::::::::::::r::::: :::::::::::
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NOTE.-A~t1·011omical obsl!rvat.ions. whether for latitude, longhude, i:1r a:.dmuth, a re indicated by*· Triangulation. inC'1u~in~ recounoissance, base 1ine&, and horizi:111tal angles. is den<.Jted by ~-
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TRANSCONTINENTAL TRIANGULATION-INTRODUCTION.
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21
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TABULAR STATEMEN! OF DISTRIBUTION OF WORK-Continued.
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t:::: :,::·: : ;.:~:.·~:~;~~:~::::::::::::::.::::::::::::::::::!:::::..::::: :::::::~~: ::;~:: :::::::,::::-::: :::::: :::~::
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I W. £.\"'h~ck.. ·· ·· ·· ·· ·· ···· ··· ·· · !::. 'I c,* \ L* L*H' i:.*H c,*ll _:_•H .'...*Hi c.*H H \ i:.H ....... 1...... .
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·······I G. A. Fairfield ................ ··· 6. 6* 1· ·· ·· · 6* .'-" · ·· ·· · · ·· · · · · · · · · · · ·· · ·· ·
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i:. i:. · · · · · · ·
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: : ~>~~-~'..;;~;~~::!:!::::::
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_H._F.J'.lynn ........
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::::::::::::::~:::
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....................
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:~J
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..... ·
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·
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··
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:> :'~:~:: :~::
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·· ······1······
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.·.~-.
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......
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1 .
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..
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-~
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. . ·.
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...
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.. ·
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······
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:·.··~~·:·:·I·:!:·:·'·:·"·:·:·:I.-~~H- ..
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::: :: ::
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~.-;'.·D;~:~.:·.:.::.::::::::::::::::c:::: :::::: :::::. :::::: i:.~H .•.~..!.~.~-- ::::::: :::::·.: ::::::: : * 1···;~··
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*
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I *H '
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]. A. Sullivan .... :.............................................................................................. .
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E. I.. Taney . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . H ................................................................ .
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C. 'ferr.'.'·· jr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .................... .
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0. I·I. l'itt11101111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .". ... ..
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~ ............................................... .
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tl:~J;;:~. >+•••• ~.?:~·•••• r~ 1
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1
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~I~:~:;~~;-~;~:::<:::::::::::::::::::1::I:J:;::•:•:·:•:•·::•:·::·::.~•:•~::>::>::.:::::-::::::•.>:::•:::•:•.:•::•:•::~::::::c~.•:::•:•:•·::•:•
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1
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I
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-·-------------·--'----'----'-Hypso111etry, either hy ineans of the ~~pirit lc-vel or ,~ertical angles. b sh•)Wll by H.
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22
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UNITED STATES COAST .AND GEODETIC SURVEY.
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The present addition to the literature of geodesy will ever remain of value, and will doubtless take its place among the epoch-making contributions to the subject.
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Although the influence of this arc in the determination of the earth's figure is one of its cardinal virtues, the work ~ill exercise its full power and accomplish its complete purpose only when combined with an arc now being measured on the ninety-eighth meridian, and which will ultimately traverse Mexico, the Uni~ed States, and the British possessions. When this great counterpart of the triangulation along the thirty-ninth parallel shall have been measured, and the results of the two have been combined, we shall be in possession of sufficient data to de.fine a surface of the country which, in the present state of exact.measurements, may b~ considered a finality.
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HENRY s. PRlTCHETT,
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Supo-i11 tnzdent.
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UNITED STATES COAST AND GEODETIC SURVEY,
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Superin.tmdent's Office, Apn'l, I900.
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PRELIMINARY STATEMENT.
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I. LOCATION, SCOPE, AND PURPOSE OF THE TRANSCONTINENTAL TRIANGULATION,
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rrs WITH HIS'.!-'.ORICAL NOTES AS TO
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INCEPTION AND PROGRESS.
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This transcontinental .triangulation· and measure of an arc of the parallel extends
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from Cape May, New Jersey, on the Atlantic coast, in longitude 74° 55'·8, to Point
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Arena, California, on the Pacific coast, in longitude 123° 41; '8. The intervening
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distance is about 4 225 kilometres, or 2 625 statute miles, corresponding to 48° 46'·0 of
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longitude. ·
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Its terminal points are near Cape May and Point Arena light-houses, which are in
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latitudes 38° 55'·9 and 38° 57'·3. respectively.
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'the desirability and necessity of uniting the main triangulations along the eastern
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·and western coasts of the lTtiited States must have impressed itself upon the minds of
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those engaged in the work. It was recognized that such a connecting bond was
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demanded in order that these separate parts might be made to depend upon the same
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geodetic and astronomic data. By this means only could the unity and consistency of'
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the work of the Survey be secured; besides, it was apparent that any proposed surveys
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of States lying in the path of the connection or adjacent thereto could at once be based
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upon the same standard data, thus securing uniformity and accuracy for the whole
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work. An operation of this character could not well be undertaken by separate State·
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action, since it would involve too many contingencies respecting uniformity of treatment
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and of timely cooperation. Its execution was therefore properly intrusted to the Coast
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and Geodetic Survey as one of its functions.
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·
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Besides its immediate practical benefit of providing a· tier of interior States with a
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nucleus of systematic triangulation at once available for the extension of surveys over
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adjacent areas and furnishing geographic positions within these extended limits, the
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measure has a much higher value from a scientific standpoint. It is a considerable
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contribution toward those data of which geodesy must ·avail itself for the more ·exact
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determination of the earth's shape and size. For thi~ and kindred measures an addi-
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tional stimulus was given in 1889, when the United States became a member of the
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International Geodetic Association for the measurement of arcs and for the special duty of investigating the geoid or deformed physical surface of th~ earth as co.ntrasted with
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that of a mathematically defined figure.
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The initial step toward the accomplishment of the measure was taken by Superin-
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tendent Benjamin Peirce. Under date of February 7. r871, he asks, in his annual report
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to Congress for the year 1870 (page 7), for a specific appropriation for this object.
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On page 4 of that report we find, "A new item is proposed in the estimates, small
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. in amount, but of inestimable .importance to the scientific accomplishment of the
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Survey." . Speaking of the geodetic connection between the Atlantic and Pacific coasts,
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2.'
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24
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UNITED STATES COAST AND GEODETIC SURVEY.
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he remarks: "It will give to the National Government and incidentally to the several
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States the best possible basis for all accurate surveys which may hereafter be required.''
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Ground was broken in July, 1871, in the vicinity of St. Louis, Missouri, by laying out
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a triangulation extending to the eastward and westward of that city and providing for
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a base line and astronomic measures. It was also evident that part of the operations
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already carried out by the Survey-in central California during nearly twt:nty years could
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be utilized or incorporated into the arc measure; likewise at its eastern encl it was
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expected that some part of the very much older triangulation ·with its astronomic
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measures would be included.
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Since the year 1871 the work has been continued under the several superintendents.
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Although the annual accretions.were small, owing to the meager appropriations _allotted,
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it can be said that at the close of the year 1896 the measure of horizontal angles of the
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triangulation was completed. The last of the base lines was measured in 1897, but
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the determination 9f heights of the Rocky Mountain stations yet demanded certain
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measures of zenith distances and spirit levels, which were ·supplied in 1898. In .the same
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year the last of the astronomic longitude determinations was made. The reduction of
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the observations· and the preliminary computation of positions were kept abreast with
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the field work, but some unavoidable delay in the final adjustment and preparation for
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the press occurred in consequence of the late supply of the height measures required for
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reducing two of the principal base lines to the sea level.
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. .
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The accompanying map A (in pocket), on a scale of .,.-111,-3·-;nru, has been specially designed to give at a glance a general view of the location and comparative extent of
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the triangulation connecting our east and west coasts. It exhibits by contrast of color
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the base nets and the intervening chains of triangulation, and by their variation in width
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it indicates the dependence of the size of the triangles on the hypsometric features of
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the country. On map B (in pocket) is shown, by means of the simple conventional signs
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adopted on the Survey, the number and d_istribution of the astronomic stations whether
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for longitudt:, latitude, or azimuth.
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In connection with the measure of this arc of the parallel it may not be out of
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place here to direct attention to the report of the Geodetic Conference of January and
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February, 1894, convened by Superintendent T. C. Mendenhall. (Appendix No. 9,
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Coast and Geodetic Survey Report for 1893, Part II, specially pp. 360-363.~ Reference
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will be found therein to other arcs measured either by the United States Lake Survey
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or by the Coast and Geodetic Survey. The measures of the great meridional arc in
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* longitude 98 ° west of Greenwiclt were commenced in 1897. This proposed arc may be
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considered· as complementary to the arc of the parallel, one giving a measure of the
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curvature in a north and south direction, the other in an east and west direction, thus
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affording within the limits of the country the means for determining an osculating
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spheroid closely approximating to the curvature of the earth's surface. The first half
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of the current year (1898) also saw the completion of the measures, geodetic and astro-
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nomic, of the great oblique arc stretching from Calais, Maine, at the Canadian boundary
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to west base, Dauphin Isla~d. Alabama, on the Gulf of Mexico, thence to New Orleans,
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Louisiana, a length of 23° 31', or 2 612 kilometres or r 623 statute miles.
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*Reconnaisance ,vas made in the tJrect:ding year.
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TRANSCONTINENTAL TRIANGULATION-:-PRELIMINARY STATEMENT•. 25
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2. SUBDIVISIONS OF THE CHAIN OF TRIANGULA'riON AND THEIR DISTINGUISHING ' CHARACTERISTICS.
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The contrast in the physical features aloqg the arc of the thirty-ni~1th parallel is so
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well pronounced as conveniently to mark out for general description three.subdivisions,
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which moreover demand, in part at least, different mathematical treatment in the reduc-
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tion of the observations. These subdivisions are designated the western, the central,
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and the eastern sections.
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The wt·stcnz. section is characterized by the great altitudes of its stations and the
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unusually large size of its triangles, many of the sides being. over I 60 kilometres, or
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roo statute miles in length. The triangulation crosses the Coast Range, the Sierra
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Nevada, the \Vasatch Range, and the main ridge of the Rocky Mountains, with many
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of its statiomi more than 3 kilometres, or nearly 2 statute miles, above the level of the
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ocean. The total linear developmerit between Point A.reua on the coast and Big Springs
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off the ·eastern flank of Pikes Peak, Colorado (as projected on the parallel of 39°) is
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nearly 1 685 kilometres, or 1 047 statutt: miles.
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The central section, which ex.tends from Big Springs, Colorado, eastward as far as
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·St. Louis, Missouri, over a distance of about 1 217 kilometres, or 756 statute miles
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(measured on the parallel of 39°), partakes of the very opposite character from its
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neighbor with respect to width of development or average length of sides. The latter
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is but 27·3 kilometres, or 1]"0. statute miles, and is therefore a minimum value. This
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feature was imposed upon it by the general flatness of the gre~t plain which lies between
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the eastern slope of the Rocky Mountains and the Mississippi River, descending very
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gradually from about r 800 metres (5 900 feet nearly) to about 135 metres, or 443 feet,
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above the sea level. As a rule the theodolite was mounted on tripods or scaffolds in
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order to overcome the earth's curva tnre and keep the line of sight sufficiently elevated
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above the ground.
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.
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The third or eastern section differs from the others by its small but diversified
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hypsometric .feattires being composed of plains,· low hills, and mountain ranges.
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V.There the triangulation traverses the Alleghenies altitudes exceeding r 300 metres, or
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4 265 feet. are met. The section crosses the Chesapeake and Delaware bays, terminating
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at the capes of the latter. Its total (referred) length is about 1 3:?J kilometres, or 822..
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statute miles.
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The triangulation across the cpuntry possesse::? great internal rigidity by reason of
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its composition throughout. Either quadrilaterals or central figures such as polygons
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fonned by combination of triangles compose the scheme, while its length is supported
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by 10 base lines suitably distributed.
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3. GJ~NERAL STATEMENT IN REGARD TO THE ASTRONOMIC "MEASURES.
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Respecting the astronomic measures there are 109 stations directly connected with the triangulation at which the latitudes were determined almost cxdusive(l1 k11 Talcott'smethod. These observations fall between the years 1846 and 189S. Eight latitudes depend on other than Coast and Geodetic Survey authority. Astronvmical azimuths were obtained at 73 of the trigonometric stations between the years 1849 and 1897. A variety of methods, suitable to the circumstances at the time, were employed in this
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UNITED STATES COAST AND GEODETIC SURVEY.
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work. On account of local deflections of the vertical, which are present to a greater or less amount at all stations, the value of an arc of the parallel depends, crrteris pm ibus, largely upon the number of subdivisions or component arcs which together make up its whole longitudinal amplitude. Ther~ are 37 astronomic longitude stations not very unevenly distributed over the arc, though rather crowded in some places. They were determined by means of the electric telegraph, and are either part of or depend directly upon the general telegraphic longitude system of the United States. An account of
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this system is contained in the annual report of the Survey for 1897. Appet1dix No. 2.*
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The longitudes were determined between the years 1869 and 1898. The stations, in consequence of the impracticability of establishing wire connections, are not, as a rule, also trigonometric stations in the main series of triangles, but all are geodetically connected with the nearest triangulation station.
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*An abstract of this paper appeared in No. 412 (September 14, 1897) of Gould's Astronomic Jourm11.
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PART I.
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UNIT OF LENGTH. BASE LINES, AND BASE NETS.
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.
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27
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Blank page retained for pagination
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CONTENTS OF PART I.
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Page.
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A. Introduction ......................................................... ·........... '. ..... . 31
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B. Unit of length ......... ·................................................................ . 31
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( r) History. of the committee metre of I 799 ........................................ ·
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( 2) Coefficient of expansion ................. : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... .
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(3) Length, in terms of the international prototype metre ........................... . 33 C. Local or station arljustment. ........................................................... . 36
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( r) General discussion . . . . . . . ................................................... .
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Ji
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D. Reductions of horizontal directions to sea level. ........................................ . 47
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E. Adjustment of base nets or other triangulation . . . . . . . . . . . . ............................. . 47 P. Remarks on weight coefficients in the net adjustment ................................... . 50
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G. Computation of spherical excess .... ." ................................................ .". 51
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H. Account of .the base lines ............................................................. . 54 . ( 1 ) General statistics ................... :.......................................... . 54 (2) Ivleasurement ........................................................... , ...... . 55 (a) Kent Island bas.: line .................................................. : . 55 Location, measurement, and length ................................ ~ ... . 55 Abstract of horizontal directions ................ : . . . . . . . .............. . 58
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Figure adjustment .................................................... . 60
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Triangles of the base net .............................................. . 61
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Probable errors ........ ·.. : ......... .' ................................ . 63
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Dtscription of stations ................................................ . 64
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(b) A:nerican bottom base Jfoe ......... ." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
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Location, measurement, and length .................................... . 66
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Abstract of horizontal directions.. . ... . . . . . . . . . . . . . .................... . 69
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Figure adjustn1ent .................................................... . j~
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Triangles of the base net .............................................. . 74
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Probable errors ....................................................... . 75.
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Description of stations . . . . . . . . . . . . . . . . . . . ............................. . 77 ( c) Olney base line ............................................. , ........... . 79
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Location, measurement, and length ....... : . : .......................... . 79 Abstract of horizontal directions ....................... .' ............... . 81
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Figure adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . S4
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Triangles of the base net .............................................. . 93 .Probable errors ....................................................... . 97 Description of stations ................................................ . "98
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(d) El Paso base line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... . 101
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Location, measurement, and length. . . . . . . . . . . . .. . . . . . . . . . . . . . . . ....... . IOI
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Abstract of horizontal direction.s ........................................ . 108
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Figure adjustment ..... :·. ............................................. . IIO
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Triangles of the base net .............................................. . II2
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Probable errors ....................................................... . 114
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Description of stations ......, .......................................... . II4
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29
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UNITED STATES COAST AND GEODETIC SURVEY.·
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H. Account of the base lines-Continued.
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Page.
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( 2) Measurement-Continued.
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.
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(e) Yolo base line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II6
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Location, measurement, and length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l 16
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Abstract of horizontal directions........................................ 121
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Figure adjustt11ent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l~.1
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Triangles of the base net.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
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Probable errors . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
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Description of stations .................... '............................ 130
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tf) Holton base line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l.33
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Location, measurement, and length ............................. '........ 133
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Abstract of horizontal directions.................................. . . . . . . l.39
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Figure adjustrnent.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.p
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Triangles of the base net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
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Probable errors ...................................................... ·.. 146
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Description of stations ................ : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
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(g) St. Albans base line ......................................... :............ 150
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Location, measurement, and length·.................... . . . . . . . . . . . . . . . . . 150
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Abstract of horizontal directions......................................... 154
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Figure adjustment ................................ .'. . . . . . . . . . . . . . . . . . . . 157
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Triangles of the base net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . r66
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Probable errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I jO
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . l 71
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(h) Salina base line......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
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Location, measurement, and length..................................... 17-I
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Abstract of horizontal clirections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18~
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Figure adjustment.. . . . . . . . . . . . . . . . . .. .. . . . ... . . . . . . . .. . . . . . . . . . . . . . . . . . 184
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Trianglt:s of the base net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
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Probable errors..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
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Description of stations .................................. : . . . . . . . . . . . . .. 188
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(i) Sa.It Lake base line....................................................... 190
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Location, measurement, and length ............ : . . . . . . . . . . . . . . . . . . . . . . . . 190
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Abstract of horizontal directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
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Figu~e adjustment .................................................... . 207
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Triangles of the base net .............................................. . 215
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Probable errors ....... ; ................................................ . 218
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Description of stations ................................................ . 219
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(j) Versailles base line ...................................................... . 222
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- Location, measurement, and length .................................... .
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Abstract of horizontal directions .............................. __ ......... .
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..,...,...-,
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Figure adjustment.. . . . . . . . . . . . . . . .. . . . . . . . . . . . .................. : .... .
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Triangles of the ba,;e net. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . ·::q.o-
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Probable errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ : ......... .
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Description of stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................. .
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(3) Synopsis of facts and results..................... :........................ , ..... ; .
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.
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.
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I. UNIT OF LENGTH. BASE LINES. AND BASE· NETS.
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(.A.) INTRODOCTION.
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In this first part of the exposition of the measurement of the arc of the parallel, stretching centrally across the country, will be presented a discussion of the unit of length upon which its whole extent is devdoped. This is followed by an individual account of each base line with its resulting length and probable error, and the adjustment of its net of triangles referring the base to a principal side of the triangulation. The methods of local and of figure adjustment of angles and sides are here explained.
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(B.) THE UNIT OF LENGTH.
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I. HISTORY OF THE COi\Il\fITTEE :METRE OF 1799·
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The unit of length of the transcontinental triangulation is the metre. Its material representative' as used on the Survey from the beginning up to the year 1390 was an iron bar standardized at Paris in 1799 by the Committee oi1 ·weights and Measures. It was brought to America in ·1805* by F. R. Hassler (afterwards first Superintendent of the Coast Survey l and presented by him to the American Philosophical Society of Philadelphia, and later placed by the society at the disposal of the Coast Survey. Mr.
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Hassler received it from J. G. Tralles, deputy to the commission from the Helvetic
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Republic. It was made by Lenoir at Paris and is one of 16 rpetres. of w11ich twelve were distributed to the foreign commissioners, and bears among other distinguishing marks that of three dots : · It is an encl metre with cross section 9 by 27 ·5 millimetres. For an account of its constrnction, the apparatus employed, and method
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adopted for cutting the several metre bars to the desired length, the pt1blications t
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given below will be found to conta~n nearly all that may be of present interest. Its use was discontinued after the receipt in November, 1889, by the Government of the United States from the lnternatioiial Bureau of \Veights and Measures at Paris of three representative platinum-iridium bars of the International or Prototype .Metre. Hence part of the triangulation depends for its length 011 the Committee Metre, or C. M., part on the International Prototype Metre and part through aLijustment on both. Under these circumstances it became imperative to carefully compare these standards, which were supposed to be equal, and.. if different, to correct the length of
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* Puh. Doc. No. :?991 H. ,)f Rep&., :?.::d Congress, 1st session, \\'ashington, 183.:?1 p. 6.
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.
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t Transaction:; American Philosophical S•Jcidy, Philadr~lphia, Vol. II, ntw serieg, No. XII. •· Papi:::rs 011 variou's
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subjects connected with the Sun·ey of the Coast of tht: United ~tat~·s.!' by F. R. Hassler. !\'larch 3, 18..::1..""' (p. ~.:..:,in par-
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ticular); United States Coast Sur\'ey Report for the year 18'5j, AtJpendix N•:i. 7 pp. 134-13j; Recherch1.:::; histi-,riqui::s 5-Ur les
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EtaIons cl<: Poids et Mesures de l'observatoire et les appareils qui ont s.:rvi ales co11&truire. Par M. C. Wolf. Paris, 1882..
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3l
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_.,,_'
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UNITED STATES COAST AND GEODETIC SURVEY,
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the older base lines depending 1)n the Committee Metre of r799, in order to express
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their length and that of the whole triangulation in terms of the International Proto-
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type Metre.
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·
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In attempting to determine their relative length, two difficulties presented them-
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selves-one due to the demand of modern science for greater accuracy and better defi-
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nition than was the case- a century ago, and the other clue to a slight yet perceptible
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deterioration of the encl surfaces of the iron metre by oxidation and by wear. It was
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hoped that the length of this metre could become known with no greater probable error
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than one micron. An error of one-millionth part of the length would produce one of
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4 ·2 metres in the width of the country in latitude 39° and would be a negligible quan-
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tity in comparison with the inevitable errors introduced through the triangulation.
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2: THE COEFFICIENT OF EXPAN$ION OF THE IRON COMMITTEE METRE, OR "C.M.".
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There is no information of a special determination of the co~fficient of expansion of
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this metre by the committee of r799. The average value for the several metres was
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rr·56 >: ro-6• Adirect determination made at Newark byF; R: Hassler in rS17* gave
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him o·ooo 006 963 5 for Fahrenheit's scale or the value for the centigrade scale of
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12·534 :< ro-'". This rather large value was supposed due to the method employed,
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which wo\1kl now be characterized as crude. The result was not adopted on the Survey,
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but the committee's value was employed fostead up to about the year rSSr, when an
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elaborate series of observations was made by Assistants C. A. Schott and H. W. Blair
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at the Survey office in connection with the work of standardizing a new 5-metre bar.
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During these observations the C.M. and 5 other metres were immersed in a bath of
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glycerin, the temperature of which, when steady, was found ·by means of standard
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thermometers. The ends of the bars protruded slightly beyond rubber diaphragms
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placed tightly in holes piercing the ends of the trough, which was then brought between
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two Bessel-Repsold screw spirit-level comparators. The range of the temperature of
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the ·glycerin and immersed bars was between 4° and 38°C. (39° and 100° F.). The
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results. from the several series were as follows :
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lSSo, Dec. 23-24 27-19
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lExpansion for r° F. 6·576tt 6 ·603
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rSS1, Jan. 3-8 2-3 4-5
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7~S
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6·613 6 .508 6 ·495 6 ·579
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) Mean ~5~~ JI
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.
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·
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equal to II ·790 ·y, ro-6 for C. scale
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.
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± 25
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.
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16-17 6·474
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Particulars of these operations will be found in Coast and Geodetic Survey Report for rSS2, Appendix No. 7 (p .. r24 in particular).
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In 1S8S and 1889, Assistant 0. H. Tittmann made a series of comparisonst for
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* 1'ran:=;. .Atner. Phil. Society, Philadelphia, Vol. I, new series, No. XVI. An account of pyro111etric t:xperitnents
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made at Newark, New Jersey, April, tSr7. By F. R. Hassler.
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t Coast and Geodetic Snn·ey Report for t889, Appendix No. 6: "The relation between the metric standards of length
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of the United States Coast and Geodetic Snn·ey and the United States Lake Survey." By C. A. Schott and 0. H. Titt111a1111, Assistants. pp. 17s--197.
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TRANSCONTINENTAL TRIANGULATION-·PART I-BASE LINES. 33
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relative lengths of the United States Lake Survey Repsokl Metre R. M. and the committee metre. These gave in connection with the coefficient of expansion of the
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R. M. (as finally given by Dr. Foerster, viz: 10·654 :< 10-0, by Lake Suryey observa-
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tions, l0"615 ~< w-6 , and by International Bureau of \V. and M., 10·563 :A 10-6 ),
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±II
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the resulting values, in combination with other measures. for coefficient of R. M. ro·6o6;..: 10-·•, and for C.M. 11 ·795 >". ro-•, a value practically identical with the
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± 25 one found in 1880-Sr. A further confirmation of this value was had through the direct comparisons of the C. M. with one of the national prototype metres. Mr. L. A .. Fischer obtained between July, 1894, and May, 1895, a large number of micrometric differences between the length of the C.M. and of the N.P.M. 2r. These observations were made in a vault at the office, in which the temperature was varied 21 }6 ° C. The optical method was employed, varied by the use of 2 prongs 3 millimeters distant on each side of the axis, the bars and thermometers being under glass cover on the comparing carriage, provided with the necessary adjustments. The details of the process being explained farther on, it suffices to state here the resulting differential expansion, viz:)'=+ 3·12311. The coefficient of expansion of the N.P.M. 21 was determined at Breteuil, viz:.+ S "665 I< ro- 6, whence the coefficient for the C. l.VI. = r r ·788 Y 10-•.
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Recapitulation of vaiues for coefficient of expansion of the C. M.:
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Ii99 1SS0-81 1888-89 1894-95
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Mean adopted
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II ·56. ·. 10-6
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II "i,90
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JI ·795 II"jSS
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II "79 I · 10-6 ± 2
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3. THE LENGTH OF THE IRON COl\'IMITTEE METRE, OR '' C.M."
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From the particulars given by F. R. Hassler* respecting the construction of the original metres it would appear that the aim of the committee was to secure an accuracy in their length which should be trustworthy to within about half a micron. It is further stated that the difference ir~ length of the temporarily selected standard and metre : · or the C. M. was two ten-millionths part of a toise, the latter being the shorter. If. this was correctly understood we would have C.M. = IJll - 0·411..
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In 1867 the C.M. was taken to Paris for direct comparison with the standards preserved there. · A full accoimt of the work done is contained in Coast Survey Report for
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1867. t During these comparison; the respective metres were immersed in melting ice.
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'l'he measures were made by means of the Silbermann comparator with the aid of two abutting pieces. The resulting length of the C. M. arrived at makes it too long b)· 3:36µ, but the first and third series of comparisons show rather a wide difference, and considering that so few series of ·comparisons were made we may regard the result as a
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weak one. The actual operation occupied but a few hours of August 2+
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* Puh. Doc. No. 299. pp. iS and 77.
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18732-No. 4--3
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t Rc:port for 1867. App<:ndix No. 7, pp. 134-r37.
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34
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UNITED STATES COAST ~!\ND GEODETIC SURVEY.
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* A more satisfactory although indirect comparison was obtained in 1889 through
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the medium of what is known as the Repsolcl steel metre of the United States Lake Survey,
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R.M., the length of which had been determined at Breteuil, near Paris, in Jamrnry,
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1883. The C.M. being an encl and the R.M. a line metre, Assistant Tittmann
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employed the optical or reflection method for comparing the two bars, which was
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effected at Washington in a cold-storage room and other localities between September,
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1888, and March, 1889. The R.1vl. is otherwise of importance through the fact that the
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length of the Olney base line in Illinois is expressed in terms of it, for which see Report
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upon the Primary Triangulation of the United States Lake S~1rvey, by Lieut. Col. C. B.
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·Comstock. t In a supplement by General Comstock, dated February 28, 1885, the
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+ length of R..M. . is -given provis.ionally, but very closely, as 1m 97·31 µ at the tempera-
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Jt
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ture of melting ice, and for any temperature t (centigrade) there is to be added 10"615!;
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but in the 1889 report, p. 18<?. the preferable value, l0"6o6 Y 10-6, is deduced for the
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± 25
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coefficient of expansion. From these \Vashington observations we derive
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Jl
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R.M. - C.M. = 8..f."28/t - I"1925 (t- II 0 "66) ±"49 ± 425
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and C.M. =rm - 0·3SJ.1 ±0·70µ
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Between July, 1894, and May, 1895, an extensive series of comparisons before alluden
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to was made at Washington by Mr. L. A. Fischer, of the Weights and Measures Office,
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between the C.M. and one of the new National Prototype Metres known as N.P.M. 21,
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received here in July, 1890. The latter is a platinum-iridium line metre of length
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Jt
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ft
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lm+2·5µ+s·665t+o·oo1 oot", as standardized at Paris. The comparisonst were
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± ·15
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made in the office comparing vault by means of micrometer microscopes clamped to a steel
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beam as support. The two standards were placed in a glass-covered box or carriage
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and were supported at two points 54 centimetres apart, with Tonnelot thermometers placed on their upper surfa~es in contact with them. The carriage rested on i.ron
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rollers and was provided with all necessary adjusting devices. For defining the ends of
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the C.M. the optical method was employed, but as the end surfaces are less perfect in
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the axis of the bar than at a short distance from it, two points 6 millimetres apart were
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placed symmetrically to the axis to admit of their direct and reflected images. Illumi-
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nation was secured by means of right-angled prisms placed about I centimetre below
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the bar, the light from incandescent lamps being .thus thrown upward. The defining
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lines of the N.P.M. were made visible by throwing the light upon them through 45° prisms placed between the two lenses of the objectives of the micro~opes. An observa-
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tion consisted of. the following operations: r. Reading of thermometers. 2. Paintings
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on C.M. 3. Pointings on N.P.M. 4. Paintings on C.M. 5. Reading of thermom-
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eters-the whole occupying about 12 minutes, during which time the thermometers
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* u. s. Coast and Geodetic Survey Report for 188<}, Appendix No. 6. "The relations between the metric standards
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of length of the u. S. Coast and Geodetic Survey and the U.S. Lake Survey, by C. A. Schott and 0. H. Tittma1111,
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pp. 179-'97·
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t Professio11al Papers Corps ef Engineers, U. S. A., No. 24, Washington, 1882. t Not y~t published.
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TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 35
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rose about o0 ·1 C. Following a regular scheme, the bars at different times were placed in different positions with respect to the observer and microscopes. The temperature of the vault ranged between 2°·7 and 24°·2 C. The· 96 individual observations when condensed into 4 groups gave the following conditional equations:
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J.l
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x+ 22· 34Ql' = 69· 71
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|
X + 7 . 442)' = 2 3 . 7 I
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= X + 3. 747)' I I '68
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|
+ X IO' 55qy = 34. 07
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|
whence the normal equations
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|
+ 4·ooox + 44·079y = 139· 17
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|
44·079x+ 678·908.Y = + 2136·97
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|
+ + hence :i- = 0·3SJ.l, or the difference C. M. - N.P.M. at o° C and _v = 3 · 1231-1 or the
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|
differential expansion per degree centigrade. The result is C.M. = w1+2·88J.1 at the
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|
temperature of melting ice. The preceding 4 determinations not being as accordant as desirable, further obser-
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|
vations were undertaken al the office by Mr. Fischer and also by Assistants G. R. Putnam and A. Braid between January 17 and March 3, 1896. These operations differed from the preceding one by the substitution of the contact piece method for the reflection method; otherwise the conditions were the same. Since no publication has been made, a somewhat more full description will be given here, taking the same from the preface as given by Mr. Fischer.* Two platinum abutting pieces were ri1ade, consisting of thin disks about 6' 3 millimetres in diameter with their central areas hollowed out in order to produce a ring contact about the axis of the C.M. On the side opposite the contact surface there was a ledge, level with the center of the disk, upon the horizontal surface of which were drawn two lines parallel to the axis of the bar and a fine perpendicular line about o·s millimetre from the plane of the disk for observation; when under comparison, the disks· were held by light springs supported by a collar clamped about the ends of the C. M. After observation had been made in one position the end pieces were taken off and their abutting surfaces placed· in contact and the distance of their fiducial lines measured. After this the end pieces were again put on the metre, its ends having been reversed. The values of micrometers Nos. 5 and 6 were found by measuring the millimetre spaces on N.P.M. 21, which were at its A enci 1008'6/t and at its Bend 997·0).1 apart. The value of r turn of micrometer No. 5 is 74·697µ and of No. 6, 75·98211 (January rS and 24); differential expansion of the two metre bars 3·12611 for 1° C.; range of temperature during the comparisons between 0°·72 and 5°·62 C.; corrections were applied to thermometers Tonnelot Nos. 4333 and 4334 for position of zero point, graduation and reduction to hydrogen. scale; distance of lines on disks when in contact, 162]' 32p; the outer lines of the N.P. M. having been observed, we have the distances 1 to 2 = 499·7 J.t, and 5 to 6 = 493 ·9J.1.
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|
*After the above had been written, a paper read before the Philosophical Society of Washington 011 May 28, 1898, by Mr. I,. A. Fischer, was received. It is entitled "On the comparison of line and end standards'' (see Bulletin Vol. Xlll, p. 241, and fol.). The result (that of 1896) is the latest 011 record, and the author thinks it is at least as trustworthy as that derived from the optical or Fizeau method.
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UNITED STATES COAST AND GEODETIC SURVEY.
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No. of series Corrected temperature of C.M. Corrected temperature of N.P.M. Observed micrometric difference of length C.M. at o° C. shorter than l m.
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|
Mean length= wr- 1"3/1 ±0·111.
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Fischer.
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|
17 4°·210 4 ·204
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|
643 ·07rp
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l ·36
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Putna111.
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9 4°·218 4 '23i 6.p ·692p l '55
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Braid.
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|
I2 2°·656 2 ·672
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|
638 ·240}1 I ·q
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S11111-111<11:11 <?f n·sultsji>r h'llgl/1 of C. 11I. hr tows of tile P. ill.
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Yt:ar.
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179<) 1867 1889 !894--9.'i 1896
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Length.
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|
!Ill - 0 ·411 +3"4 -0·4 +2"9 - l ·3
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Indiscriminate mean Im +o·Sp ±0·711.
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Scanning these results, it would appear that they represent rather irregularities of the surfaces about the axis than measures of the true length of the bar. If. so, equal weight would attach to them. On the other hand, the value of 1867 rests upon a: very meager number ofobservations, on which account less weight< one-half) might be assigned to it, whereas somewhat greater weight (two) u1ight be given to the 1896 comparisons by reason ,of the great care bestowed upon. the measures and in particular on the determination of the temperature of the bars. Applying these weights we get the length of the C.M. at o° C. =rm +0·211. The probable error of the determination being much
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±o"6tt larger than the difference in length of the bar from one metre, we may take the C.M. to be equal to the prototype standard without any serious error and with a probable uncertainty of about three-quarters of a micron.
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(C.) THE LOCAL OR STATION ADJUSTMENT OF HORIZONTAL ANGLE AND DIRECTION OBSERVATIONS.
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The abstract of resulting directions from theodolite measures and the adjustment of the triangles composing the base nets, together with the computation of the probable errors of resulting sides, demand further exposition of the methods employed.
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The great majority of the angular measures were made in series with different positions of the circle. These are called direction observations. At three only of the base nets do we find some angular measures by means of repeating theodolites. In the ·latter case the weights introduced will depend on the number of repetitions. The least square adjustment to satisfy the conditions among the measured angles generally proceeds by the method employing correlate equations.* By addition, tlie adjusted angles are referred to an initial direction and the results given in the abstracts are in the order in which azimuths are counted (i. e., clockwise). For some of the base nets
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•The process is so well understood as to need 110 further remarks: rderenc~ may be made to T. W. Wrights'.
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Tn:atise 011 the Adjustment of Observatious, New York, r88.\, Chapters IV, V, and Part of VI.
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·
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TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 37
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the station abstracts include a column giving rough values of prolpble errors of the respective directions, which were not in all cases computed, and had herc::tofore been
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made use of only in one instance-that of
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"''· ·.
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the:: Yolo Base net, as will be explained
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l
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further on.
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1--"-'1--
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I. GENERAL DISCUSSION FOR LOCAL ADJUSTMENT OF DIRECTION OBSJ<:RVATIONS.*
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" Let 0 be the station occupied and 1, 2, 3. . . . . . . the station!? sighted at in order of azimuth. Let some one direction, as 01, be selected as the zero direction. and let .4, B, ...... denote the most probable values of the angles which the directions of the different signals make with this direction."
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In the first series of readings let X, de-
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1
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I
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.\\ II
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I I
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\r -r1-.r-.z--
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\ ' \ I
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\ I
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\ I
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,,I I
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\I
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1,
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\1
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0-
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/
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/
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' '\
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' \
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\B
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I I I I I
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note the most probable value of the angle
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between the direction defined by the zero
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of the limb of the instrument and the direc-
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3
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tion 01. Let 11:!,', 11£,", 111,"', . . . . . . denote the readings of the limb on signals
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I, ·2, ,''\, . . . . . .
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Then for the first series of readings we may write the following observation equa-
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tions, one for each reading: t
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.\·, - !If,' = "-'.' .\·, -t· .-1 - Al," = "-' ,"
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.\", + B - 111,"' = v, '"
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Similarly for the second series of readings we may write
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,\'"o
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- JI/,' = 'i' .'
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.\", + .-1 - 111," = 'i',11
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.Y, + B - 111/" = z•,'"
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................... (1)
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and so on, for all the series.
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The number of observation equations is equal to the number of readings (signal sightings) at the station, and is designated by n..
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The subscript in each case indicates the number of the series, while the superscript indicates the signal sighted.
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The unknowns are X,, X , .\~,••••••• , one for each series, and A, B, C, ...... , one 0
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for each direction except the initial direction. The total number of unknowns is
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+s d - 1, in which s =number of series and d =number of directions. (or signals
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*See Wright's Treatise on Adjustment of Observations, New York, r884, pp. 315-320. t The essential difference between dinction observations and angle obsen·ations, from the point of view of least squares, is that with dfre·clio1t observations there is an obsen•ation equation for each 1·eadi11g, while with a11gle observations there is an observation equation for eacl1 augle 111easun:d.
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UNITED STATES COAST AND GEODETIC SURVEY.
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sighted upon). Of these unknowns it is important to note that the X's are 110!
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nvuired; they are unknowns introduced by the method of observation. _..,/, B. C.
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. . . . . . are the required unknowns, and the solution is to be put in such form as to give only these unknowns and not the X's.
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To insure that only small numerical terms shall occur in the solution, let
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~Y, =ill,'+ x,
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+ = ,\'2 ilI/ .1"2
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A~ ...J'+( •..J)
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+ B=B' (B)
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where .!If:, llf.', ...... , the readings upon· the initial direction, are taken as convenient
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approximate values of X,, X , •••••• : and A', B', . . . . . . are ~pproximate values of 0
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...,/, B, ..... . .
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+ . + l Then the observation equations showri in (I) may be written_
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.r1
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=t'/
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x, + (../) -111/1 = <.•,"
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.i-1 (B} - 111/" = ;:•/"
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x.
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.r.
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+
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(,./)
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-
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111.''
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=v.'
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= ''•"
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(B)
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,,,_ - ,,, ................. (2)
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-1.2
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. - /JI':! - ''2
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.. . . . ... .. . ...
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in which m/' = 111,11 -111,' - ../'
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111,"' = 111/" -- ill/ - B 1
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111/' = llf.'' - ill.' - ../' m/'' = 111.'" - ill.' - B'
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The absolute term in the first equation of each group is necessarily zero ( = 171_' - il/",', 111.' - 111.'. . .... - ) . .
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Let the weights of the various observations be P,'. p,", ..... , P.'. P.'' . ...... , the
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subscripts and superscripts havii1g the same meanings as before. Then the normal equations formed from the observation equations shown in ( 2) are
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[p,]-r.,
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j +P.''( •..J)+P.'"(B)+ ........ - · [p,m,]=o
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I [p.]x. I +p~'.''. ~~! +~~,:~~~).+ ·. ·. ·.: ·. ·...·.- .. -~~~,'.'.·~ ~ ~ r· ······* (3)
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p," .i-, +Po" x. + .... + [P"](A)
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- [P" m"] =o
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N"x, +N"x.+....
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+ ~:.'~?,(~~ .........- [~'.'~'.'~~'? =~ ... ;·: .. .(4)
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Since the unknowns x,. x •. x, . ..... are not required, we may eliminate them from the full set of normal equations shown in ( 3) and ( 4) by substituting their values as derived from the separate equations of (3) in each of the equations of (4). The result will be a set of equations, shown in symbolic form in ( s), equal in number to the required corrections (A ), (Bl ...... and from which (A), (B) ...... may be derived directly without resorting to the long set of equations shown in (3) and (4).
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+ l + [aa](.4) [ab](B) [ac]( ~) ............... - [al] =O
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[ab](A) + [bb](B) +[be]( l) ............... - [bl] =o
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.. ...... ... [.'~~J-I~:~·~·+[b·~](BJ+[·~·'.](C) ::.::::·::::::::-[./C]o.=~ i·················(S)
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*'The square bracket [ ] is used as usual to indicate the summation of similar terms.
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|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 39
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in which
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[aa] =
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[P" ] -:
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(Pl' J0 [p.f -
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(
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p." l0
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[p.]
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-
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......... -... -------
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[ bb] =
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[P'"] -
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(P[P/x"]l" -
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(P.'"l" [P~J
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................... .
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(p,")(f,"') (}.")(}."')
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[ab]= -
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[p,] · -
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[p.]
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- .............. .
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(P/' J( p,'"') (p." JI P.''" J
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. ................ (6)
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[ac] = - · [p,]
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-
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[p.] - .............. .
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[al]= [bl] --
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[
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p
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l
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/ .111
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II]
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p,11[p,111,] p."[p,1110]
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- [p,]
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-
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[p.] -
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[p111 ,,, ] Pl11 [p,m,] p."'[p.111.]
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. Ill
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-
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[p,] -
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[p.]
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The symbols, p, reprer;;enting the relative weights have been used in the preceding
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equations merely to keep the equations in a convenient general form. In actually
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making the local adjustment all observations are given equal weight, and the various
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p• s are all called unity. It is known .that observations upon some signals (which appear
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d\stinct and steady) are more accurate than others (upon signals which appear unsteady
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or indistinct). But the difficulty of properly estimating the relath·e weights, and the
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extra labor of making the computation after they have been introduced, make it advis-
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able to assign equal weights to all observations. ·The actual computation of the coeffi-
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cients and absolute terms in (s) is therefore much less laborious than would appear from
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the forms shown ii1 ( 6). This computation is also considerably shortened by grouping
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together all series in which every one of the (d> signals were observed, all series in
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which (d - 1) signals were observed, and so on. Within these groups subgroups are
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also arranged comprising series upon the same combination of signals.
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+ Under equations (5) the following additional check equation [oo]O [oa] (A)+
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+ [ob] (B) [01] C . .. .. . . .. .. . .. .. .. ..
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- [ol] = o
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. . .. . .. ....... ·..... <fl
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may be written.
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This equation is to be used simply to furnish checks. In form it bears the sa111e relation to the initial direction 01 that the first of (5) bears to the direction 02. Thus
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[oo]
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=
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(.p ,.) -
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(p,')"
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[p,] -
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([Pp.'l."f- ...... ..
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[ ] _ (p,') CP,") .CP.' l (P.'')
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. oa - - [p,]
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[pJ
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[o!] _ _ Pr'[p,1n..J _P.'[P.mJ _
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-
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[p,]
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[p.]
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...... ..
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In eq11ations ( 5), as thus augmented by the addition of equation ( 7), the sum of the coefficients in t·ad1 vertical column is zi;:ro. For example, in the column containing
|
|
+ + (A) [aa.J [ab]+ [ac] ......... [oa] = o. Also the sum of the absolute terms + + [al]+ [bl]+ [cl]+ .... .... [o!] = o. The sum of the diagonal coefficients [oo] [aa] + [bb] + ....... : = n - s = number of observations - 11umber of series, when
|
|
all the p's are made unity. Also the sum of the coefficients in formula <fl is zero. By
|
|
writing out in detail the literal. equation corresponding to each of these checks it may be shown to reduce to an identity in each case. Hence the muuerical checks will be
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|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
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|
|
completely satisfied, except for the small effects of omitted decimals. if the computation
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|
|
. is free from mistakes.
|
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|
·
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|
|
All the observations having been given equal weight the rigorous formula for the
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|
|
probable error c of a single observation of a direction is
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|
|
+ .o _
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|
|
0·455~v·
|
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|
|
_ 0·4552.J•
|
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|
· ,.
|
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|
|
t - No. Obs.-No Independent Unknowns - 11 - s- d
|
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|
|
........ (::;)
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1
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|
· ·
|
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|
(S) gives a rigorous determination of e if the observations up01i all signals are actually
|
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|
|
of equal accuracy. .If the observations upon different signals are of different degrees of
|
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|
|
accuracy, even though they have been assigned equal weight, ( S.>will furnish an average
|
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|
|
value for c.
|
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|
|
To derive e, the probable error of an adjusted angk. by the rigorous method
|
|
|
|
involves so much heavy computation in solving the various weight equations, that one
|
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|
|
is forced to use some approximate formula for computing it.
|
|
|
|
Although observations upon different signals (different directions) have been given
|
|
|
|
equal weight in the adjustment, it is nevertheless recognized that a difference of
|
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|
|
accuracy exists and that it is desirable that it should be taken into account in computing
|
|
|
|
the probable errors. This may be accomplished to a certain extent by making the
|
|
|
|
computed probable error for each direction depend upon the residuals from that direction
|
|
|
|
only, instead of basing it upon the whole group of residuals.
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|
|
\Ve may assume that t,_0·, the square of the probable error of a single observation
|
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|
|
upon
|
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|
|
signal
|
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|
x,
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|
is
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|
to
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|
e0 ,
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|
the
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|
square
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|
of
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|
the
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|
|
probable
|
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|
|
error
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|
of
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|
the
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|
|
average
|
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|
|
single
|
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|
|
observation,
|
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|
|
as the average .J• upon signal x is to th~ average .:Y at the station, i. e.,
|
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|
|
.:·2 c.,.!:' == s_,.
|
|
|
|
.J' x .............. ; .............. (9)
|
|
|
|
in which s, is the number of sightings upon signal x and the subscript of the upper :8
|
|
|
|
indicates that the summation includes only the .J• 's pertaining to the direction x which
|
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|
|
is being treated.
|
|
|
|
If
|
|
|
|
(9 l is solved fort,"
|
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|
|
and
|
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|
|
the value
|
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|
|
of
|
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|
|
0
|
|
t'
|
|
|
|
is
|
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|
|
substituted from
|
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|
|
(S">,
|
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|
|
there is
|
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|
|
obtained
|
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|
|
c/ = 0·4552,.J• .l-l- ......................... (. 10)
|
|
|
|
n-s-d+x~
|
|
|
|
·
|
|
|
|
.(fall siguals are ,>bst·n1cd in e<.•oy series at the ~tation then 11 = sd and s = s,. After
|
|
|
|
substituting these values for 11 and s, ( IO) may be written
|
|
|
|
c"· = .
|
|
|
|
o·,~5'.c;d~ ' Li=
|
|
|
|
........ ·..................
|
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|
|
.
|
|
(II)
|
|
|
|
' (_d-I)(S-1)
|
|
|
|
In the usual case· occurring in practice, in which not all t?{ th1: signals are obser<.1t•d in
|
|
ead1 series, < 11 sd and s > s,. and the transformation from <.IO) to ( 11 "J is approximate.
|
|
|
|
t':, A detailed comparison of <.IO) and ( 11) indicates that. for the usual case in practice
|
|
( 11) gives values of which are slightly too small.
|
|
Having c,. the· probable error of a single observation upon signal x, the rigorous
|
|
|
|
expression for E, the probable error of the adjusted angle between signal x and the
|
|
|
|
initial signal, is given by
|
|
|
|
e= = t',0 Q ................. ·............. (12)
|
|
|
|
TRANSCONTINENTAL .TRIANGULATION-PART I-BASE LINES. 4r
|
|
|
|
in which Q is the reciprocal of the weight of the adjusted angle and is determined from
|
|
the following weight equations in which the coefficients are identical with those in (J) and (4).
|
|
The weight equations for angle .-1 (second direction) are ·
|
|
|
|
[p,]q,
|
|
+ [p,]q,
|
|
|
|
+ f.''QA + P,"'qn + ···· ······= o + P."QA + A"'qs +. ·...... ·. = o
|
|
|
|
+ + ...... + P.''q, P,"q,
|
|
|
|
........ ( 13)
|
|
[p"] QA ................. - I= 0
|
|
|
|
P,"'q,+p,"'q, + .... ··
|
|
|
|
+[P"']qn .......... = o
|
|
|
|
A similar set of weight equations may be written for each of the other angles B,
|
|
C. ...... in turn.
|
|
To solve each set. of weight equations of the form indicated in ( I 3) by the usual method of elimination is so heavy a task that an approximate solution must be sought.
|
|
'fhe following procedure furnishes a quick solution which is exact when all series are complete, and which is approximate when some of the signals are omitted from
|
|
some series. In the first half of equations ( 13) change all signs-that is, nmltiply each term
|
|
+ by - 1; multiply the equation which contains the absolute term -- I by ::? , and write
|
|
the remaining equations unchanged. Equations 113) as thus modified are:
|
|
|
|
- [p,]q,
|
|
-[pJq,
|
|
|
|
- P.''Q.1 - P,"'q11- .... ...... = o
|
|
- P,"QA - P."'q,,- .... ...... = 0
|
|
|
|
::?P," q, + ::?P," q, + ........ + 2 [p"] Q.1
|
|
|
|
P,"'q, + P,"'q" +
|
|
|
|
+ [p"']qn
|
|
|
|
-::! == 0 =o
|
|
|
|
Adding together all the equations in this group, remembering that the subscript in·
|
|
|
|
each case is the number of the series and the superscript is the number of the signal
|
|
|
|
observed upon, and that each p is unity, there is obtained the, following equations.
|
|
|
|
If a/I scri.:s are comp/de, the addition gives*
|
|
|
|
·
|
|
|
|
-which may be written whence, without approximation
|
|
|
|
= [p"]Q.., - 2 0
|
|
sQ..i - 2 = o
|
|
|
|
Q =::? .••.••..••...•...•.....••• (14)
|
|
s
|
|
|
|
On the other hand, {/some c?i Ilic stTics arc incomfldc, the above addition gives
|
|
|
|
+ ± q, ± qo ±. • • .. • ..... • [p"] QA
|
|
|
|
-2=0 ........ (15)
|
|
|
|
*The term involving qi disappears in the addition, becaul;e 2P1'' = P1' + P1'' (('-ach p being unity) and hence 2p1'' + f1"' + ..... = [P1]. Shnilarly the term~ in,·olving rJ:i '/:.· ..... disappear.
|
|
|
|
42
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
in which the coefficients of q,. q , ••••• • are always unity or zero. The coefficient will in
|
|
+ 0
|
|
each case be l if the initial signal is not observed in the series in question while the second* signal is observed, will be - 1 if the initial is observed .but not the second signal, and will be zero if both the initial and the second signal are observed, or if both
|
|
are omitted. The form of equations ( lJ) shows that the various q's are in general small in
|
|
comparison with Q. Also [p] will in general be much greater than unity. Hence it will be a close approximation to drop the terms ± q, ± q, .... .. from (15) and write
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whence, as before
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[p"] Q_~ - 2 = 0
|
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Q=2-······ ........................ (16)
|
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Sx
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|
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in which sx is the number of series in which the signal in question was observed.
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|
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Equation (12), after introducing the value of ex• from (II) and Q from (1+) now
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becomes, ?f all series are complete',
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t•· == 2d. (0·45.5.) ~x.J=. ......................... ( 17)
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s(d-1)(s-1)
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·
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From equations (6)jt may be seen that the diagonal coefficient in. each normal eqttation (5), viz: [aa], [bb], etc., when all series are complete, is
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|
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s· s(d-r)
|
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s-y= d
|
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|
|
Hence (17) may be written
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-~ ,;· . =
|
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|
|
2(0•455) ~,.d· . . ( s - 1) (diagonal coefficient)
|
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·
|
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·
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|
·
|
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·
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·
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·
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|
.
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...............
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(
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18)
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If some' qf t!te so-ies art' incomplde, the approximate value of Q from ( 16) instead of (14) must be substituted in (12), whence there is obtained the approximate formula
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l:"=s.2(dd"(_0·I4~~)5("S>,;. g...,:!.]•l)
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.
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.......................... (l9)
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x .
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. ..•
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Also, approximatc(1•, the diagonal coefficients in l.5) are
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.s ----=s..,..._ sx(.d-1">. .
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x d-
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d
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whence (19) may be written, as an approximation,
|
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o -
|
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r. - (Jx -
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:? (0•455) ~x.J• I) (diagonal coefficient)
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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·
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C20)
|
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|
|
Formula ( 19"> is evidently somewhat more accurate than (20).
|
|
To sum up, formula (:10) may be used for both complete and incomplete series with
|
|
the understanding that it is exact if all series are complete, but is otherwise approximate only. In this formula ~xLJ• inch1des only the .1•s from pointings upon the particular
|
|
signal under consideration, sx is the number of pointings t upon that signal, and the
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|
|
|
"The second signal being the one which, with tlie initial, defines the angle A.
|
|
f The mean of t•vo pointings, one in the direct and one in the re"erse position of the telescope, being here counted
|
|
as one 'Pointing.
|
|
|
|
TRANSCONTINENTAL .TRIANGULATION-PART I-BASE LINES. 43
|
|
|
|
"diagonal coefficient" is the [aa] or [bl>] •... of the normal equation (S) corresponding to that signal.
|
|
It should be kept clearly in mind that the E is the probable error of the augk between the sign::il under consideration and the initial signal. When for use in the
|
|
= triangulation the angle between, say, 02 and 03 (B - ...J ), see figure p. 37, is required,
|
|
it should be noted that angles A and B, as derived from the adjustment, are not independent.· The errors due to erroneous pointings upon the i1~itial signal are comnion to both angles and are canceled out from their difference. Hence, assuming that errors in A are due in equal parts to errors in pointing upon the initial signal and upon the second signal, and similarly for B, we may write
|
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|
|
............ (::?I)
|
|
|
|
The following portions of the local adjustment at the station Mount Helena, California. will serve to illustrate the arrangement of the numerical work.
|
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|
•.J.bsin1d t?J. dirtYflOJIS.
|
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|
. I 1876.
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|
|
Mt. Table Snow Az. Mvairllyes-
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----1-D-i-ab_l_o_._l\_:1_t._J\_H. ( E ). J\-:I-ar_k_·_n_r_it-te_._Lola.
|
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|
Pine Round MontiHill. Top. cello. Vaca.
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Assumed directions
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01
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0/
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II
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oo ·o
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.II
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57 '.:!
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Arithmetic oo"·o 02"·8
|
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complement
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oo·o
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II
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44 7
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"
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|
IS ·3
|
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12 ·s
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oo·o
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0
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II
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49·s
|
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II
|
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IO'S 07 7 SS ·2
|
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0
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II
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II
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4S 7 42 ·9 30·4
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0
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II
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43·s
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II
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16 ·s
|
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13 7 OI '2
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I/
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10·2
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II
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49·8 47·0 34·s
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0
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/I
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41 'l
|
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,,
|
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rS·9 16 'l 03·6
|
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0
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II
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II
|
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43 ·s
|
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4I 'O 28·s
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0
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/I
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44 ·3
|
|
II
|
|
rs 7 12 ·9 00·4
|
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|
|
Oct. II a. m. Pos. 12 Series33
|
|
Oct. I:? a. m. Pos. 13 Series 36
|
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21 ";64
|
|
17 ·32 19"48 oo·oo oo·oo
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|
I/
|
|
I9 ·22 IS ·s6
|
|
17'39 oo·oo oo·oo
|
|
,,
|
|
19·67 16 'IO,
|
|
17·88 5S·40 01 ·20
|
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|
II
|
|
07·39 04·83 o6 'II 48·72
|
|
or ·22
|
|
|
|
II
|
|
Tr ·27 09·71 10·49 53 'IO oo·So
|
|
II
|
|
IS ·27 w·6r 12'94 53 ·46 03 ·96
|
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|
II
|
|
37 ·28 32·43 34·8s 17·46 00·36
|
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|
|
II
|
|
3179 2979 30·79 JI '31 01 'II
|
|
|
|
"
|
|
36 78 3S'Ol 35·89 lS·so 59·50
|
|
"
|
|
37 ·oo 35·06 36·03 16 '5.5 00·3s
|
|
|
|
06"·02 os ·12
|
|
05 'Si 48 ·18 01 ·08
|
|
"
|
|
05·39 05·5s 05 ·47 45 ·99 01 ·69
|
|
|
|
44
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
The assumed directions A', B', C' .... were taken from the field computation. The arithmetical complements of the seconds of these angles are to be used to transform subtractions into additions. They are giveh for each signal in turn used as an initial.
|
|
In the abstract proper two series only, the thirty-third and thirty-sixth, are here given out of the 152 series shown in the original computation. The first line gives the seconds of the mean reading of the three microscopes for each signal sighted with the telescope direct. The corrections for run have already been applied. The second line gives the corresponding readings with the telescope in the reverse position, when sweeping back over the same signals in the opposite direction. The third line is the mean of the first and second. The fottrth line is derived by subtracting the first value in the third line from each of the values on that line. The fifth line is derived by adding to each value in the fourth line the corresponding arithmetical complement · from the table shown. The values on the fifth line are the m's of the observation equations ( 2). To avoid negative signs, 59 ·50 is understood to be equivalent to - o· 50.
|
|
An abstract of the m's is next made, as illustrated below. It is made in a rearranged order such as to facilitate the formation of the normal equations ( 5 J. All series of pointings upon nine signals were placed in the first group (no series included all ten signals), upon c~g-lzt signals in the second group, and so on. Also. ·within each group all series involving precisely the same combination of signals were placed together.
|
|
|
|
•-lbs/rad l~l di111i11is/i,·d mea.rnres.
|
|
|
|
No. Mt. Table Snow Az. l\'.IarvsSeries. Diablo. l\'It. l\'It.~El l\'Iark. ville. Lola.
|
|
|
|
Pine Round MontiHill. Top. cello. Vaca. [Means.
|
|
|
|
II
|
|
|
|
"
|
|
|
|
36 oo·oo OI "20
|
|
|
|
J3I oo·oo 00·08
|
|
|
|
,,
|
|
03·96 58·35
|
|
|
|
ll
|
|
01 "II 59·62
|
|
|
|
ll
|
|
00·35 00·58
|
|
|
|
ll
|
|
|
|
ll
|
|
|
|
OJ ·69 +r ·385
|
|
|
|
59·50 -0 ·312
|
|
|
|
33
|
|
|
|
oo·oo 01 ·22 oo·So 00·36
|
|
|
|
59·50 oJ ·os +0·493
|
|
|
|
Sums. No.
|
|
|
|
oo·oo S:i
|
|
|
|
+0·98 6o
|
|
|
|
+4"34 Sr
|
|
|
|
-9·17
|
|
12::?
|
|
|
|
+i ·37 -12 "0) -JO "32
|
|
|
|
56
|
|
|
|
54
|
|
|
|
55
|
|
|
|
·---3·54 -10·97 -rs ·oo
|
|
|
|
so
|
|
|
|
6i
|
|
|
|
56
|
|
|
|
The means of the horizontal lines, as given in the last column, serve to furnish the negative terms in the expression for [a!], equations ( 6), while the sums of the columns, as shown at the bottom, are [p" m."], [p"' 111"'], . . . . . . . . . The numbers of entries in the separate coltmms, as shown at the bottom, are [p'] [P"] [p'"], ........ .
|
|
The normal equations corresponding to (5 ), as formed from this abstract, are shown below, together with the checks upon their form~tion.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES.
|
|
|
|
45
|
|
|
|
1Vor111al i·qmlfi,ws.
|
|
|
|
. <A I
|
|
|
|
(lj'/
|
|
|
|
ID1
|
|
|
|
(E!
|
|
|
|
(Fi
|
|
|
|
!G!
|
|
|
|
(H)
|
|
|
|
Ill
|
|
|
|
+-l-7 "S:?S - 4 ·841 - S ·927 - 3 ·447 - .2 ·oS6 - ~ -~")5 - 1 ·f,t;q - 8 ·564 - 7 ·3,;4
|
|
- +·8.J1 +62·893 -14':!5.? - 6·19'~ - 9·227 - 5·736 - 6·639 - 4·701 - =3"368
|
|
- s·9:i7 -q·25:: +90·251 - s·s91 - s·q~ -1(·115 - 6·s.:.+ -11·900 - 9·427
|
|
- ,2. ·447 - 6 "19'~ - 8 ·591 +44 ·t.S.7 - .3 ·952 - .; '4'-'tl. - 4 ·531 - 3 ·673 - 3 ·1~,) - ::·oS6 - 9·227 - 8·14$ - .)'~:l.5.? +41 ·540 - .3·-1-67 - 5·:::43 - 2·054 - 1 ·229
|
|
- 2'9?S - 5"7'86 -II ·11.; - 5·4S4 - ._;·467 +4.~·os::: - :!'945 - 2'9.?0 - 2'795
|
|
- I ·807 - 6-~;39 - 6·534 - 4 ·531 - 5·2.i3 - ::?'945 +3~1·i.:-S - ;-;::S3 - 1 ·750
|
|
- S ·564 - 4 701 -Il ·¢0 -- J '673 - 2 ·054 - :? ·920 - 2 ·2S3 +SI ·985 - S "823
|
|
- 7 ·._;6-t- - ..~ ·3f:S - 9 ·427 - ,'.\ "190 - I ·~:-9 - .:! "i95 - I "750 - $ "8.?.3 +44 ·218
|
|
|
|
Ahso· lute term.
|
|
+ 3·0&; =o
|
|
-- "·o.io =o
|
|
-12·0-:09 =O
|
|
-- s·6~o =O
|
|
+10·637 =O
|
|
-- 0·942 =O
|
|
-- I "(•°'9 =O
|
|
+ 7 ·;t..i =O +I! ·54> =O
|
|
|
|
[0<1] ·· 7·797 -
|
|
Sum:-<. ,·, ·oi::10 -
|
|
|
|
lodj . [od kfl
|
|
/"8$2 -II ·299 - 5·6~1 - 6"1J.5 - 5·576 -
|
|
|
|
rJ ·001 - o ·oo:?
|
|
|
|
o ·oci0
|
|
|
|
o "0t.o0 - o ·001 -
|
|
|
|
7·597 o ·001
|
|
|
|
[vii) [oi] 7"•)L•7 - 1)·273
|
|
o ·ooo - o ·001
|
|
|
|
[<>!)
|
|
+ i ·s22 + o "L•OI
|
|
|
|
+ [aa] = 47 ·S2S + [bb] = fo ·893
|
|
[<'<"] = + 90 ·251
|
|
[dd] =+44·6S7
|
|
+ [ci·] = 41 ·540 + [J/] = 43 ·082 + [g!("] = 39 ·p'l
|
|
[lili] = + 51 ·985 + [ii] = 44 ·:!!8
|
|
[<><•] = + 65·1~7
|
|
|
|
[oa] = - 7 "797 [ob]= - 7·S82
|
|
|
|
[vc] =-11·299
|
|
|
|
[od]=- .5 ·621
|
|
|
|
[<>t'] = - 6 ·135
|
|
|
|
[<~(] = - 5 ·576
|
|
|
|
[~!.?"] = - i ·597
|
|
|
|
[0!1] = - 7·007
|
|
|
|
[oi]
|
|
|
|
6·273
|
|
|
|
[<'0] =+ 65 ·1S7
|
|
|
|
,, I [A] = --o ·058
|
|
|
|
II
|
|
.-- 0 ·008
|
|
|
|
[B] =+0·2121
|
|
|
|
[C] = +0·143
|
|
[D] = + o ·223
|
|
[£] = -·0·159
|
|
[FJ =+o·o8o
|
|
|
|
Residuals from normal equations.
|
|
|
|
+0·027
|
|
+ 0·002
|
|
-0·009
|
|
+0·017 -0·017
|
|
|
|
[G] =+0·077
|
|
|
|
-0·013
|
|
|
|
[H] = '- o ·129
|
|
[fl = -0·230
|
|
|
|
-0·025
|
|
• + o ·cor
|
|
|
|
+ 152 ·ooo=No. of series. - 683 ·c<00 =No. of observationj;.
|
|
|
|
o ·ooo = Sum.
|
|
|
|
o ·001 = Su11J.
|
|
|
|
The •·residuals from normal equations'' were obtained by substituting the adopted values for (A), (B) .... in the normal equations.
|
|
The values of (.4), (B) .... being substituted in the" abstract of diminished measures'' there is obtained an ''abstract of remaining differences'' written in precisely the same form. In this latter abstract if the mean of the horizontal line as given in the last column is subtracted .from each of the individual values in that line the differences are the .J's from which the probable errors are computed by (20) and (21).
|
|
A portion of the abstract of remaining differences and of the abstract of values of L1 and .:J• is shown below.
|
|
|
|
•-lbstrad <?l 1-emai11il~t; d(ffe•n·11ci·s-.llf"omt1 Hde11a.
|
|
|
|
No. SerieS.
|
|
|
|
Mount Table Snow
|
|
|
|
Az.
|
|
|
|
])iablo. Mountain. Mt. (El. Mark.
|
|
|
|
l\·Iarvs-
|
|
,·Hie.
|
|
|
|
Lola.
|
|
|
|
Pi11e Hill.
|
|
|
|
Round MontiTop. CE:.Jlo.
|
|
|
|
Vaca. Meai;is.
|
|
|
|
36 oo·oo or ·26 I3I oo·oo 00·14
|
|
|
|
03·S2 58·21
|
|
|
|
QI ·03 59·54
|
|
|
|
00·48 OI ·92 00 71 59 73
|
|
|
|
or ·42 5972
|
|
|
|
33
|
|
|
|
00·06 01 ·01 00·66 00 ·14
|
|
|
|
59·63 01 ·..~. I
|
|
|
|
00·47
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY•
|
|
|
|
•-lbstrad of mlucs <?f .J and .J0 -1lf,11ml Hdm,1.
|
|
|
|
No. I Mount Table Snow Series. Diahlo. l\Jount'n. Mt.(El
|
|
J. .J.O .J. .J.• .J. ·.J.•
|
|
|
|
Az. Mal'k.
|
|
.J. .J.<
|
|
|
|
~tarys-.
|
|
ville.
|
|
.J. .J.O
|
|
|
|
Lola.
|
|
.J. J.•
|
|
|
|
Pine Hill.
|
|
.J. .i.•
|
|
|
|
Ronnd Top.
|
|
.J. .J.•
|
|
|
|
l\'Ionti-
|
|
cello.
|
|
J. J.•
|
|
|
|
Vaca. .J. .J.•
|
|
|
|
.16 -1 ·4, ~ "(J
|
|
J3J + ·os O'l
|
|
········ ...... ...
|
|
..........
|
|
Sums .. No .....
|
|
|
|
- ·16 o·o
|
|
+ '4' 0'2
|
|
- ·41 O".?
|
|
31 '6
|
|
"°
|
|
|
|
+"'4" 5·~ -1 ·s1. .'.!'3
|
|
.. . ..... ...
|
|
+ ·54 n·3 + ·19 o·o
|
|
..... .. . ..... ...
|
|
|
|
- ·.:.:.3 O'l
|
|
|
|
- ·39 O":?
|
|
-·1s o\.,
|
|
... ····· .. . ...
|
|
|
|
- ·94 (• "•)
|
|
+ ·99 f'r)
|
|
... ..... ...
|
|
-'84 •) 'i
|
|
|
|
+ ·50 0·3 + '01 '-"' \.l
|
|
+ •84 •) ·;
|
|
|
|
f...7 ·9 :!. .l.2 =40.~ ·7
|
|
|
|
6;
|
|
|
|
51)
|
|
|
|
Hence the probable error of a single observation of a direction is by formula (_ 8)
|
|
|
|
. ""1t - = t" I 0·455 :E .J• ~ I (0·455) (408'il = ± 0"·60 S - d + I ""683 - 152 - IO+ I
|
|
|
|
The probable error of the angle between Table Mountain and Mt. Diablo is, by
|
|
|
|
formula
|
|
|
|
J = J'\ .. · =' o·910 ~ .J0
|
|
|
|
(· 20 ), E=
|
|
|
|
\.s,. -
|
|
|
|
."' ..
|
|
|
|
·
|
|
|
|
.
|
|
|
|
I) (chagonal coefficient)
|
|
|
|
0·910'> (,~'l ."6') (60) (47"8)
|
|
|
|
/0- °0- 100=±0"·10
|
|
|
|
similarly the probable error of the angle between Snow Mountain and Mount Diablo is·
|
|
|
|
By formula (2 I) the probable error of the angle between Table Mountain and Snow
|
|
|
|
Mountain is
|
|
|
|
+ J}-6 (0·0100 0·0069) = ± 0·09
|
|
|
|
In case of the adjustment of the Yolo Base net, already referred to above as the only one where special weights to the resul~ing directions from station adjustments were
|
|
|
|
introduced in the net adjustment, these weights were not those obtained by p =EI. as
|
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|
|
.
|
|
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|
'
|
|
|
|
roughly approximate values, but they were modified by adding to the respective prob·
|
|
|
|
able error a constant one depending on the closing of the triangles. This latter probable
|
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|
|
error is shown to be much greater than the above E, and the eff~ct was to to1ie down
|
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|
|
the variations in the respective final weights to the directions. · In connection with this
|
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|
|
it may be noted that the influence of weights rather diminishes with an increased
|
|
|
|
geometric complexity of the net. For particulars of the treatment of the Yol9 Base
|
|
|
|
net, see Appendix No. 9, report for 1885.
|
|
The value of e, or the probable error (p. t".) of a single observation of a direction at
|
|
|
|
a station, as given along with the abstract of the clirectiqns at the station, merely serves
|
|
|
|
the purpose of giving some general information bearing upon the accuracy' of the means
|
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|
employed.
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|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 47
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|
(D.) REDUCTION OF HORIZONTAL DIRECTIONS TO SEA LEVEL.
|
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|
The resttlting directions at a station, as given in the abstracts, still m:ed a small
|
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|
|
correction to redttce them to what they would have been had the object observed upon
|
|
|
|
been at the sea level. The altitude of the observing station and the distance between
|
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|
|
them does not enter into the case: the reduction is due to the circumstance that, in
|
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|
|
general, the verticals at the two stations are not in the same vertical plane. The cor-
|
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|
rech.on
|
|
|
|
..
|
|
¥
|
|
|
|
.
|
|
1s
|
|
|
|
g-..1ven
|
|
~
|
|
|
|
by
|
|
|
|
-c•
|
|
:!
|
|
|
|
·
|
|
|
|
h-p
|
|
|
|
s1. 112tr
|
|
|
|
.
|
|
|
|
cos-•,P,
|
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|
|
when::,•·-=
|
|
|
|
a-•-- . -b0
|
|
,i-
|
|
|
|
and h =alti•tude of
|
|
|
|
the sta-
|
|
|
|
tion observed upon. p = radius of curvature in the plane normal .to the meridian,
|
|
a = azimuth of the line< counted from south around by west) and tf.i = latitude of place.
|
|
|
|
With log c• = 7·s305 and log P = 6"8054 for ,P = 39° and Clarke's spheroid (of 1866),
|
|
|
|
and dividing the expression by sin 1", we get for the correction in seconds and the
|
|
|
|
height in metres
|
|
|
|
o"·ooo 066 sin2«.h
|
|
|
|
This correction has been applied systematically to all. measured directions of the base nets and intervening triangulation from the Salina base to the Pacific coast, but no application was made to the triangulation east of S_alina base on account of the ·lower altitudes and consequent smallness of the correction in this part of the arc. In comparison with the magnitude of the average triangle closing error, the effect of omitting this correction, except for the higher altitudes, seems justified. About the Salina base stations the average reduction of a sight to the sea level is but 0"·02.
|
|
The probable error of a single observation of a direction </> is given under the list
|
|
of directions at each station as a convenient index of the accuracy of the observations. When the parenthesis (D. and R.) is used, the observations were made with a direction instrument. A single observation of a direction comprises two paintings upon the signal, one with telescope direct and one with telescope reversed, and two readings (forward and backward) of each micros.cope, of which there are usually three, for each pointing. c' is computed by formula (8) shown on page 40.
|
|
When the parenthesis ( 6 D. and 6 R.) is used, the observations were made with a repeating instrument and a single observation q/ an angle comprises rz paintings upon each of two signals, 6 with telescope direct and 6 reversed, and 3 readings of the P,orizontal circle, at the beginning and end of the direct measure and again at the end of the reversed measure. The quantity given is the probable error of a single observation of a
|
|
direction (not angle) and is ~"2 times the probable error of a single observation of an
|
|
|
|
angle. It was also computed by the formula (S) shown on page 40. The parenthesis (3 D. and 3 R.) has a meaning analogous to ( 6 D. and 6 R. ).
|
|
|
|
(E.) ADJUSTMENT OF BASE NETS OR OTHER 'I.'RIANGULATIONS.
|
|
The method is the same as that usually employed to satisfy the geometrical conditions of a triangulation by application of the niethod of least squares. For the sake of convenience the leading fornmlre referring to condition observations, together
|
|
*"Geodesy," by Col. A. R. Clarke,' Oxford, iSSo, p. 113.
|
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|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
with those for the computation of the probable error of a function of the adjusted
|
|
|
|
quantities, will he briefly recapitulated here.*
|
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|
|
Suppose we have given as the direct ·result of observation the 111 quantities I, ! / ••••
|
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|
|
0 3
|
|
|
|
which are connected by 11 conditions.
|
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|
|
Let
|
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|
x,
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|
|
x,,
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|
.r 3
|
|
|
|
••••
|
|
|
|
be their most
|
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|
|
probable values;
|
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|
|
also let i•, 'Z' '', •••• he the corrections to the observed values, so that in general we have
|
|
|
|
xi =
|
|
|
|
2
|
|
Ii+ ·vi;
|
|
|
|
remembering
|
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|
|
that
|
|
|
|
necessarily
|
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|
|
m > n
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|
|
in order
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|
|
that
|
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|
|
any
|
|
|
|
adjustment
|
|
|
|
may
|
|
|
|
exist, then the conditions involved may be expressed by 1l equations, of linear form,
|
|
|
|
thus:
|
|
|
|
+ + + + ... . o = a 0
|
|
|
|
a,x,
|
|
|
|
a 2 :1·0
|
|
|
|
a3x 3
|
|
|
|
+ + + + ... . O = b 0
|
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|
|
b,x,
|
|
|
|
b0:1:2
|
|
|
|
b3:~;3
|
|
|
|
+ + + + ... . = o c,. c,x, c0x 2 c_r1·3
|
|
|
|
Introducing the observed quantities these equations will not be satisfied, but will
|
|
|
|
leave the discrepancies w, w '<X', ...... viz: 2
|
|
|
|
zc•, =
|
|
W0 =
|
|
w,=
|
|
|
|
a,.+
|
|
+ b0
|
|
c0 +
|
|
|
|
a/,+
|
|
b/, +
|
|
c/+
|
|
|
|
a/ 2
|
|
/>/,
|
|
t /2
|
|
|
|
+ +
|
|
+
|
|
|
|
a/3 bc//33
|
|
|
|
+ +
|
|
+
|
|
|
|
.... · · · .
|
|
....
|
|
|
|
where the sign of wr is to be taken in the sense of observed value minus true value. We have then the n condition equations:
|
|
|
|
+ + + ...... + a,·v,
|
|
|
|
a,z
|
|
|
|
1 0
|
|
|
|
av 33
|
|
|
|
·w, = o
|
|
|
|
+ + + b,'i', />2 7.•2 bpi+ · · ... · = 'Zf'0 0
|
|
|
|
+ + + ...... + C1'-'1 C2t'.:!. £~·;13
|
|
|
|
= tt'3 0
|
|
|
|
Letp, P, p •••• be the weights of the quantities I, I, / •••• then the quantity [p. zizi]
|
|
|
|
3
|
|
|
|
3
|
|
|
|
must be inade a minimum; this leads to the equations of correlates which introduce the·
|
|
|
|
multipliers C, C C, 0
|
|
|
|
as yet unknown. These correlate equations are :
|
|
|
|
P,<', = a,C, + b,C2 + ,~C3 + ... .
|
|
p;v2 =a/.". ",+ b,C0 + c,l~ + ... . P,i•, = al",+ b,C,, + + c3C3 ... .
|
|
|
|
and the normal equations become
|
|
|
|
[apa]
|
|
|
|
C l
|
|
|
|
+ [apb]
|
|
|
|
C 2
|
|
|
|
+ [l!p!J
|
|
|
|
C J
|
|
|
|
+ ....
|
|
|
|
+tc•. I
|
|
|
|
=
|
|
|
|
0
|
|
|
|
[apb] C, +[bpb] C, +[bpe] C3 +.... +w, = o
|
|
|
|
[be] (_" (_- + + [~p·] J
|
|
|
|
p
|
|
|
|
+ c c~J +~ 2
|
|
|
|
p
|
|
|
|
J
|
|
|
|
''"
|
|
|
|
= tlIJ
|
|
|
|
Q
|
|
|
|
* Cf-T. \V. Wright's Treatise on the Adjustment of Ob:;eryations, New Yurk, IS-'!4, Chapter V, t>. 213 and fol.,
|
|
and W. Jordan'' Vermessuug,kumle, Vol. I t 1SSS), p. io.i and fol.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 49
|
|
|
|
which may be written, putting 11 = 1.ip
|
|
|
|
[.ii.aa]
|
|
|
|
C,
|
|
|
|
+ +
|
|
|
|
[p.ab] [11.bb]
|
|
|
|
C, C
|
|
0
|
|
|
|
+ [11.a1J
|
|
+ [11.br] + [Ji.cc]
|
|
|
|
C 3
|
|
C~
|
|
_C
|
|
|
|
+ + +
|
|
|
|
.... .... ....
|
|
|
|
+ w, + w, + w
|
|
|
|
=
|
|
=
|
|
=
|
|
|
|
o o o
|
|
|
|
3 -t ... . 3
|
|
|
|
Solving these equations the values of C; become known, and consequently also the values of ;:11 and x;.
|
|
|
|
The
|
|
|
|
mean
|
|
.
|
|
|
|
error
|
|
|
|
of an
|
|
.
|
|
|
|
observation of unit weight is
|
|
|
|
given by 111, =
|
|
|
|
~./[pt•Ht•]
|
|
|
|
where
|
|
|
|
the sum [pv-.:1] is found by means of the individual corrections and checked in the case
|
|
|
|
of the base nets by the relation [pi•i1] = - ["wC] .
|
|
|
|
.
|
|
|
|
To find the weight and probable error of an adjusted value of an observation, also
|
|
|
|
the weight P of any function of the adjusted observations, we put
|
|
|
|
which function can not contain· all the x' s, but only 111 - 11 of them.
|
|
|
|
The coefficients/i are found by partial differentiation, viz.:
|
|
|
|
;:=/, l
|
|
|
|
JF . dx, =J.
|
|
|
|
-Jd.F. -_
|
|
|
|
f
|
|
3
|
|
|
|
,
|
|
|
|
etc .
|
|
|
|
•\: J
|
|
|
|
\Ve next form the sums
|
|
|
|
, ,[J'J [~] [~]
|
|
|
|
[1] etc., also
|
|
|
|
and combine them with the former normal equations, at the same time introducing a
|
|
|
|
new set of indeterminate quantit_ies R, R, R •••• in the place of the former C, C C ••••
|
|
|
|
3
|
|
|
|
0 3
|
|
|
|
then. the requirement of the coaditionecl minimum leads to the following ·so called
|
|
|
|
·transfer equations:
|
|
|
|
·
|
|
|
|
[u.a.a] R, + [u.ab] R + [u.ac] R + ........ + [u.1if] = o
|
|
|
|
+
|
|
|
|
[u.bb]
|
|
|
|
0
|
|
R
|
|
|
|
+
|
|
|
|
[u.b1]
|
|
|
|
+ 1
|
|
R
|
|
|
|
........
|
|
|
|
+
|
|
|
|
[u.lf]
|
|
|
|
=
|
|
|
|
o
|
|
|
|
+0 [u.cc] R 3 + ........ + [u.if] = o
|
|
|
|
3 + ....... .
|
|
|
|
Solving we have the values R;, and consequently also Fi by the relations
|
|
|
|
<R +· .. . F, =J,+a,R,+ b,R,+c,R3 + . ._.
|
|
|
|
+ F0 = f.,
|
|
F3 = /~
|
|
|
|
+ a0 R, +
|
|
a3R 1 +
|
|
|
|
b,R, b3 R 0
|
|
|
|
+ +
|
|
|
|
3
|
|
c3 R 3
|
|
|
|
+
|
|
|
|
...
|
|
|
|
.
|
|
|
|
and finally we have the reciprocal of the weight P of the function F by ~ = [u .FF] Also
|
|
|
|
the mean error of
|
|
|
|
:;p m,v For mp= =
|
|
|
|
[u.FF] and the probable error of For 1·F = 0·6745 nip
|
|
|
|
18732-No. 4--4
|
|
|
|
50
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
(F.) REMARKS ON WEIGHT COEFFICIENTS IN THE NET ADJUST~ENT AS DEPENDING ON THE STATION ADJUSTMENTS.
|
|
|
|
In accordance with Bessel's method of proceeding, the corrections as determined in
|
|
|
|
the net adjustment depend with respe'ct to weights on coefficients furnished by the gen-
|
|
|
|
eral solution of the station or local adjustments; although theoretically strict, this pro-
|
|
|
|
ceeding has in later times either been greatly modified or abandoned for reasons imposed
|
|
|
|
by practical considerations. . It has been from the beginning the practice on the Survey to treat these adjustments independently of each other and to give equal or nearly equal
|
|
|
|
weight to the directions in the net adjustment. This separate treatment is justified by the following consideration: The errors incident to the angular measures as indicated
|
|
|
|
by the local adjustment either depend on other causes or at most are of a subordinate
|
|
|
|
character to the error in the subsequent operation-that is, in the net adjustment. In the latter combination of the measures new sources of error show their effects; as, for
|
|
|
|
instance, the effect of the deflec.tion of the plumb line causing the angles to be measured out of the normal horizontal plane, want of coincidence of the center of a station and of
|
|
|
|
heliotropes or targets subsequently mounted ovei; it, persistent lateral deviation of the line
|
|
|
|
of sight, constant or uncompensated graduation errors of the instrument .. all of which causes exert no influence on the station ·adjustment. It is a matter of experience that
|
|
|
|
the value of the probable error of a direction derived from the measures at a station is much smaller than the same when derived from the triangle dosing errors-thus if weights
|
|
|
|
are introduced at all they should be made to exert but a comparatively weak influence. As an example of the process followed, the adjustment of the Yolo Base net may be
|
|
|
|
referred to (Coast and Geodetic Survey Report for 1885. Appendix 9, pp. 447-448).
|
|
Let t"s =average value of ·the probable error of a direction as derived from the station
|
|
adjustment. c1 =average value of the same as derived from the closing errors of the triangles co1~1posing the net. Put c/ = t"t" - t".°. Cc" is a constant quantity for the figure . under consideration, and is to be combined with every probable error of observation c,
|
|
|
|
in order to obtain the appropriate probable error and .consequent weight of each direc-
|
|
+ tion as needed for the figure adjustment. Hence we have e• = t".° t'c" and the weight
|
|
|
|
+ p --
|
|
|
|
e.=
|
|
|
|
-I
|
|
|
|
-
|
|
Cc"
|
|
|
|
0
|
|
|
|
In this manner the weights from the station adjustment are made to
|
|
|
|
undergo a considerable equalization.* In connection with the above consideration we may note also the important feature that the process theoretically called for, involving
|
|
|
|
.the introduction of weight equations from the local adjustment, becomes prohibitive for
|
|
|
|
any extended triangulation on account of the excessive labor introduced thereby. The
|
|
|
|
modified weights p = e; ~ t'/ are introduced in the adjustment of t~1e triangulation
|
|
|
|
betwee1~ El Paso and Yolo Base nets, whereas in other parts of the triangulation equal or unit weights are assigned to all cli'rections.
|
|
|
|
*We have the following values of Cs and e, in the west<:r? section of the arc:
|
|
|
|
Locality.
|
|
|
|
Number of Result· Number of Resnit·
|
|
directions. inges. triangles. • ing e,,
|
|
|
|
El Paso base net Triangulation El Paso to Salt Lake Salt Lake base net Triangulation Salt Lake to Yolo Yolo base net .
|
|
|
|
16
|
|
|
|
±0·32
|
|
|
|
67
|
|
|
|
±0'094
|
|
|
|
2J
|
|
|
|
±0"27
|
|
|
|
·56
|
|
|
|
±O"o8$
|
|
|
|
33
|
|
|
|
±0'28
|
|
|
|
9'l
|
|
|
|
±o"oSo
|
|
|
|
30
|
|
|
|
±0"20
|
|
|
|
34
|
|
|
|
±o'o81
|
|
|
|
19
|
|
|
|
±0'24
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 51
|
|
|
|
(G.) THE COMPUTATION OF THE SPHERICAL EXCESS OF THE TRIANGLES.
|
|
|
|
For all that part of the triangulation which lies east of the Rocky Mountains,
|
|
|
|
and which traverses the plains and gentle slopes of Kansas, Missouri, and Ohio,
|
|
|
|
the comparative shortness of the sides of the triangles admits of the application of
|
|
|
|
Legendre's theorem in its sirµple form. The spherical excess E (in seconds) is given
|
|
|
|
by a1~1 s.in ~:. where a,b,C, refer to sides and i~cluded angle of a plant• triangle, whose
|
|
|
|
2r sm 1
|
|
|
|
·
|
|
|
|
angles are those of the corresponding small spherical triangle after each has been dimin-
|
|
|
|
ished by .I.·'3 E. When greater precision is required as for the larger triangles which
|
|
|
|
stretch across the peaks and ridges of the Allegheny Range, we introduce the radius
|
|
|
|
of an osculating sphere (referring to the center of the triangle) and take
|
|
|
|
·
|
|
|
|
e--
|
|
|
|
a1b1 sin C1 2p p" sin 1"
|
|
|
|
--
|
|
|
|
a.b, sin C1
|
|
|
|
[
|
|
|
|
2a0 (1 - ti') sin 1"
|
|
|
|
1 - C S•l• l l• ' I,,',]"
|
|
|
|
111
|
|
|
|
[1 - e• sin "tp]"
|
|
|
|
The quantity w• ( _ e") sin ,, has been tabulated with the latitude <p as argument,
|
|
|
|
1
|
|
|
|
1
|
|
|
|
for which see Coast and Geodetic Survey annual report for 1894.*
|
|
|
|
For triangles of unusually large size and approaching the limit for possible obser-
|
|
|
|
vation, certain terms in the development of the theorem which ordinarily could be
|
|
neglected need examination.. It has been shown that spherbidal triangles may be com-·
|
|
·puted as spherica1 and hence as plane ones by application of the same theorem
|
|
extendecl.-f Various forms have been given to the development of the theorem. t Let
|
|
|
|
+ S =surface of the corresponding plane triangle = 1
|
|
|
|
Jf a, b, sin C1,
|
|
|
|
and let 111" = }'3 ~a.,•+ b," c,"), then
|
|
|
|
+ + .. ) ,, -
|
|
|
|
Sl (.-
|
|
|
|
E
|
|
|
|
-
|
|
|
|
P,,,P11
|
|
|
|
• Slll
|
|
|
|
11
|
|
I
|
|
|
|
I ·. .
|
|
|
|
S__P!!1!1_1P__0
|
|
|
|
.
|
|
|
|
where Pm and p are the radii of curvature in the plane of the meridian and normal to 11
|
|
it, and Eis to be distributed unequally over the angles,§ viz:
|
|
|
|
+ E . E 111.•-a •
|
|
|
|
.
|
|
|
|
-
|
|
|
|
/
|
|
|
|
.
|
|
|
|
-1A3.
|
|
|
|
=6-0+
|
|
|
|
- · - -1
|
|
PmP,.
|
|
|
|
E E m"-b 2 B-B1 =3+60 PmP,,' +
|
|
|
|
E
|
|
|
|
E 1112 -c•
|
|
|
|
C - Cl = 3+ 60 p,,.p,: +
|
|
|
|
1 + - - - . or -E (~
|
|
|
|
111?-a1"')
|
|
|
|
3 , 20PmP...
|
|
|
|
b,".) - r+-- E (-
|
|
|
|
JJt"-
|
|
|
|
3 , 2op,,.p,.
|
|
|
|
- r+-- E (
|
|
|
|
c. 11t"- 1")'
|
|
|
|
3 , 2op.,p,.
|
|
|
|
A convenient logarithmic formula has been given by the late C. H. Kummell, tables of the factors log A and log B of the Coast and Geodetic Survey method for the·
|
|
|
|
*Appeudix No. 9, pp. 290-291. tThe spherical excess of.a spheroidal triangl<: is equal to that of a spherical triangle whose augular points have
|
|
|
|
the same latitudes and longitudes as the corresponding points of the spheroida.l triangle-Clarke's Geodesy (rSSo), pp.
|
|
|
|
49 and 107.
|
|
|
|
.
|
|
|
|
: Helmert's Theorieen der Hoheren Geodasie (18$o), vol. 1, pp. SS-rn1.
|
|
|
|
eHelmert, ibid, p. 98.
|
|
|
|
52
|
|
|
|
UNITED STATES COAST.· AND GEODETIC SURVEY.
|
|
|
|
compt1tation of geographical positions being on hand (Appendix No. 9, report for 1894). Put in the latest form given by him,* let L::.. = area of the plane triangle,
|
|
|
|
log m = log .-l +log B + :r384 545
|
|
|
|
.
|
|
|
|
f
|
|
|
|
log e =log /11 +log 2 L::.. + 6~log cliff. r" for the three angles.
|
|
|
|
For the larger triangles within the region of the Rocky Mountains and of the Sierra·
|
|
Nevada the spherical excess rises to r', and even.exceeds this amount. To show the
|
|
effect ·of the higher terms, also the change of e when computed for the Clarke and the
|
|
Bessel spheroids, t the following example has been added.· For the largest triangle-
|
|
Tushar, Wheeler Peak, Mount Nebo-we ·have the following approximate data, and for
|
|
distances given in metres-
|
|
|
|
Distance.
|
|
log a,= log (Wheeler P. to Mt. Nebo)= 5 ·376 146o
|
|
log c~ =log (Wheeler P. to Tushar) = 5 ·247 S364 log b,=log (Mt. Nebo to Tushar) =5 ·215 5r:q
|
|
|
|
Lat. of Tushar Lat. of Wheeler P. Lat. of Mt. Nebo
|
|
|
|
0
|
|
38 25·1 39 4S·5 38 59 ·r
|
|
|
|
log a, b, sin C. = 10 ·463 150
|
|
log 1/2 Pm p,. sin r" = r ·404 6ro (see table appended)
|
|
|
|
log first term
|
|
|
|
= r ·S67 760 First term 73" ·7497
|
|
|
|
log m•
|
|
|
|
= 10·5S3
|
|
|
|
log Pm p.,_
|
|
|
|
13·009
|
|
|
|
logs
|
|
|
|
0·903
|
|
|
|
log lit •JS Pm p,.
|
|
|
|
6·071
|
|
|
|
log first term
|
|
|
|
I '868
|
|
|
|
log second term
|
|
|
|
i ·939 Second term = o ·0087
|
|
|
|
e = 73 ·7584
|
|
|
|
<p.,.
|
|
= log (111•-a,o)
|
|
|
|
,.IO '26
|
|
|
|
39 04
|
|
|
|
log I/:20 p,,. p,.
|
|
|
|
5·09
|
|
|
|
log.!·; e
|
|
|
|
,.5·35
|
|
I ·.~9
|
|
|
|
Similarly-
|
|
log(A~A.-D
|
|
-D log(B-s,
|
|
c.-D log(c-
|
|
|
|
,,
|
|
•.6. 74 -0.00055
|
|
|
|
+ 6·32
|
|
|
|
0'00021
|
|
|
|
6·53 +0·00034
|
|
----
|
|
Checksum=o
|
|
|
|
and the distribution to the spherical angles becomes
|
|
|
|
to A to B to C sum
|
|
|
|
II
|
|
- 24 ·5856 - 24 ·5863 - 24 '5864
|
|
73·7583
|
|
|
|
This example shows that on account of the second term the third place in the decimals of the ·difference between the spherical and plane angles is not ·affected by as much as a unit.
|
|
Difference in the above value of E clue to a change of reference spheroid.
|
|
|
|
*Astrono1nische Nachrichten No. 2116.
|
|
|
|
.
|
|
t\Vehave
|
|
|
|
c-fE;-=-2dat1 +
|
|
|
|
2
|
|
|
|
cos
|
|
|
|
~IJ'ede.
|
|
|
|
C.See Die" geod3.tischen Hauptpunkte," etc.
|
|
|
|
Dr. E. Lamp, Berlin, 1gis. pp. 300-30,\. l
|
|
|
|
Von G. Z~chariae, translation l":y
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-.PART I-BASE UNES.
|
|
|
|
53
|
|
|
|
By direct computation the values stand as fol.lows:*
|
|
|
|
Clarke spheroid
|
|
|
|
Bessel spberoid.
|
|
|
|
log a, b, siil C.
|
|
|
|
10 ·463 150
|
|
|
|
log 1/2 p,. p,. sin 111 I ·404 610
|
|
|
|
IO ·41)3 150 1 ·404 711
|
|
|
|
The difference in the value of E is 011 ·017 1. or :rh:r ·part
|
|
|
|
log first term First term Second term Resulting e
|
|
|
|
I '867 760 73 11 ·749 7 +o ·oo.S 7 7311 758 4
|
|
|
|
I 0 867 861
|
|
73 766 s
|
|
+o ·oo.S 7
|
|
7311 "775 5
|
|
|
|
of itself.
|
|
|
|
The computation o~ e according to Kmnmell's logarithmic form stands as follows:
|
|
|
|
0
|
|
|
|
II
|
|
|
|
Angle at Tushar SS 16 o6
|
|
|
|
Angle at Wheeler 4.~ 40 13
|
|
|
|
Angle at Mt. Nebo 48 03 41
|
|
|
|
log cliff. 111 +1
|
|
|
|
in seventh place of
|
|
|
|
+22
|
|
|
|
dee's.
|
|
|
|
+19
|
|
|
|
log A=:=
|
|
logE log const.
|
|
|
|
8. 509 142 1. From table app. 8 ·5ro 922 .I 9, rep. .for 1894.
|
|
4·384 545
|
|
|
|
log a, =s ·376 146
|
|
|
|
log b,
|
|
|
|
5 ·215 512
|
|
|
|
log sin C, 9·S7r 492
|
|
|
|
log 2.d
|
|
|
|
w ·463 150
|
|
|
|
Sum ~..~ sum
|
|
log }"6 sum
|
|
|
|
42 7 0·845 l
|
|
|
|
log 1st + 2d term I ·867 8
|
|
|
|
516
|
|
|
|
2 71·2 9
|
|
|
|
logm
|
|
|
|
1·404 609
|
|
|
|
log 2,6.
|
|
|
|
log 1st+2d
|
|
|
|
. term 3d tenn
|
|
|
|
I ·867 759 or 7311 "749' 5
|
|
+ 52
|
|
|
|
Resulting log E 1 ·867 81 l and E = 7311 758 3 as before
|
|
|
|
Values of log lfop,,,p,. sin l" for the spheroids of Clarke (1866) and Bessel (184(!
|
|
and argument <P between latitudes .P = 30° and .P = 50°. Here p,,, = rad_ius of curvature in the meridian and p,. radius of curvature in the
|
|
plane normal to it; the dimensions of the spheroids are those given in Appendix No. 91 Report for 1894, p. ::iSo, and are expre~sed in metres.
|
|
|
|
Clarke's spheroid.
|
|
|
|
Di ff.
|
|
|
|
Bessel's spheroid.t
|
|
|
|
Piff.
|
|
|
|
•P
|
|
|
|
log p,,.
|
|
|
|
log p ..
|
|
|
|
for 11 log 1/2 p,., in 6th p" sin 1'-' place.
|
|
|
|
'log p...
|
|
|
|
log Pn
|
|
|
|
for 11 log r/2 p.., in 6th Pu Sl•ll I II place.
|
|
|
|
0
|
|
|
|
30
|
|
|
|
6·So2 852 6·So5 066 1·405 477 r50
|
|
|
|
6"So2 823 .6°805 006 1·405 566 1"48
|
|
|
|
3r
|
|
|
|
2 919
|
|
|
|
5 089
|
|
|
|
3S7 ·1·53
|
|
|
|
2 890
|
|
|
|
5 0:'.!8
|
|
|
|
477 r50
|
|
|
|
32
|
|
|
|
2 <jSS
|
|
|
|
5 1!2
|
|
|
|
295 1"55
|
|
|
|
2 957
|
|
|
|
5 051
|
|
|
|
387 r53
|
|
|
|
33
|
|
|
|
3 058
|
|
|
|
5 135
|
|
|
|
202 ns
|
|
|
|
3 026
|
|
|
|
5 074
|
|
|
|
295 r55
|
|
|
|
34
|
|
|
|
3 129
|
|
|
|
5 159
|
|
|
|
107
|
|
|
|
3 096
|
|
|
|
5 097
|
|
|
|
202
|
|
|
|
I"6o
|
|
|
|
r5S
|
|
|
|
35
|
|
|
|
3 201
|
|
|
|
5 183 l"405 O!l 1·62
|
|
|
|
3 167
|
|
|
|
36
|
|
|
|
3 274
|
|
|
|
5 207 1·404 914 1°63
|
|
|
|
3 239
|
|
|
|
37
|
|
|
|
3 348
|
|
|
|
5 231
|
|
|
|
816 1·6s
|
|
|
|
3 312
|
|
|
|
38
|
|
|
|
3 422
|
|
|
|
5 256
|
|
|
|
717 r67
|
|
|
|
3 385
|
|
|
|
39
|
|
|
|
3 497
|
|
|
|
5 281
|
|
|
|
*For computation by the formula for
|
|
|
|
617
|
|
|
|
3 459
|
|
|
|
. Ill.
|
|
c!.:.. wehave: da = -809·,,
|
|
|
|
5 I2I
|
|
|
|
107 I"6o
|
|
|
|
5 145 r·405 OJI !"62
|
|
|
|
5 169 1·404 914
|
|
|
|
5 194
|
|
|
|
816
|
|
|
|
r63 r63
|
|
|
|
5 218
|
|
|
|
718
|
|
|
|
a=- - da
|
|
|
|
0"000 I.27, d,· = - o·aoo 56, and
|
|
|
|
+ + d•
|
|
,;de.· = - o·ooo 046; hence -; =
|
|
|
|
o·o)o 234, or df: =
|
|
|
|
0 11 ·01 7 ~.
|
|
|
|
tSee Table 35e of radii of curvature in Dr. Albrecht's Fo~mel!t uncl Hiilfstafeln fiir geographische Ortsbestim-
|
|
|
|
mungeu; Leipzig, 189'1, pp. >68-,159.
|
|
|
|
54
|
|
|
|
UNITED STATE~ COAST AND GEODETIC SURVEY.
|
|
|
|
Clarke's spheroid.
|
|
|
|
log p..,
|
|
|
|
log p,.
|
|
|
|
log 1/2 Pm p,, sin 1 11
|
|
|
|
Diff. for 11 in 6th place.
|
|
|
|
Bessel's spheroid.
|
|
|
|
Diff.
|
|
|
|
for 11
|
|
|
|
log p,. ,log p,.
|
|
|
|
log ~/2 P·• in 6th p,. sin 1" place.
|
|
|
|
0
|
|
|
|
r70
|
|
|
|
40 41
|
|
|
|
3 5i3 3 650
|
|
|
|
5 30i 5 332
|
|
|
|
515 . r70 413 r70
|
|
|
|
3 534
|
|
3 609
|
|
|
|
5 243 5 268
|
|
|
|
618 518
|
|
|
|
42
|
|
|
|
3 726
|
|
|
|
5 358
|
|
|
|
3n 1"7G
|
|
|
|
3 685
|
|
|
|
5 293
|
|
|
|
417
|
|
I"iO
|
|
|
|
43
|
|
|
|
3 So3
|
|
|
|
5 383
|
|
|
|
209 r72
|
|
|
|
3 761
|
|
|
|
5 319
|
|
|
|
315 1°68
|
|
|
|
44
|
|
|
|
3 S~o
|
|
|
|
. 5 409
|
|
|
|
I06 1"72
|
|
|
|
3 837
|
|
|
|
5 344
|
|
|
|
214 1"68
|
|
|
|
45
|
|
|
|
3 957
|
|
|
|
5 435 Y·404 003 1"72
|
|
|
|
3 913
|
|
|
|
5 369
|
|
|
|
II,~ I"jO
|
|
|
|
46
|
|
|
|
4 035
|
|
|
|
5 46o ·1·403 900 I"i2
|
|
|
|
3 989
|
|
|
|
5 395 1·404 011 r6S
|
|
|
|
47 48
|
|
|
|
4 Il2 4 189
|
|
|
|
5 486 5 512
|
|
|
|
797
|
|
694
|
|
|
|
1"72 1·70
|
|
|
|
4"o65 4 I41
|
|
|
|
5 420 1·403 910 r6S
|
|
|
|
5 445
|
|
|
|
809 r68
|
|
|
|
49
|
|
|
|
4 265
|
|
|
|
5 537
|
|
|
|
592
|
|
I"iO
|
|
|
|
4 216
|
|
|
|
5 471
|
|
|
|
7o8 r6S
|
|
|
|
50
|
|
|
|
4 342
|
|
|
|
5 563
|
|
|
|
490
|
|
|
|
4 292
|
|
|
|
5 496
|
|
|
|
6o7
|
|
|
|
(H.) ACCOUNT OF THE BASE LINES,
|
|
their positions, apparatus. used, measurements, resulting lengths and probable errors, together with the abstracts of angles and adjustment of triangles forming the base nets, with description of stations composing the ·same.
|
|
|
|
GENERAL STATISTICS OF THE DASE LINES, ARRANGED IN THE ORDER OF TIME OF
|
|
|
|
MEASUREMENT.
|
|
|
|
No. Name of line.
|
|
|
|
State.
|
|
|
|
Table I.
|
|
Date of n1easure.
|
|
|
|
Chief of party.
|
|
|
|
·A pparatu• used.
|
|
|
|
l The Kent Island Base Md.
|
|
|
|
1844, May and Juue.
|
|
|
|
J. Ferguson
|
|
|
|
The Hassler base apparatu5, 4
|
|
|
|
iron bars of 8-111etre joint.
|
|
|
|
2 The A111erica1I Bot- Ill.
|
|
|
|
1872, Oct. and Sept.
|
|
|
|
C.H. Boyd
|
|
|
|
length, optical contact. The 6-m<:tre contact~slide iron
|
|
|
|
tom Base
|
|
|
|
rods Nos. 1 and 2.
|
|
|
|
3 The Olney Base
|
|
|
|
111.
|
|
|
|
18;9, July to Sept.
|
|
|
|
E. S. Wheeler*
|
|
|
|
The Repsold 4-metre steel and zinc coinbint-d bar, t•ptkal
|
|
|
|
c:01.1ta.c.t.
|
|
|
|
4 The El Paso Base
|
|
|
|
Colo.
|
|
|
|
1879, Ang. and Sept.
|
|
|
|
0. H. Tittmann
|
|
|
|
The 6-metre steel contact-slide rods Nos.3 and 4.
|
|
|
|
s The Yolo Base
|
|
|
|
Cal.
|
|
|
|
1881, Sept., Oct., No\'. · G. Da,~idson
|
|
|
|
Schott's 5-metre contact-slide compensating steel and ziuc
|
|
|
|
bars Nos. 1 aud 2.
|
|
|
|
6 The Holton Base
|
|
|
|
Ind.
|
|
|
|
1891, July, Ang., Sept.
|
|
|
|
A.T.Mosman
|
|
|
|
The 5-metre contact-slide steel
|
|
|
|
rods Nos. 13 and q. and steel
|
|
|
|
tape 111easures, also used in
|
|
|
|
7 The St.Albans Ba~e
|
|
|
|
w.va.
|
|
|
|
189~. October
|
|
|
|
R. s. Woodward
|
|
|
|
part, steel bar No. 17, in ice. ·rwo IOcHnetre steel tapes Nos.
|
|
85 and 88.
|
|
|
|
8 The Salina Base
|
|
|
|
Kans.
|
|
|
|
i8¢, June a!1d July
|
|
|
|
F. D. Granger
|
|
|
|
The 5-metre contact-slide steel
|
|
|
|
rods Nos. 1.~ and 14.
|
|
|
|
9 The Salt Lake Base
|
|
|
|
tTtah
|
|
|
|
1896, Sept. and Oct.
|
|
|
|
W.Eimbeck
|
|
|
|
Eimbeck's s-metre contactslide duplex apparatus. steel
|
|
|
|
and brass rods.
|
|
|
|
IO The Versailles Base
|
|
|
|
Mo.
|
|
|
|
1897, June
|
|
|
|
A. L. Baldwin
|
|
|
|
The 5-metre contact-slide rods
|
|
Nos. 13 and q; and the so-
|
|
|
|
metre steel tape No. 204.
|
|
|
|
*Gen. C. B. Comstock, ti. S. E .. in charge United States I.ake Sul'\•ey.
|
|
|
|
TRANSCONTINENTAL TRIANGULATIO~-PART I-BASE LINES.
|
|
|
|
55
|
|
|
|
2. THE MEASUREMENT OF '.tHE BASE I.INES.
|
|
The measure of the linear extent of the triangulation, or what comes here to the same thing, the width of the country, is made to depend on the measure of 10 base lines located at ·suitable distances and connected with the triangulation by means of base nets. Through these nets, by gradual expansion, the comparatively short length of a base is developed to that of the sides of the principal triangles. The bases were measured with a variety of apparatus and in time range over a period of fifty-three years, the first one having been measured long before the survey across the country was contemplated.
|
|
In what follows we shall give for each base complete, yet brief, information respecting : The geographic position, nature of the ground traversed, its altitude above the sea, description and standardization of the apparatus, observer and method of measure, resulting length with probable error, and other matter pertinent thereto. This is followed by abstracts of the angular measures-at the stations composing the net, by its adjustment and final length of its triangle sides; finally there is given the probable error of the sides of the net which bind it to the main triangulation on both sides of it.
|
|
(a) .Kmt Island Base Lhu:, JJ:lt.11J•land, I811·
|
|
LOCATION, MEASUREMENT, AND I,ENGTH.
|
|
Kent Island, in Queen Anne County, Maryland, on the western shore· of which the base was measured, is situated on the east side of Chesapeake Bay and nearly opposite Annapolis Harbor, Maryland. Originally the base in this locality was intended to serve as a check 011 the length of the sides of the primary triangulation brought south from Fi.re Islaud, New York, and to provide a basis for the triangulation of the Chesapeake Bay, but its situation close to the parallel _of 39° has made it available for the transcontinental triangulation, proposed more than a quarter of a century later. The surface of this' part of the island is slightly undulating, composed mostly of cultivated fields, but in parts swampy and wooded. It is little elevated above the mean sea level. The northern terminal monument was placed near Broad Creek, and its foundation was laid in the sand, one and a half metres below the surface, with a course of rubble masonry. The end point of the base was marked by copper bolts in a stone slab below and an upright stone above ground. /The southern terminus at Prices Creek was similarly marked, and both monuments were finally covered with an earthen mound for farther. protection. When visited in 1888, it was found that the shore of the southern p~r.t of the isfand had been washed away and that the southern monument had disap-_ peared below the waves.
|
|
The length of the base is S.2.--3 kilometres, or nearly 5 ·4 statute miles; its middle point is in latitude 38° 56' about, in longitude 76° :n', and the azimuth of the line from
|
|
the sot1 them end is 194° JS' nearly. The alignment of the base was made by placing a
|
|
theodolite over a point near its middle, and marking out the line by flags. · The ineasurement of the base was intnisted by Superintendent Bache to Assistant
|
|
James Ferguson, aided by Mr. R. D. Cutts, who made a preliminary measure and.drove stakes at every 200 metres of the line.
|
|
The apparatus used was that known as the Hassler Base Apparatus. It is described in the Transactions of the American Philosophical Society (Philadelphia) for the year
|
|
|
|
UNITED STATES COAS'f AND GEODETIC SURVEY.
|
|
|
|
1825, pp. 273-286 (illustrated by Plate III), and had been used for the measure of the
|
|
|
|
Fire Island base by Superintendent Hassler in 183+ It consists of a box in which are
|
|
|
|
placed, in line, 4 rectangular iron bars, each 2 metres long, the joined length being S
|
|
|
|
metres. Over the forward end of the box a microscope was mqunted on a tripod, the
|
|
|
|
No. 3,
|
|
|
|
cross hairs 0f which
|
|
|
|
served again as a fixed
|
|
|
|
point when the rear encl
|
|
|
|
of the box was. later
|
|
|
|
brought under the same
|
|
|
|
fiducial lines of the mi-
|
|
|
|
croscope. The focus of
|
|
|
|
the . fixed microscope
|
|
|
|
was never changed after
|
|
|
|
it had onct:: been placed
|
|
|
|
in position. The level
|
|
|
|
of the combination of
|
|
|
|
bars was indicated by
|
|
|
|
means of a sector at-
|
|
|
|
tached to one of the
|
|
|
|
bars (A) and their tem-
|
|
|
|
perature was indicated
|
|
|
|
by means .of thermome-
|
|
|
|
ters. At distances of
|
|
|
|
1 kilometre two stakes
|
|
|
|
were driven, one on each
|
|
|
|
side of the line, but no •
|
|
|
|
permane1it marks were
|
|
|
|
left; there is, however,
|
|
|
|
a stoneware cone in line
|
|
|
|
1 kilometre from the
|
|
|
|
north end. Transfers
|
|
|
|
of the end of a bar to
|
|
|
|
ground at the close of a
|
|
|
|
day's work were made
|
|
|
|
either by means of a
|
|
|
|
plummet or by means of
|
|
|
|
0
|
|
|
|
10
|
|
|
|
,.K1lome1res
|
|
|
|
••
|
|
|
|
so
|
|
|
|
35
|
|
|
|
St<>tu.te Miles
|
|
|
|
a theodolite. But one measure was m~de, and the time occupied was
|
|
|
|
0
|
|
|
|
10
|
|
|
|
•o
|
|
|
|
between May 3 and June
|
|
|
|
5, r844.
|
|
|
|
The ::?-metre iron bars, known as the Hassler bars A, B, C, D, were made by
|
|
|
|
'l'roughton & Simms about 1813, and were standardized in February and March, 1817,
|
|
|
|
by means of the committee metre, which is of the same cross section (17·5 by 9 milli-
|
|
|
|
·metres) and· the iron Lenoir Metre-all the bars being i't·l>out. Hassler again determined
|
|
|
|
their length in May, 1834, and in March, 1835, with the aid of the Troughton scale.
|
|
|
|
TRANSCONTINENTAL TRIANGUT4ATION-PART I-BASE LINES.
|
|
|
|
57
|
|
|
|
In May, 18+i, and January, 1845, Messrs. J. Saxto1i and W. Wiirdemann and Superin-
|
|
tendent A. D. Bache again cpmpared them by means of a Bessel comparator. The valqes were :
|
|
|
|
In 1817, :E = 7"999 950 6111 at o 0 C.
|
|
|
|
.1834-35,
|
|
|
|
7"999 976 4 m at oo C.
|
|
* 7 ·999 871 6 111 at o 0 C.
|
|
|
|
± .5 5
|
|
|
|
which last value was adopted by the obser\rers and verified by Assistant J. E. Hilgard
|
|
|
|
on July 11, 1854, and was to he used for the Kent Island as well as for the· Massa-
|
|
|
|
clmsetts base measured in the same year: The coefficient of expansion of the bars was
|
|
|
|
determined by Superintendent Hassler in 1817 at Newark,t the value found by him
|
|
|
|
was o·ooo 006 963 534 for the Fahrenheit scale, or o·ooo 012 534 for the centigrade scale. This value has been supposed to 6e rather large, yet it may be corr~ct for these
|
|
|
|
particular bars and has been taken so by all previous investigators.! We shall, how-
|
|
|
|
ever, increase the probable error of the leng"th of the base by the effect of a change in
|
|
|
|
the adopted coefficient of expansion amouhting to its "fi1Tj part, which amount is supposed
|
|
|
|
to cover the whole uncertainty.
|
|
|
|
We find for the length of the base :
|
|
Metres.
|
|
1086 boxes of 8 metres each ................................................ , .......... . 86SS·oooo
|
|
|
|
Defect of each box on 8 .metres, 1086 / o·ooo 128 35 ........................ : ... ·....... . Correction for excess (25°·44 C.) of temperature of bars above o° C. and graduation error of
|
|
thermometers {- o0 · 255 C. ) ....................................................... . Correction for inclination of boxes ................................................... .
|
|
|
|
-0·1394
|
|
+ 2 ·7424
|
|
- I "0007
|
|
|
|
Excess of box at south end, as measured by bar D and scale· ........................... . -2·05o8
|
|
|
|
Reduction to half tide level of bay, for surface elevation and height of box 5·0 m ........ . -0·0069
|
|
|
|
Resul~ing length of base·, ......... ,............................................. 8687 ·5446
|
|
|
|
The probable error of this value can only be estimated, since the base was measured but once. Supposing the combined length of the metres subject to ± 2011, the effect on the base will be± 0·022 metre; an assumed error of ±-du part in the expansion coefficient would produce ± 0·055 metre; again, the effect for imperfect temperature correction for inequality in number of boxes laid with rising and with falling temperature may be taken as ± 0·034 metre, while other minor uncertainties may be omitted.
|
|
Combining the several values for probable error, we get ± o·o6S~netre, equal to TH~TjiJ
|
|
of the length nearly. This may be taken to.represent the measuring error, and to include the probable error due to our practical unit of length, the Committee Metre, taken as
|
|
± Hfl.
|
|
Resulting length of the Kent Island Base 8687 ·5446 metres,
|
|
· ± ·o6So
|
|
and its logarithm 3·938 897 05.
|
|
± 3 40
|
|
|
|
*Coast Sur\"ey Report for 1865, Appendix No. 21, pp. 187, 1SS, and 189, and Coast Survey Rtport for 1866, Supple-
|
|
ment to Appendix No. 8; I,ength of the Kent Island Base, p. 140.
|
|
t Trans. Amer. Phil. Soc., Vol. I, new series. Philadelphia, 1818, pp. 210-22~. t In connection with this it may be worth remarking that the co<:ffident of expansion for the 82-inch Troughton
|
|
brass scale, which was df.terntined by l\Ir. Hassler at the sa111e tin1e and by the sa111e ineans, also '"·as found rather
|
|
large, viz: 0·01>> 010 509 for Fahrenheit's scale, or o·ooo 018 916 for the centigrade scale. On the Qther hand, we have
|
|
Fizeau's determination for onr brass o.ooo OIS 410, yet brasses probably differ e,·en more than different kinds of iron. A
|
|
search was made for the recovery of the fonr Hassler bars, bnt without succtss.
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
ABSTRACT OF RESULTING HORIZONTAL DIRECTIONS OBSERVED· AND ADJUSTED A't STATIONS FORMING THE KENT ISLAND BASE "NET, I844, I846-47-48-49:-50, 1868 AND 1896-97.
|
|
Ji(enf Island So11t11 B11sc, Queen Anne County, Maryland. May 30 to June 4, 1847. ,30-centimetre repeating theodolite, No. 11. E. Blunt, observer.
|
|
|
|
No. of direction.
|
|
|
|
Objects observed.
|
|
|
|
Resulting direc- Corrections Final seconds
|
|
|
|
tions from station from base-net
|
|
|
|
in
|
|
|
|
adjustment.
|
|
|
|
adjustment. triangulation.
|
|
|
|
Marriott
|
|
|
|
0
|
|
|
|
II
|
|
|
|
o oo oo·oo
|
|
|
|
II
|
|
+0·03
|
|
|
|
II
|
|
00·03
|
|
|
|
2
|
|
|
|
Taylor
|
|
|
|
58 53 46 ·24
|
|
|
|
+o·o6
|
|
|
|
46·30
|
|
|
|
J
|
|
|
|
Kent Island North Base
|
|
|
|
111 41 18 ·25
|
|
|
|
·-O ·09
|
|
|
|
18 "16
|
|
|
|
Poplar Island
|
|
|
|
283 38 46 ·74
|
|
|
|
= Probable error of a single observation of a direction (6 D. and 6 R. i ± o'1 ·69.
|
|
|
|
Km! Isla•11f Nort/1 Base·, Queen Anne County, Maryland. May 21 to May 28, 1847. theodolite, No. 11.. E. Blunt, observer.
|
|
|
|
4
|
|
|
|
Kent Island South Base
|
|
|
|
" ~
|
|
0 00 oo·oo
|
|
|
|
+0"·19
|
|
|
|
30-centimetre
|
|
,,
|
|
00·19
|
|
|
|
5
|
|
|
|
Marriott
|
|
|
|
6 Taylor
|
|
|
|
50 05 05 ·36 SS 35 36·91
|
|
|
|
-0·47 -0·12
|
|
|
|
04·89 36·79
|
|
|
|
7
|
|
|
|
Linstid
|
|
|
|
121 02 04 ·33
|
|
|
|
+o ·16
|
|
|
|
04·49
|
|
|
|
S Swan Point
|
|
|
|
181 09 45 ·47
|
|
|
|
-j-o ·24
|
|
|
|
45 "71
|
|
|
|
Probable error of a single observation of a direction ( 6 D. and 6 R. ) = ± o'1 "6S.
|
|
|
|
Swan Poi11t, Kent County, Maryland. October 16 to October 21, 1848.
|
|
,., 1I. E. Blunt, observer. 0
|
|
|
|
34
|
|
|
|
Kent Island North Base
|
|
|
|
o oo oo ·oo
|
|
|
|
30-centimetre theodolite, No.
|
|
|
|
II
|
|
--o ·2.,
|
|
|
|
II
|
|
59 ·n
|
|
|
|
35
|
|
|
|
Linstid
|
|
|
|
56 oS · 57 ·92
|
|
|
|
+o ·52
|
|
|
|
58 ·44
|
|
|
|
36 . Pooles Island
|
|
|
|
169 16 25 ·5 r
|
|
|
|
-o ·29
|
|
|
|
25 ·22
|
|
|
|
= Probable error of a single observation of a direction (6 D. and 6 R.) ± 111·35.
|
|
|
|
Tay/01·, Anne Arundel County, Maryland. June 8 to June 16, 1847. 30-centimetre theodolite, No. II. E. Blunt, observer.
|
|
|
|
IO
|
|
|
|
Kent Island North Base
|
|
|
|
0
|
|
|
|
I/
|
|
|
|
0 ()() oo·oo
|
|
|
|
II
|
|
+0·36
|
|
|
|
II
|
|
00·36
|
|
|
|
II
|
|
|
|
Kent Island South Base
|
|
|
|
38 36 52 ·37
|
|
|
|
-0·23
|
|
|
|
52 ·q
|
|
|
|
12
|
|
|
|
Marriott
|
|
|
|
II9 32 44·32
|
|
|
|
+0;53
|
|
|
|
44·85
|
|
|
|
9
|
|
|
|
Linstid
|
|
|
|
247 12 54·29
|
|
|
|
-o·.66
|
|
|
|
53·63
|
|
|
|
Probable error of a single ol_:iservation of a direction ( 6 D. and 6 R.) = ± 0"·66.
|
|
|
|
Pooks Island, Harford County, Maryland. May 17 to May 27, 1848. 30-centimetre theodolite, No.
|
|
|
|
·
|
|
|
|
I 1. E. Blunt, observer.
|
|
|
|
0
|
|
|
|
II
|
|
|
|
II
|
|
|
|
II
|
|
|
|
31 J Swan Point
|
|
|
|
0 00 00'00
|
|
|
|
+o ·30
|
|
|
|
00·30
|
|
|
|
32
|
|
|
|
Linsticl I
|
|
|
|
36 22 15 ·13
|
|
|
|
+0·17
|
|
|
|
15·30
|
|
|
|
33
|
|
|
|
Finlay
|
|
|
|
II6 o6 54·92
|
|
|
|
-0·47
|
|
|
|
54 ·45
|
|
|
|
Osborne's Ruin
|
|
|
|
170 34 06·56
|
|
|
|
Turkey Point
|
|
|
|
225 05 01 ·56
|
|
|
|
= Probahle error of a single observation of a direction (6 D. and 6 R.) ± 0 11·69.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 59
|
|
|
|
Webb, Anne Arundel. County, .Maryland. July 10 to August 14, 1848. 6o-centimetre theodolite,
|
|
No. 2. A. D. Bache, observer. October 21 to December 2, 1850. 75-centimetre .theodolite, No. 1,
|
|
A. D. Bache, observer. September IS to S·eptember 25, 1868. 75-centimetre theodolite, No. I,
|
|
C. 0. Bot1telle, observer.
|
|
|
|
0
|
|
|
|
0
|
|
|
|
II
|
|
|
|
II
|
|
|
|
26 Linstid
|
|
|
|
0 00 oo·oo
|
|
|
|
-0·02
|
|
|
|
27
|
|
|
|
Marriott
|
|
|
|
76 16 06·19
|
|
|
|
-t-0·25
|
|
|
|
Hill
|
|
|
|
129 26 58·53
|
|
|
|
Soper
|
|
|
|
178 32 04·72
|
|
|
|
Stabler Azimuth Mark
|
|
|
|
r86 55 II ·56 275 40 Ol ·37
|
|
|
|
25
|
|
|
|
Finlay
|
|
|
|
~89 44 43·01
|
|
|
|
-0·23
|
|
|
|
Probable error of a single observation of a direction ( D. and R.) = ± 0 11 ·94.
|
|
|
|
"
|
|
59·98 o6 ·44
|
|
42·78
|
|
|
|
Jlfarrioll, Anne Arundel County, Maryland. November 18 to December 9, 1846. 30-centimetre
|
|
theodolite, No. II. E. Blunt, observer. May 18 to June 18, 1849. 60-ce11timetre theodolite,
|
|
No. 2. A. D. Bache, observer.
|
|
|
|
Hill
|
|
|
|
Soper
|
|
|
|
13
|
|
|
|
Webb
|
|
|
|
Azimuth mark
|
|
|
|
14
|
|
|
|
Linstid
|
|
|
|
15 Taylor
|
|
|
|
16 Kent Island North Base
|
|
|
|
l/
|
|
|
|
Kent Island South Base
|
|
|
|
Poplar Island
|
|
|
|
Blake
|
|
|
|
0
|
|
0 00 32 o6 70 08 82 23 107 33 125 56
|
|
147 53 166 06 206 5S 24S 21
|
|
|
|
Probable error of a single observation of a direction-
|
|
|
|
II
|
|
|
|
II
|
|
|
|
11,
|
|
|
|
oo·oo
|
|
|
|
10·36
|
|
|
|
37 ·17
|
|
|
|
-0·24
|
|
|
|
36.93
|
|
|
|
48·68
|
|
|
|
48·30
|
|
|
|
+0·34
|
|
|
|
48·64
|
|
|
|
32·84
|
|
|
|
-0·20
|
|
|
|
32 ·64
|
|
|
|
I6'8o
|
|
|
|
-0·10
|
|
|
|
16 70
|
|
|
|
54·12
|
|
|
|
+0·19
|
|
|
|
54·31
|
|
|
|
03·32
|
|
|
|
51 ·62
|
|
II
|
|
(6 D. and 6R. )=±0·67 in 1846 • (D. andR.) '==±!"IO in 1849
|
|
|
|
Liustid, Anne Animlel County, Maryland. May 24 to June 26, 1848. 6o-centimetre theodolite,
|
|
No. 2. A. D. Bache, observ.er. January 8 to January 31, 1897. 30-centimetre theodolite, No. 16.
|
|
F. w. Perkins and W. B. Fairfield, observers. Telescope above ground (in 1897) :?7"89 metres.
|
|
|
|
18
|
|
|
|
Finla;v
|
|
|
|
19
|
|
|
|
Pooles Island
|
|
|
|
Clough
|
|
|
|
20. Swan Point
|
|
|
|
Hope
|
|
|
|
21
|
|
|
|
Kent Island.North Base
|
|
|
|
22 Taylor
|
|
|
|
23
|
|
|
|
Marriott
|
|
|
|
24
|
|
|
|
Webb
|
|
|
|
0
|
|
0 00 46 42 69 13 77 .13 I02 07 140 56
|
|
175 43 209 40 275 -58
|
|
|
|
. Probable error of a.single observatio·n of a direction-
|
|
|
|
II
|
|
oo·oo
|
|
|
|
II
|
|
-t-070
|
|
|
|
II
|
|
00 70
|
|
|
|
57 '73
|
|
|
|
-0·1S
|
|
|
|
57·55
|
|
|
|
07·73
|
|
|
|
16'97
|
|
|
|
-0·52
|
|
|
|
r6·45
|
|
|
|
23 "JO
|
|
|
|
37·60
|
|
|
|
-0·26
|
|
|
|
37·34
|
|
|
|
02 ·43
|
|
|
|
·+o 75
|
|
|
|
03·18
|
|
|
|
1 I '28
|
|
|
|
-0·50
|
|
|
|
1078
|
|
|
|
53 ·59
|
|
|
|
+0·02
|
|
|
|
9 53·61 v
|
|
|
|
(D. andR.) =± l'l:? in 1848
|
|
|
|
(6 D. and 6 R.)=±0·73 in 1897
|
|
|
|
60
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
Finlay, Baltimore County, Maryland. · August· 29 to Septemher· 11, 1844. 6o-ce·ntimetre theodolite,
|
|
|
|
No. 2. J. Fergu_son, observer. October 1.5 to December 27 1 1896. 30-centimetre theodolite,
|
|
|
|
No. 16. G. A. Fairfield, observer. Telescope above grou1~d rs metres.
|
|
|
|
· Osborne's Ruin
|
|
|
|
0
|
|
|
|
II
|
|
|
|
,,
|
|
|
|
0 00 oo·oo
|
|
|
|
"
|
|
|
|
Still Pond
|
|
|
|
28
|
|
|
|
Pooles Island
|
|
|
|
Clough
|
|
|
|
29
|
|
|
|
Linstid
|
|
|
|
30
|
|
|
|
Webb
|
|
|
|
I Rosanne
|
|
|
|
30 48
|
|
48 0__3,
|
|
5S ?• JOI 36 127 19 IS9 25
|
|
|
|
Probable error of a single observation of a direction-
|
|
|
|
·tr ·9s
|
|
|
|
34 ·rs
|
|
|
|
+0·4S
|
|
|
|
34·63
|
|
|
|
20·93
|
|
|
|
Ol "26
|
|
|
|
-0-"72
|
|
|
|
00·54
|
|
|
|
37 ·46
|
|
|
|
+0·25
|
|
|
|
37 ·71
|
|
|
|
03 ·26
|
|
II
|
|
( D. and R. ) = ± l ·52 in 1844
|
|
·(6 D. and 6 R.) ±O ·65 i11 1896
|
|
|
|
FIGURE ADJUSTMENT.
|
|
|
|
Obs,'1<•alio11 •'q11alio11s.!'
|
|
|
|
+ ( + + ( O= 1"05 - ( 2) 3) - (4) 6) - ( IO) -f- ( P )
|
|
|
|
2 o=-0·62- (5)+ (6)-(10)+(12)-(15)+(16)
|
|
+ + + 3 o= 0·49- 1.r"l (3)-,- (4) (_5) - ( 16) + (17)
|
|
I
|
|
41 o_=-2·31- (6)+ (7)- (9)+(10)-(21)+(22)
|
|
|
|
5 0=+2·97+ (9)-(12)-(14)+(15)-(22)+(23)
|
|
+ ( 6 0 = - l '37 - (I 3 ) + ( J4) - ( 23 ) + ( 24) - ( 26) 27 ) .
|
|
7 o ~ - rS7 + ( l 8) - ( 24) - ( 2S) + (26) - ( 29) + (30) s o=+n3-(18J+119)--(28J+l29)-<32)+(33)
|
|
+ + + + 9 o= !'26- (19) (.::o)- (31 J {_;2) - (35) U6)
|
|
|
|
IO o=-ro7- (iJ+(8)-(::io)+(21)-{34)+(35)
|
|
I + JI o= :- 39 + I7"1(4) - 1r6(5) 0·5(6) + 26·4( 10) -· 29·8( II)+ 3·4( 1:i) + 24·9( 15) -63·9( 16)
|
|
|
|
+39·0(17)
|
|
|
|
12 cj =+JI+ 26·4(s) - 59·5(6) + 3.~ 'I( 7) -t- 63·4( 14) -- u5·6( IS)+ 52·2~ r6) + ,N'3(21) - 61"6( 22)
|
|
|
|
+31·3(z3)
|
|
+ + 131 o= - 28 + 7 ·3(5) - 19"4( 7) ·+-12·1(8) 27'5( 13)"-:- 52·3( q) 24·8( 16) +·7'6{ 25) - 12·7( z6 i
|
|
|
|
+ 5•1(27) + 15·5(28) -59·2(29) + 43·7(30) + 28·6(31) -.32·4(32) +3"8(33) + 14"2(34)
|
|
|
|
- s·2(3s)--9·0(36) .
|
|
|
|
. .
|
|
|
|
Lorrdak t-q11atio11s.
|
|
|
|
Corn~c-I
|
|
'ic11JS..
|
|
|
|
c,
|
|
|
|
c.
|
|
|
|
C3
|
|
|
|
C4
|
|
|
|
Cs
|
|
|
|
c6
|
|
|
|
c 7
|
|
|
|
Cs
|
|
|
|
c 9
|
|
|
|
C,o
|
|
|
|
Cu
|
|
|
|
C,.
|
|
|
|
C,3
|
|
|
|
( l)
|
|
|
|
-:-:I
|
|
|
|
( 2)
|
|
|
|
-I'
|
|
|
|
(3) +1
|
|
|
|
+r
|
|
|
|
(4) -I
|
|
|
|
-1
|
|
|
|
+17 'l
|
|
|
|
(5)
|
|
|
|
-I +r
|
|
|
|
I (6) -t-r -f-I
|
|
{ 7)
|
|
|
|
-I
|
|
+r
|
|
|
|
-17'6 + 26 ·-1- + i '3
|
|
|
|
+O'S - 59·5
|
|
|
|
-I
|
|
|
|
+ 33 ·1 -r9·4
|
|
|
|
I (8)
|
|
(9)
|
|
|
|
- I +r
|
|
|
|
+1
|
|
|
|
+12 'I
|
|
|
|
* Nun\ber of eqnati.·-11u; 1·etating h-, -;.\nu!:- of angles ro. ancl to ratio of sicles ,;. total number 1;\; the ~idt: eQimtions
|
|
|
|
were established with 7 places of decimals in the logarithms and the differenceg for i'' are given i1~ units of t]mt place.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 61
|
|
|
|
FIGURE ADJUSTMJ;:NT-continued.
|
|
|
|
ll>rrelalt! e·q11atitms--Conti11ued.
|
|
|
|
Corrections.
|
|
|
|
C,
|
|
|
|
c.
|
|
|
|
C3
|
|
|
|
C4. Cs
|
|
|
|
c.
|
|
|
|
C1
|
|
|
|
Cs
|
|
|
|
C9
|
|
|
|
C,o
|
|
|
|
c ..
|
|
|
|
c,•. C,3
|
|
|
|
(IO) - I
|
|
(II) +r
|
|
:1.:i)
|
|
(13) ( 14) (rs) . (r6) ( 17) ( 18) ( 19) (w) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32)
|
|
i33l (34).
|
|
(35) (36)
|
|
|
|
-I
|
|
+r
|
|
-I
|
|
+1 -I +r
|
|
|
|
+1 -r
|
|
-I
|
|
-1 +1 +I
|
|
-r +1 -I
|
|
+1 -r +1
|
|
-I
|
|
+1
|
|
|
|
-j ·I --I +r
|
|
--r -r +1
|
|
-I
|
|
·-! +r -j I
|
|
-r
|
|
+r
|
|
.....
|
|
|
|
+i6·4 -29·8 + 3·4
|
|
+24"9 -63·9 +39"0
|
|
|
|
+ 63 ·4
|
|
-rrs ·6
|
|
+ 52 ·2
|
|
|
|
+27"5 -52·3
|
|
+24·8
|
|
|
|
-I
|
|
+1 -I +r
|
|
|
|
+ 30·3
|
|
- 61 •6
|
|
+ 31 ·3
|
|
|
|
-I
|
|
+1
|
|
-1 - I -j-1 +1
|
|
|
|
+ 7·6 -1.2 "7 + 5·1 +rs ·5 -95·2 +43 ·7 +28"6 -32 ·4 + 3·8 +14·2 - 5 ·2 - 9·0
|
|
|
|
Normal cq11ali~11s.
|
|
|
|
C1 C2 Cs C4 c. c. C7 c~ C9 C10
|
|
|
|
Cu
|
|
|
|
C,2
|
|
|
|
C13
|
|
|
|
o=+ 1"05 +6 -+- 2 +2 _..,
|
|
|
|
-72·8 .-59·5
|
|
|
|
- 0·62 + 0·49
|
|
|
|
+6 -2 -2 -2 +6
|
|
|
|
- 93·7
|
|
+68 ·2
|
|
|
|
+81 ·9 -25·8
|
|
|
|
+ 17 ·5 -17 ·s
|
|
|
|
- 2·31'
|
|
+ 2·97 I
|
|
|
|
+6 -2 +6 -2
|
|
|
|
-2 +25"9 + 21 ·s
|
|
|
|
+ 0·7 -86·1
|
|
|
|
- 19·4 -t-52·3
|
|
|
|
- 1·37
|
|
|
|
+6 -2
|
|
|
|
+32"1
|
|
|
|
-62·0
|
|
|
|
- .1·87
|
|
|
|
+6 -2
|
|
|
|
+s·2·6
|
|
|
|
+ 2 "73
|
|
+ I "26
|
|
- I "07
|
|
-39
|
|
|
|
+6 -2 +6 -2 +6.
|
|
+.S.423 ·2
|
|
|
|
- 2·8
|
|
6 ioS ·4
|
|
|
|
-38·5 -64·8 + 12 "I l 713 "2
|
|
|
|
+31 -28
|
|
|
|
+31 132·9 2 470·7
|
|
+ 12 774 ·1
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
Rt?stelti11g v.il11es of corrdait's and <!f cori"<Ylio11s to a11gielar dirt?dio11s.
|
|
|
|
c i= -0 ·059 67
|
|
C2 +0·305 45
|
|
C3 -0·031 00
|
|
.c.,, +0·45·2 So
|
|
C- -0·204. 00
|
|
c6 +0·249 54
|
|
c 7 +o ·232 93 c 8 -0·470 07
|
|
C9 -0·285 20
|
|
CIO +0·232 83
|
|
c1; -\-o ·005 79
|
|
Cu -o·oor 47
|
|
Cia + ? ·oo::i 367
|
|
|
|
Corrections.
|
|
|
|
II
|
|
|
|
II
|
|
|
|
(1)=+0·031 0
|
|
|
|
(13) = - 0 ·239 4
|
|
|
|
(2)=+0·059 7 (3)=-0·090 7 {4)=+0·189 7
|
|
|
|
(14)=+0·341 I
|
|
(15) = -0·195 4
|
|
(16)=-o·ror 2
|
|
|
|
(5)=-0·471 6
|
|
|
|
(17)=+0·194 8
|
|
|
|
(6)=-0·116 7
|
|
|
|
(18)=+0·703 0
|
|
|
|
(7)=+0·16-1 2
|
|
|
|
(19)=--0·184 9
|
|
|
|
(8)=+0·'237 3
|
|
|
|
(20)=-0·518 0
|
|
|
|
(9)=·-0·656 8
|
|
|
|
(21)=-0·2645
|
|
|
|
(ro)=c:-t-0·359 9
|
|
|
|
(22)=+0747 4
|
|
|
|
{11)=-0·232 2
|
|
|
|
( 23) = - 0 ·499 6
|
|
|
|
.(12)=+0·529 I
|
|
|
|
(24)=+0·0166
|
|
|
|
Checks: Sum of+ corrections 55·35 and .:5'P<'v = + 4·867
|
|
Sum of- corrections 55·32 -.:5'wC= + 4·872
|
|
|
|
II
|
|
( 25) = - 0 ·230 I (25)=-0·021 3 (27)=+0·251 4 (28)=+0·475 8 (29)=-0·724 7 (30) = + 0 ·249 0 (31) = +0·295 7 (32)=+0·173 0 (33) =-o ·468 7 (;'>4)= -0·227 6 (35)=+0·516 I (36)=-0·288 5
|
|
|
|
v v . Mean error of an observed ·dirt?ction (of unit weight) m1= /[Pr"<'] = 11
|
|
|
|
/ 4 ·S7o = ± 0 11 061
|
|
13
|
|
|
|
11 =number of conditions.
|
|
|
|
Meai! error of an a11glt: 111>= m1 ,./2- ~ ± 0 11 ·87 and probable error of the same ± 0 11• 59.
|
|
|
|
where
|
|
|
|
TRIANGLES OF THE KENT ISLAND BASE NET, MARYLAND, 1$44 TO 1897.
|
|
|
|
No. Stations.
|
|
|
|
Observed angles.
|
|
|
|
{ T•ylo• 1 ~ent I. ~· Base ·
|
|
J;,.eut I. ~- Base
|
|
|
|
0
|
|
38 36 88 35 52 47
|
|
|
|
II
|
|
52·37 36·91 32·01
|
|
|
|
Spher- SJ?herC?rrec- ical 1cal
|
|
|
|
tlons. angles. excess.
|
|
|
|
II
|
|
|
|
II ,,
|
|
|
|
-0·59 51 ·78 o·os
|
|
|
|
·-0·31 36·60 0·08
|
|
|
|
·-() ·15 31·86 o·oS
|
|
|
|
Logs.
|
|
3•938 897 I 4 ·143 529 I 4·044 816 9
|
|
|
|
{ M•rriott 2 Tavlor ·
|
|
Kent I. N. Base
|
|
|
|
01 ·29 21 56 43·96 119 32 44·32 38 :,o 31 ·55
|
|
|
|
+0·09 +0·17 +o·:,6
|
|
|
|
44·05 44·49 31·91
|
|
|
|
0·24 0·15 0 ·15 0 ·15
|
|
|
|
4·044 816 9 4 "4II 76_5 6 4 ·266 498 4
|
|
|
|
r Marriott
|
|
l3 Taylor Kent I. S. Base !Marriott 4 Kent I. N. Base
|
|
Kent I. S. Base
|
|
|
|
59 ·83 40 IO 21 ·28 So 55 51 ·95 58· 53 46·24
|
|
59·47 18 13 37·32 50 05 05·36 III 41 18 ·25
|
|
|
|
+0·39 +076 +0·03
|
|
|
|
:!1 ·67 52 "71 46·27
|
|
|
|
0·45 0·21
|
|
0·22
|
|
0·22
|
|
|
|
+0·29 -0·66 -0·12
|
|
|
|
37·61 04 70 18 ·13
|
|
|
|
0·65 0·14 0 ·15 0 ·15
|
|
|
|
4 °143 529 I 4·328 444 0 4·266 498 5
|
|
3 ·938 897 I 4·328 444 I . 4 ·411 765 8
|
|
|
|
{ Lln,tid , 5 · Kent). N. Base
|
|
Taylor
|
|
|
|
00·93 34 46 24·83 32 26 27·42 1!2 47 05 "71
|
|
|
|
+ 1 ·01 +0·28 +I 002
|
|
|
|
25·84 27·70 06 "73
|
|
|
|
0.44 0·09 0·09 0·09
|
|
|
|
4·044 816 9 4·018 198 2 4·253 398 I
|
|
|
|
57 •96
|
|
|
|
o"'n
|
|
|
|
Distances in metres.
|
|
8 687·545 13 916·47 II 0'37 ·07
|
|
II 087·07 25 &08 °67 18 471 ·34
|
|
13 916 ·47 21 303 °16 IS 471 ·34
|
|
8 687·545 21 303 ·16 25 8o8 "68
|
|
II o87 ·07. IO 427 °9.~ 17 922 •48
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 63
|
|
|
|
TRIANGLES OF THE KENT ISLAND BASE NET, NARYLAND, IS.:14 TO 1S97-continued.
|
|
|
|
No. Stations.
|
|
|
|
Observed angles.
|
|
|
|
r Linstid
|
|
6 ~ Taylor
|
|
l Marriott
|
|
|
|
0
|
|
|
|
/I
|
|
|
|
33 57 oS ·85
|
|
|
|
127 40 09·97
|
|
|
|
IS 22 44·54
|
|
|
|
ILinstid
|
|
7 Kent. I. N. Base Marriott
|
|
|
|
03·36 (?S 4.3 33 :68 70 56 58·97 40. 19 28 ·50
|
|
|
|
IWebb
|
|
S Linstid Marriott
|
|
|
|
01 ·15 76 16 o6 ·r9 66 18 42 ·31 37 25 II "13
|
|
|
|
·1 Finlay
|
|
9 Linstid Webb
|
|
|
|
59·63 25 43 36·20 84 01 06 ·41 70 15 16·99
|
|
|
|
.Pooles Island IlIO J,inslid
|
|
Finlay
|
|
|
|
59·60 79 44 39 "79 . 46 42 57 ·73 53 32 27 "II
|
|
|
|
ISwan Point
|
|
II Kent I. N. Base Linstid
|
|
|
|
04·63
|
|
s6 oS 57·92
|
|
60 07 41 ·r4
|
|
63 43 20 ·63
|
|
|
|
ISwan Point
|
|
12 Linstid Pooles Island
|
|
|
|
59·69 113 07 27 ·59 30 30 19 ·24 36 22 IS ·13
|
|
|
|
C <;>rr~c-
|
|
|
|
Spherical
|
|
|
|
SJ?herteal
|
|
|
|
hons. angles. excess.
|
|
|
|
II
|
|
|
|
II
|
|
|
|
II
|
|
|
|
- I "25 07 ·6o 0 "13
|
|
|
|
- 1 ·18 oS 79 o ·13
|
|
|
|
- o ·54 44 ·oo o ·13
|
|
|
|
- 0 ·24 +0·64 -0·44
|
|
|
|
33 ·44 59·61 28·06
|
|
|
|
0·39 0 ·37 0·37 0·37
|
|
|
|
+0·27 +0·52 +0·58
|
|
|
|
06·46 42·83 11"7I
|
|
|
|
I "II
|
|
0·33, 0·33 0·34
|
|
|
|
I "00
|
|
+0·97 37·17 0·49 + 0 ·69 07 "IO 0 "49 -:ro·2r 17·20 0·49
|
|
|
|
- 0 "64 - o ·S9
|
|
--'I "20
|
|
|
|
39 "I 5 56 ·S4 25 "91
|
|
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|
T 0 47 0 •64 0 ·63 0 ·63
|
|
|
|
+ 0 ·74
|
|
+0·07 +0·26
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|
58 •66 41 "2I 20·89
|
|
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|
I ·go 0 ·25 0"25 0·26
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|
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|
0 76 - o ·Sr 26 ·78 o ·23 - o "33" rS ·91 o ·23 -0·12 IS ·01 0·24
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|
Logs.
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|
Distances in metres.
|
|
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|
4·266 498 5
|
|
4·417 956 2 4·01~ 198 2
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18 47I "34 26 179 :19 TO 427·93
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4 ·4u 765 7 4·417 956 2 4 ·253 3g8 2
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25 Sos ·67 26 179 ·19 17 922·48
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4·417 956 2 4·392 324 7 4 ·214 204 0
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26 179 ·19 24 67S·S4 I6 375·86
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4·214 204 0 4 "5.74 26r 9 4·550 316 3
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I6 375·86 37 519·92 35 507·19
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4·550 316 3 4 ·419 418 8 4·462 716 4
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35 507 ·r9 26 267·50 29 021 ·27
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4·253 398 2 4 •272 151 I 4·286 689 I
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17 922·48 18 713·33 19 350·36
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4 ·462 716 4 4·204 626 3 4·272 151 2
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29 021 ·27 16 018 ·66 18 713·34
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070
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PROBABLE ERRORS.
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|
Dclt'r111i11atio11 of Iii<' probable errors <?f llit• le11gtli of ll1e sides common to botli l11e nt't and tl1e 11dj11ce11t dzai11s of tri1111g11/atio11.
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For the side Finlay to Linstid, as adjusted, we make use of the expression-
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Finlay to Linstld sin (3 -- 1) sin (7 - 5) sin (14 - 13) sin (26 - :25) Kent Id. Base sin (17 - 16) sin (23 - 21) sin (27 - 26) sin (30 - 29)
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UNITED STATES COAST AND GEODETIC SURVE'<'.
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hence the function-
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F= log sin (3 - l) +log sin (7 - 5) +log sin (14 - 13) +log sin (26'.- 25) - log sin ( 17 - 16) - log sin (23 -21) - log sin (27 .- 26) - log sin ( 30 - 29)"
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Establishing and solving the transfer equations, we find the reciprocal of weight
|
|
~ = 27·23, also the mean error lllF and the probable error rF, both ~xpressed in units of
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|
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the sixth place of decimals in their logs., viz: ± 3·18 and± 2·15 respectively: hence
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|
|
log. distance Finlay to Linstid 4·550 316 3 and the distance 35 507·19 nietres. The
|
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|
±21
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|
±0"18
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|
probable error is about TH\n;u part of the length.
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|
|
|
'fo this must be added the proportional error depending upon that of the base
|
|
|
|
measure, or ± 0"068 X ~ 's'i 6<8;077 = ± 0·278 .metre, hence-
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|
|
Probable error of length of side Finlay to Linstid ../(0"18)2+ (0·278)2 = ±0·33
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|
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|
metre. For the side Webb to Marriott, we use the expression-
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|
|
Webb to Marriott Kent Island Base sin (27 - 26) sin (23 - 21) sin (17 - 16) F= log sin (24 - 23) +log sin (7 - 5) +log sin (3 - 1·) - log sin (27 - 26) - log
|
|
sin (23 - 21·) - log sin (17 - 16)
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|
|
|
Establishing and solving the transfer equations-
|
|
Vle get~= 1]"91, also mF= ± 2·53 and rF= ± 1·74, hence log. distance \Vebb to
|
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|
|
Marriott 4·392 324 7, and distance= 24 678·84 metres. The probable error is about
|
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±I 7
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|
±0"10
|
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yn1ollli part; adding to this the proportional error arising from the base meast!re or
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|
0·068 X -2:_4;_668-77-8 = ± o· 193 metre, we have
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|
|
Probable error of length of side Webb to Marriott J(o"ro) 2 + (_0·193)2 = ±0·22
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metre.
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|
DESCRIPTION OF STATIONS FORMING THE KEN~ ISLAND BASE NET, l\IAR\"LAND.
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}fr11t lsla11d 1Vorll1 Bast', Queen Anne County: established in 1844 by James Ferguson.
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The island i"s situated on the east side of Chesapeake Bay nearly opposite Annapolis
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Harbor. The station is located on _the south side of Broad Creek,_ near its mouth, on
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the western shore of the island. The end of the base line was carefully marked, both
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by underground and surface monuments. It is reported by persons living in the vicinity
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in r8g6 that the ground at this encl of the base has been washed away.
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· I<cnt ls.land South Bas<', Queen, Anne County; established in 1844 by James Ferguson.
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|
The station was situated near the extreme encl of the point of land between Prices Creek
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and Chesapeake Bay, and was.marked in a similar manner to North Base. A careful
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|
|
search for this point in 1888 proved that the ground h;:id been washed into the bay years
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before.
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·
|
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TRANSCONTINENTAL TRIANGULATION"'"-PART I-BASE LINES. 65
|
|
Ta_ylor, Anne Arundel Count~·; established in 1844 by James Ferguson. The station is situated on the west sicle.of Chesapeake Bay, on Greenburg Point, bet.ween Mill.Creek and the Severn }liver. The geodetic point is on the most prominent spot on a hill, 91 feet above the level of the bay, belonging to Capt. Lemuel Taylor. It is about onefourth mile frnm his house, on the north side of the road leading to the Severn Ferry. Its position was marked by three stakes, each 40 feet distant, one in the direction of '·Marriott,'' another in the line to '· Linsticl,'' and the other one on that line extended southwardly. It is also 226 feet from a small chestnut tree toward the line to " Marriott." This point was searched for in 1859 and iii 1888, but no trace of it could be found.
|
|
Swa11 Point, Kent County; est!lblished in 1842 by James Ferguson. This station was originally situated on a point of land on the north side of the mouth of Chester River, on the eastern shore of Chesapeake Bay. A resurvey of. this shore in 1896 shows that the site of the original station is some distance out in the bay.
|
|
11/arriott, Anne Arundel County; established in 1844 by James Ferguson. This station is situated about :?O miles east of \Vashington City, 6% miles southwest of South River, and about 9};j'. miles southwest of Annapolis. The geodetic point is on the property of B. Marriott, about 100 yards east of the road leadjng from Annapolis to St. Marys. It is 99 feet from the main post of an old \vindmill and 34 feet I I inches from a small hut on the south side of the hill. Three stakes were driven into the ground, each 30 feet distant, one in the direction of ''Taylor'' and the other t\VO at right angles to that line.
|
|
(No mention is made in the original description of either surface or underground marks, but I presume an earthenware cone was buried there, as seen's to have been the custom at that time.-G. A. F.,)
|
|
f.Pcbb, Anne Arundel County; established in 1846 by A. D. Bache. This station is situated about I 2 miles northwest of Annapolis and about 2}·~ miles, by road, east of Odenton, the junction of the Baltimore and Potomac Railroad and the Annapolis branch of the Baltimore and Ohio Railroad. The land now ( 1896) belongs to James Woodward, president of the Hanover National Bank, New York City. The geodetic point is on a small hill covered with a thick growth of young trees about 45 feet high, and is marked as follows: The subsurface mark is the usual earthenware cone, the top I ·7 feet below the surface, and over this a small granite block, 7 inches square and 5 inches thick, the top l ·1 feet below the surface of the ground. The surface mark is a rough block of granite l ·2 feet long with a 4-inch square dressed on top and two shallow cross· lines marking the center. As reference marks 3 granite posts-each 2 feet and 2 inches long and 5 inches square at the top, with diagonal ljnes cut on them-were set 5 feet distant from the geodetic point; one clue north, one clue south, and one due east.
|
|
. Lin.slid, Anne Arundel County; established in 1S44 by James Ferguson. 'fhis station is situated on the west side of Chesapeake Bay, on what is known as Eagle IIill, near the head of Broad Creek on the north shore of Magothy River. It is about one-half mile in a northerly di;rection from the old Linstid ~louse and just east of the road which passes over the west side of the.hill. The station was re-marked, in January, 1897, as follows: The underground mark is·an earthenware cone. 15 l.nches high, upper diameter 6·5 in~hes and lower diameter 12·5 inches: the center marking the station.
|
|
I8732-No. 4--5
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|
66
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
The top is 26 inches below the surface. About 2 feet north of the center and 9 inches below the surface a granite block (6 by T by 18 inches, with one end dressed to 5 inches square and diagonal cross lines on it), was laid horizontally, the dressed end toward the center. The surface mark is a rough granite block 1S inches long, the head dressed to 5 inches square with a hole one-half iiich in diameter a'ncl three-eighths inch deep in the center; the top being even with the surface of the ground. The reference marks are triangular blazes cut in 2 chestnut trees, with sixtypenny nails driven in the center. One tree is::?".~ feet in diameter, bearing north 76°'5 east magnetic, and distant +s·87 feet, and the other 1·7 feet in diameter, bearing south 2°·7 east magnetic, and distant IJ"3I feet from the station.
|
|
Fhzlcu'. Baltimore County; established in 18++by James Ferguson. This station is situated on Cub Hill, about 9 miles from Baltimore on the old Harford road and about 5 miles east of T<:>wson. It is located on the old Finlay farm-now (1896) the property of Mr. Theodore Fastie-about 300 feet east of the old Harford road and five-eighths of a mile west of the Harford turnpike. The geodetic point was re-marked in 1896 as follows: A glazed drain tile 4 inches in diameter and 30 inches long, filled with cement and gravel, was sunk in the ground so that the upper encl was 3·feet below the surface. It was set in cement and gravel and a sixtypenny nail at the center of the tile marks the station. The surface mark is a chestnut post, the top being even with the surface of the ground and having a fortypenny nail in the center.
|
|
The northeast corner of an olcl.log house-now used as a blacksmith shop-distant 253·71 feet, bears north 47° 06' west (true); a large cherry tree, distant 126·85 feet, bears south 22° 46' east (true), and the east gable of the stone barn on the Fastie place bears north 9° 27' east (true) from the geodetic point. ·
|
|
Proia Island, Harford County; established in 1844 by James Ferguson. Pooles Island is in Chesapeake Bay, near its. head, about opposite the mouth of Gunpowder River. The geodetic point is located near the south end of the upper half of the island, about 450 feet in a northwesterly direction from the large dwelling house of Mr. John Masheter, present (1896.l owner of the island.
|
|
A careful search was made for this point in 1896, but as all surface and reference marks, except one, had been destroyed many years before, the miderground marks could not be found.
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|
|
( b) •..J mcrican Bollom Base Linc, J//i11ois, IS72.
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|
|
LOCATION, MEASUREMENT, AND LENGTH.
|
|
This base is located in St. Clair and Madison counties, Illinois, in the bottom lands of the Mississippi River, on the eastern or Illinois side of it, and ·nearly opposite· ·st. Louis, Missouri, and about 16 kilometres ( 10 statute miles J distant from it. It served, in the first instance, for a local survey about St. Louis. The t\:vo encl points are upon spurs of bluffs about 15 metres (say 50 feet) or more elevated above the general level of the bottom lands. These elevations were desir;lble in order to have a clear line of sight over the forests that fringe the low lakes, ponds, and swamps which occupy the middle portion of the lowlands. The middle point of the base is in latitude 38° 3S'·2 and in longitude 90° 02':0, nearly; the azimuth of the lower or southern point, as seen from the northern end, is 24° 40': the total length is 7'27 kilometres, or 4·52 statute
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART !-_ASE LINES. 67
|
|
miles. The line lies for more than nine-tenths of its length over·wheat and corn "lands, crosses 3 main roads, 2 railroads, and S bridges over creeks and dry nms. The latter structures were of a simple 'kind, and designed only to support the measuring bars. The measurement was made with two 6-metre contact-slide rods, known as Nos. l and 2. A description of the apparatus, embodying the principle and construction of Colonel Mudge's apparatus, and as modified and improved, will be found in Appendix No. 17, Coast and Geodetic Survey Report for lSSo, pp. 341-345. Only one measure was made, and the work was in charge of Assistant C. H. Boyd, aided by Assistant Van Orden and Mr. Featherson, civil engineer; it occupied th~ time between October 30 and November I 1, lSp. A line of spirit leveis was carried from the so-called City Directrix at St. Louis to the Lower Base Monument. The St. Louis bench mark is counectecl with the Gulf and l\tlantic levels.
|
|
No. 4.,
|
|
SugctrLoar Neou.nd
|
|
lTpperBase
|
|
1
|
|
|
|
Dru!i"'"
|
|
|
|
•
|
|
|
|
0
|
|
|
|
0
|
|
|
|
Statu.te M-il"s
|
|
|
|
JO
|
|
|
|
Kilom.etres
|
|
|
|
10
|
|
|
|
·~
|
|
|
|
zo
|
|
|
|
••
|
|
|
|
io
|
|
|
|
~b
|
|
|
|
30
|
|
|
|
••
|
|
|
|
The Upper Base or northern terminus is marked by a limestone monument with marks above and below the ground; that on the monument is a cross cut in a copper· bolt, while under the center and about l ·2 metres (4 feet) below ground is an earthenware pyramid. After these terminals had been built for about a month, the line was staked out at distances of 120 metres; during the measurement every twentieth bar was plumbed clown and secured by a stake and copper tack; the bars were protected by a portable tent; their inclination was had from sector readings, which also gave the profile. of the whole line. A thermometer was attached to each bar and recorded.
|
|
The 6-metre contact-slide rods, Nos. I and 2, were made at the Survey office in August, 1867. The last determination of their length before the measure of the Aiuerican Bottom Base was in April and August, 1870, and was made by comparisons with the 6-metre standard bar No. 2. The length of this last bar, which dates back to
|
|
|
|
68
|
|
|
|
UNITED STATES COAST _AN.D G~9.PE_TIC SURVEY.-
|
|
|
|
February, 1855, was determined in April, rS6o. by Assistant J. E. Hilgard, with the
|
|
|
|
result-
|
|
|
|
s. = S ·999 982 3 metres at o0 C.
|
|
± IO
|
|
|
|
Its coefficient of expansion was not determined until March, 1897 (see Assistant A. Braid's report of March 27, 1897.l; it was found equal to o·ooo or r 25 for tbe centigrade
|
|
s. scale. The comparisons of "with rods Nos. 1 and 2 were made by means of a Repsold
|
|
lever comparator, of which r turn= 316·75 microns and I division= 3·16Sp. The comparisons of April 29, 1870, give-
|
|
|
|
+ 0
|
|
|
|
rl
|
|
|
|
Ill .
|
|
|
|
S, ·-No. r at 6o ·3 F. = 33 ·50 or No. l = 6 ·001 149 5 at 15 ·72 C.
|
|
|
|
S0 -No. 2at60·1 F.=-;:.5·17 or No. 2 = 6 ·-:ioo 924 6 at 15 ·61 C.
|
|
|
|
The.comparisons of August ;)o, 1870, give-:-
|
|
|
|
d
|
|
|
|
· m
|
|
|
|
o
|
|
|
|
S0 -No. lat73·07F.=+31·40 or No.r=6·oor 622 lat22·82C.
|
|
|
|
S.- No. 2 at 72 ·90 F. = - 35 ·91 or No. 2 =6·001 402 lat 22 ·72 C.
|
|
|
|
Hence we have-
|
|
|
|
Length of rod No. r at 19 ·27 C.
|
|
Length of rod No. 2 at 19 ·16 C.
|
|
|
|
Mean,
|
|
|
|
19 ·215
|
|
|
|
6 ·001 385 8 111. 6 "001 163 4 Ill.
|
|
6·001 274 6
|
|
|
|
In the absence of other determinations for the coefficient of expansion of the rods Nos. l and 2 we deduce from the above comparison for-
|
|
|
|
No.1a=11·roµ} N0.2 . II"I9/1.
|
|
|
|
for
|
|
|
|
the
|
|
|
|
C.
|
|
|
|
scale.
|
|
|
|
For the elevation of the base above the mean sea level we have from the unadjusted (not yet completed) lines of spirit levels the "height of the St. Louis City Directrix,
|
|
transferred to the bridge across the Mississippi I 25 ·s ±a·3 metres; also by spirit level-
|
|
ing in rSS2 by Assistant A. Braid, top of monument (copper bolt) at Upper Base above
|
|
the City Directrix 32 ·79 metres: hence the elevation of Upper Base is 158 '6 metres: also by spirit leveling in November, 1Sr1, by \V. Bauer, top of monument at Lower Base above the City Directrix 2.r ·67 metres, and elevation of Lower Base 147"5 metres. The difference in height of the base ends r r ·r metres is verified by the sector readings during the base measure. \.Vhence we gc:::t the average elevation of the base a"bove hal.f tide level of the ocean 132 · l metres, to which is to be added 1·r metres for height of apparatus above ground. The total elevation is therefore 133 ·2 metres; log radius of curvature 6"So3 S.
|
|
\.Vi th the-above data the length of the American Bottom Base comes out as follows:
|
|
|
|
Lengtl! of l 210 mean rods Nos. l and 2 at an average temperature of 5$0 ·69 F. or q 0 ·828 C.
|
|
Length of rod No. 1 at 15°·0 C Excess of Lower Hase mark over the last bar laid Correction for inclination "Reduction to sea level
|
|
Resulting length 6f base
|
|
|
|
.11/d11·.s.
|
|
+7 261 ·187 3 6·001 7
|
|
-!- o·S56 9
|
|
I ·010 r
|
|
0 '152 l
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 69
|
|
|
|
As the base was measured but once, the· accuracy of the result can only be roughly
|
|
|
|
estimated. 'fo the mere comparing error ( ± I 'OJI) of S we add ± 6µ-that is,_ I micron 0
|
|
for each metre.,--hence probable 'error for .base or 1 :2 11 bars, ± 7' 4 millimetres, 'rhe
|
|
|
|
temperature of th~ rods may be uncertain by± o0 ·2 C, considering that there was but
|
|
|
|
one thermometer· attached to a rod: the effect of this upon the letigth of the base is
|
|
|
|
± I6'2 .millimetr~s. · . A probable error of o· 5 metre in the adopted elevation of th& base
|
|
|
|
would produce ±.0'6 millimetre. 'faking the probable error of a single measure of a
|
|
|
|
kilometre to be± I '2 millimetres (Salina Base), that of the base becomes± s·7 milli-
|
|
|
|
metres. Combining these fou;r · probable errors we get± 19 ·9 millimetres or 11 n 1;Hio of the length. 'fhis may be taken to represent the measuring error.; combining it with
|
|
|
|
the probable error due to our practical unit of.length, the Committee Metre, taken as±
|
|
|
|
%.Jl, we get J<.19·9)'+ (5·4)0 == ± :20·6 millimetres or about 1!n\ruo part of the length.
|
|
|
|
Final result for length of base 7 266"883 7 metres,
|
|
|
|
± 20 6
|
|
|
|
and logarithm of its length
|
|
|
|
3·S61 348 21
|
|
|
|
± I 23
|
|
|
|
ABSTRACT OF RESULTING HORIZONTAL DIRECTIONS, OBSERVED AND ADJUSTED AT THE STATIONS
|
|
FORMING THE AMERICAN BOTTOM BASE NET, 1871-72-73 AND 188o.
|
|
A111<·ric.w Bottom Low,'r Base, St. Clair County, Illinois. November 12 to No\·ember 13, 1872. 25-centimetre theodolite, No. 92. C. H. Van Orden, observer. May 24 to May 28, 1873. 2Sccenti· metre theodolite, No. loo. C. H. Boyd, observer.
|
|
|
|
No.of direction.
|
|
|
|
Objects ohseI"Ved.
|
|
|
|
Insane Asylum
|
|
|
|
Resulting directions from station
|
|
adjustment.
|
|
|
|
0
|
|
|
|
/I
|
|
|
|
o oo oo ·oo
|
|
|
|
Corrections ·from base-11et
|
|
adjustment.
|
|
,,
|
|
+o ·33
|
|
|
|
Final seconds in
|
|
triangulation.
|
|
,,
|
|
00·33
|
|
|
|
2 Minoma
|
|
|
|
2S o6 02 ·46
|
|
|
|
+o ·31
|
|
|
|
02 "77
|
|
|
|
Standpipe
|
|
|
|
28 I4 37 ·u
|
|
|
|
3 1 Sugar Loaf Mound
|
|
|
|
109 16 57 "79
|
|
|
|
I 4
|
|
|
|
AmericanBottomUpperBase II4 45 13·03
|
|
|
|
-o ·Sr +0·17
|
|
|
|
56 ''}'3
|
|
13·20
|
|
|
|
Probable error of a single observation of a direction (3D. and 3R. )= ±1"·14.
|
|
|
|
.A111aica11 Bottom Upper Base, Madison County, Illinois. October 24 to November 13, 1872. 25-centi-
|
|
|
|
111etre theodolite, No. 74. C. H. Boyd, observer. May 8 to May 23, ;873. 28-centimetre theodo-
|
|
|
|
lite, No. 100. C. H. Boyd, observer.
|
|
|
|
0
|
|
|
|
,,
|
|
|
|
,,
|
|
|
|
,,
|
|
|
|
5
|
|
|
|
American Bottom Low~r Base 0 00 oo·oo
|
|
|
|
+o ·17
|
|
|
|
00 ·17
|
|
|
|
6
|
|
|
|
Clarks Mound
|
|
|
|
I 7
|
|
|
|
In~n< A•ylum
|
|
|
|
2 04 23 ·41 49 IO 58·48
|
|
|
|
+0·57 ..l...0·62
|
|
|
|
23·98 59·10
|
|
|
|
Standpipe
|
|
|
|
67 SI 38 ·28
|
|
|
|
8
|
|
|
|
Minoma
|
|
|
|
75 09 13 ·s8
|
|
|
|
-1°36
|
|
|
|
I2 '22
|
|
|
|
Probable error of a single observation of a clirection ( ;i,D. and 3R. )= ± l"· 19.
|
|
|
|
70
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
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|
|
Dre.yer, St. Clair County, Illinois. October 26 to October 27, 1871. 30-centimetre theodolite, No. 32. R. E. Halter, 0. · H. Tittmann, observers. June. 20, 1873. 25-centimetre theodolite, No. i4· C. ·H. Van Ordei1, observer. November 19 to December' 1; 18So. 30-centimetre theodolite, No. 107. G. A..Fairfield, observer. Telescope above ground 10·21 metres in lSSo.
|
|
|
|
31
|
|
|
|
Kleinschmidt
|
|
|
|
0
|
|
|
|
II
|
|
|
|
0 00 oo·oo
|
|
|
|
II
|
|
+0·77
|
|
|
|
32
|
|
|
|
Insane Asylum
|
|
|
|
56 04 42·32
|
|
|
|
-l ·40.
|
|
|
|
Standpipe
|
|
|
|
85 08 41 ·16
|
|
|
|
33
|
|
|
|
Clarks Mound ·
|
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|
|
140 o8 32·76
|
|
|
|
+0·63
|
|
|
|
Turkey Hill
|
|
|
|
184 o6 27 "79
|
|
|
|
Probable error of a single observation of a direction (D. and R.) = ± 011·9S.
|
|
|
|
II
|
|
00 "77 40·92
|
|
33·39
|
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|
|
Clarks llfozmd, St. Clair County, Illinois. ·October 13 to November 10, 187I. 30-centimetre theoclo-
|
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|
|
lite, No. 32. R. E. Halter, 0. H. Tittman, observers. M;ay 28 to May 31 1 1873. 25-centimetre theodolite, No. 74. C. H. Van Orden, observer. August i3 to September 4, 1880. 30-centimetre
|
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|
|
theollolite, No. 107. G. A. Fairfield, observer. Telescope above ground 10·o6 metres in 188o.
|
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0
|
|
|
|
II
|
|
|
|
II
|
|
|
|
·,,
|
|
|
|
25
|
|
|
|
Dreyer
|
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|
|
0 00 oo·oo
|
|
|
|
+ 0 ·39
|
|
|
|
00·39
|
|
|
|
26 Kleinschmidt
|
|
|
|
I7 23 30·35
|
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|
|
- I ·So
|
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|
|
28·55
|
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|
|
27
|
|
|
|
Insane Asylum
|
|
|
|
46 08 58 ·34
|
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|
|
+075
|
|
|
|
59·09
|
|
|
|
28 Minoma·
|
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|
|
73 51 07 ·94
|
|
|
|
+0·73
|
|
|
|
08·67
|
|
|
|
Stamlpipe
|
|
|
|
77 38 29··97
|
|
|
|
29
|
|
|
|
Sugar Loaf Mound
|
|
|
|
149 26 05 ·45
|
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|
|
+0·95
|
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|
|
o6·40
|
|
|
|
30
|
|
|
|
American Bottom Upper Base 154 17 03 ·14
|
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|
-1 ·02
|
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|
|
02·12
|
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|
|
Berger
|
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210 04 34·22
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, Turkey Hill
|
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|
256 or II "05
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|
= Probable error of a single observation of a direction (D. and R.) ± 111"39 C.
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|
St1gt11· Loil_/ J1/01111d, Madison County, Illinois. May 12 to May 24, r8j3. 25-centimetre theodolite, No. 74. C. H. Van Orden, observer. September r3 to September 24, r8So. 30-centimetre theodolite, No. 107. G. A. Fairfield, observer. Telescope above ground, 14·20 meters in 1880.
|
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|
Parkinson
|
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|
0
|
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|
//
|
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|
|
//
|
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|
0 00 oo·oo
|
|
|
|
Berger
|
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|
30 24 26·70
|
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|
|
. 21
|
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|
|
America.11 Bottom Lower Base II.f. 53 21 ·82
|
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+0·09
|
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22 23
|
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|
IClarks Mound Insane Asylum
|
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|
|
II7 35 06·48 161 07 27·22
|
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|
|
-0·24 -0·33
|
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|
|
Standpipe
|
|
I 24 Minoma
|
|
|
|
174 35 29·21 185 II 47 ·19
|
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|
|
+0·48
|
|
|
|
Probable error of a single observation of•a direction (D. and R.) = ± 111·20.
|
|
|
|
·''
|
|
21 ·91 o6 ·24 26·S9
|
|
47·67
|
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|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES.
|
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|
7r
|
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|
Jnsai1e Asylnm, St. Louis County, 'Missouri. · ·November 8 to November Io, I871. 30-centimetre ·
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|
theodolite, No. 14. W. Eimbeck, observer. October 2 to October I2, I872. 25-centimetre
|
|
theodolite, No. 92. C.H. Van Orden, obsen'er. June 5 to June 23, 1873. 28-centimeter theodo-
|
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|
|
lite, No. 100. C. H. Boyd and C. H. Van Orden, obs_ervers.
|
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|
I4
|
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|
|
Minoma
|
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|
0
|
|
|
|
"
|
|
|
|
0 00 oo·oo
|
|
|
|
,,
|
|
-0·27
|
|
|
|
II
|
|
59 "73
|
|
|
|
Standpipe
|
|
|
|
39 46 44·35
|
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|
|
15
|
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|
|
Sugar Loaf Mound
|
|
|
|
65 21 o6·63
|
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|
16 ·American Bottom Upper Base 73 46 19 ·17
|
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|
+1 ·27
|
|
- ·88
|
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|
07·90 . IS ·29
|
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|
I7
|
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|
American Bottom Lower Base 89 50 07·81
|
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|
-1 ·oo
|
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|
|
o6 ·Sr
|
|
|
|
I8
|
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|
|
Clarks Mound
|
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|
98 31 40·32
|
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|
+ ·29
|
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|
40·6I
|
|
|
|
I9
|
|
|
|
Dreyer
|
|
|
|
I48 IS 49·26
|
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|
|
+ 066
|
|
|
|
49·92
|
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|
|
20 Kleinschmidt
|
|
|
|
200 16 I2"64
|
|
|
|
:..... ·07
|
|
|
|
I2. 57
|
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|
|
Patterson
|
|
I Kessler
|
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|
|
235 1S 46 ·97 27I 34 38 "II
|
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|
|
Morgan
|
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|
|
3o6. 29 3o·S8
|
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|
|
= Probable error of a single observation of a direction (3D. and 3R.) ± 1"·30.
|
|
|
|
J(/ei11sd1111idl, St. Louis County, Missouri. November 21 to December 9, 1871. 30-centimetre theodolite, No. 32. \V. Eiml:ieck, observer. June ~1 to June 22, I873. 25-centimetre theodolite,
|
|
No. 74. C. H. Van Orden, observer.
|
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|
|
Patterson
|
|
|
|
0
|
|
|
|
II
|
|
|
|
II
|
|
|
|
0 00 oo·oo
|
|
|
|
Morgan
|
|
|
|
85 05 58·51
|
|
|
|
34
|
|
|
|
Insane Asylum
|
|
|
|
124 05 37 "73
|
|
|
|
+0·5s
|
|
|
|
Azimuth Mark
|
|
|
|
124 37 35 ·99
|
|
|
|
Standpipe
|
|
|
|
132 54 24 "I4
|
|
|
|
35
|
|
|
|
Clarks Mound
|
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|
|
173 35 37 "II
|
|
|
|
-0·76
|
|
|
|
36
|
|
|
|
Dreyer
|
|
|
|
196 03 35·63
|
|
|
|
+0·19
|
|
|
|
= Probable error of a single observation of a direction ( 3D. and 3R.) ± 0 11 ·90.
|
|
|
|
II
|
|
38·31
|
|
36·35 35·82
|
|
|
|
llfinoma, St. Louis County, Missouri. June 5 to June II, IS73. 25-centimetre theodolite, No. 74. C. H. Van Orden, observer.
|
|
|
|
0
|
|
|
|
II
|
|
|
|
9
|
|
|
|
Sugar Loaf Mound
|
|
|
|
0 00 oo·oo
|
|
|
|
IO
|
|
|
|
American Bottom Upper Base IO 18 59·95
|
|
|
|
"
|
|
- I 020
|
|
+1·6o
|
|
|
|
Standpipe
|
|
|
|
28 II 26·91
|
|
|
|
II
|
|
|
|
American Bottom Lower Base 28 30 38·95
|
|
|
|
+0·52
|
|
|
|
12 Clarks Mound
|
|
|
|
36 48 21 ·53
|
|
|
|
-1 ·08
|
|
|
|
13
|
|
|
|
Insane Asylum
|
|
|
|
90 34 30·33
|
|
|
|
+0·16
|
|
|
|
J Morgan
|
|
|
|
164 32 12·93
|
|
|
|
Probable error of a single observation of a direction t3D· and 3R.) = ± o'1•84.
|
|
|
|
II
|
|
58·8o 61 ·55
|
|
39·47 20·45 30·49
|
|
|
|
,_"'?
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
FIGURE ADJUSTMENT.
|
|
|
|
Obscr- a' "011 ,-q11alir>11s.*
|
|
|
|
No.
|
|
|
|
0=+2·74.+(rr)-(w)+ fS)- f5)'-\- (4)- (2)
|
|
|
|
2 o=+nr+(r7)--'l.I4i+lr3)-(rI)+ (2)- (r)
|
|
|
|
3 0=+3·83+(23)--(u)+ (3)- (r)+(r7)--{r5)
|
|
|
|
4 o= -37r-r(r3)-- (9)-1-(24)-(23)-!-(15)-(14)
|
|
|
|
5 0=+0·55+(30)-(27)+(18)-(16)+ (7)- (6)
|
|
|
|
6 0=+6·36+(,'I0)-(2~)+(12)-··(10"1+ (8)·- (6)
|
|
|
|
7 a= - I"7i + (28)- (27) +(IS)- (14) + (13)-(12)
|
|
|
|
8 o=-J"o6+(29)--(2S)+(r2J- l9i +(24)-(22)
|
|
|
|
9 O=- 2·76+ (33) - (.32) + ( 19) - (18) + (27)- (25)
|
|
+ IO O= +3·29+ (36)-(34) ..j... (20) -{I9) (32)-(31)
|
|
|
|
rr o=+ 1·38+ (33)-- (3i) + (36)-(35) + (26)- (25)
|
|
+ 12I0=+4·0-r26l5)+1°82\7) -0·56(8) -6·4o(rn) +rs2(n)-n2(13) r31(16l-r31(17) + + 13 O= 5·3 -4·68( I)+ 3·94( 2) + 0°j4(3) + 0·02(9) + 1"12( II)- 1"14( 13) - 2"02( 21) 6·74(23)
|
|
|
|
-4·72(24)
|
|
|
|
.
|
|
|
|
+ 14 O= 1]"4- 1"31(6) + 1·95(ii -0·64(8) -- 4·22( IO)+ 5"7i( 12) - 1'55( 13) + 0·31( 14) + 4·57( 16)
|
|
|
|
-4·88(18)
|
|
|
|
.
|
|
|
|
15 0 = - 0·6- 2·82( 9) + 4·37( 12) -- 1·55(13) + 0·31( 14) + 3·22( rs) - 3·53(18) - _r35(22) +2·22(23)
|
|
|
|
-0·87(24)
|
|
+ 16 o = 18·7 - q3( 18) + 3·43( 19) - r65( 20) - no( 25) + 6·72( 26) - 2·02( 27) - 0·68(34)
|
|
|
|
+ 5·09(35) -4·41(36)
|
|
|
|
<...orrdali' eq11atio11s.
|
|
|
|
c, Co
|
|
|
|
Cs
|
|
|
|
I ~
|
|
|
|
(.;)
|
|
|
|
-I
|
|
|
|
-I +z
|
|
|
|
-I
|
|
|
|
(3)
|
|
|
|
+z
|
|
|
|
(4)
|
|
|
|
+r
|
|
|
|
(5)
|
|
|
|
-1
|
|
|
|
.... .... ....
|
|
|
|
(6)
|
|
|
|
-I -I
|
|
|
|
( i.l
|
|
|
|
+r
|
|
|
|
(St +1
|
|
|
|
+1
|
|
|
|
(9)
|
|
|
|
(10)
|
|
|
|
-I
|
|
|
|
-I
|
|
|
|
-I
|
|
|
|
-I
|
|
|
|
....
|
|
|
|
(II.I
|
|
|
|
+r -1
|
|
|
|
( 12 /
|
|
|
|
+1 -I +r
|
|
|
|
(13)
|
|
|
|
+1
|
|
|
|
+1
|
|
|
|
+r
|
|
|
|
( '4)
|
|
|
|
-r
|
|
|
|
-I
|
|
|
|
-I
|
|
|
|
I.Isl
|
|
|
|
-I +1
|
|
|
|
(!6)
|
|
|
|
-r
|
|
|
|
(17). ( 18)
|
|
|
|
+r +1
|
|
|
|
+r
|
|
|
|
+1
|
|
|
|
-1
|
|
|
|
( 19)
|
|
|
|
+z -r
|
|
|
|
(20)
|
|
|
|
+z
|
|
|
|
( 21)
|
|
|
|
-I
|
|
|
|
( 22)
|
|
|
|
-r
|
|
|
|
(23)
|
|
|
|
+r -1
|
|
|
|
(24")
|
|
|
|
+1
|
|
|
|
+r
|
|
|
|
(25) (26)
|
|
|
|
-I
|
|
|
|
-I
|
|
|
|
+r
|
|
|
|
( 27)
|
|
|
|
-I
|
|
|
|
-1
|
|
|
|
+r
|
|
|
|
I 2S)
|
|
|
|
-I +z -I
|
|
|
|
-4·6$
|
|
+3"94 +0·;4
|
|
|
|
-1·2(.
|
|
+1 ·s2
|
|
-o·~
|
|
-6·40 +;·52
|
|
-I'I.:!
|
|
+1·31 -7·31
|
|
|
|
+0·02 +1·12 -1·14
|
|
-.1'0:?
|
|
+6·74 -4·;2
|
|
|
|
--1 ·31
|
|
+1·95
|
|
-0·64
|
|
-4·2z
|
|
+5·;7 -1 ·55 +0·31
|
|
+4 ·57
|
|
-4 ·ss
|
|
|
|
-2·82
|
|
+4 ·37 -1 ·55 +0·31 +:;·22
|
|
-3·53
|
|
-1 ·35 +2"22 -0·87
|
|
|
|
-178 +3°43 -1 ·65
|
|
-4·70 +672
|
|
-2·02
|
|
|
|
*Number of angle equations 11 and of side equations 5; the latter are established with 7 place logarithms. difference!"o for i'' refer to tht: sixth place of decimals.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 73
|
|
FIGURE ADJUSTMENT-continued. Corrdaf,, t'qllatio11s-Conti11ued.
|
|
|
|
+1 +1 +1 ....
|
|
|
|
-1 -I
|
|
|
|
-1 +1
|
|
|
|
+1
|
|
|
|
+1
|
|
|
|
-i
|
|
|
|
-l
|
|
|
|
Ti +1
|
|
|
|
-o·6S
|
|
|
|
....
|
|
|
|
+5'09
|
|
|
|
-4 ·41
|
|
|
|
JVormal cq11atio11s.
|
|
|
|
~
|
|
|
|
~
|
|
|
|
~
|
|
|
|
~ ~ ~ ~ ~ ~ ~~
|
|
|
|
Cr~
|
|
|
|
C14
|
|
|
|
C15
|
|
|
|
C16
|
|
|
|
o=+ 2·74
|
|
+ I 'II + 3·83
|
|
- 3•71
|
|
+ 0·55 + 6"36
|
|
- 1 ·77
|
|
- 1·06
|
|
- 2·76
|
|
+ 3·29 + l ·38 + 4·0 + 5·~
|
|
+17·4
|
|
- o·6
|
|
+18·7
|
|
|
|
+6 -2 +6 +• +• +6 -2
|
|
|
|
+• +o
|
|
|
|
+ 14 ·62 - :! ·:S2 + 3 ·5S - 15'95 + 6"36 - I 86 - 7 ·31 + 14 ·1a,
|
|
|
|
+6
|
|
|
|
+2 +•
|
|
|
|
- 1·12 - 12·62 - 1·86
|
|
|
|
+6 +• +2
|
|
|
|
-2
|
|
|
|
+6 -2 +2
|
|
|
|
5·49
|
|
+ 5·84
|
|
|
|
- 6'19
|
|
+ 10'66
|
|
|
|
+6 -2 -2
|
|
|
|
- I'll - 1'14 - 10'51
|
|
|
|
+6
|
|
|
|
- 4 '74 + 5 '77
|
|
|
|
.... .... .... ....
|
|
|
|
+6 -2 +•
|
|
+6 +2
|
|
|
|
+ 4 ·&~
|
|
|
|
¥
|
|
+•10 ·S5 + 9 ·71 + 66 'o6
|
|
+11.:?·31 + 1·77
|
|
|
|
'+IC'4 '23
|
|
|
|
Res11lti11g val11es of correlates and of,vrredio11s lo a11g11/11r dir..ctio11s.
|
|
|
|
- l'S6
|
|
- 1 ·oo
|
|
+ 1·09
|
|
- 3·53 + 0·24 + 4 ',\7 -9'76 ·+ 0'24
|
|
+ 7 '67 + 3 ·53 + 7 '89
|
|
- s·s1 + I~ + l '74 + 2 0 · 7s +44 '94 + 8 '69 +59'88 + 6 28
|
|
+134 ·So
|
|
|
|
C ,=+o·r74
|
|
c. -1 ·742
|
|
|
|
Corrections.
|
|
|
|
C3 -I '229 C4 +1 ·742 Cs +0·453
|
|
c6 -I '470
|
|
C1 +0·20S Cs +0·950
|
|
C9 +0·972 C,o -0·429 C,, -0 ·342 C,. -0·270
|
|
C,3 +0·565 C,,, +0·338 C,s -0·527 C16 -0·217
|
|
|
|
II
|
|
|
|
(1)=+0·327
|
|
|
|
(2) + ·310
|
|
|
|
(3)
|
|
|
|
·Su
|
|
|
|
(4) + ·'174
|
|
|
|
(5) + ·166
|
|
|
|
(6) + ·574
|
|
|
|
(7) -i- ·621
|
|
|
|
(S) -- I •361
|
|
|
|
(9) - I ·195
|
|
|
|
(IO) -f- I ·59S
|
|
|
|
( 11) +0·519
|
|
|
|
(12) - I 'o8I
|
|
|
|
II
|
|
|
|
( 13) = + 0 ·159
|
|
( I4) - ·266
|
|
|
|
( 15) + l ·274
|
|
|
|
(16)
|
|
|
|
·SS2
|
|
|
|
( 17)
|
|
|
|
·997
|
|
|
|
(18) + ·286
|
|
|
|
( 19) + ·657
|
|
|
|
(20)
|
|
|
|
·071
|
|
|
|
(2I) + ·ot;S
|
|
|
|
(22)
|
|
|
|
·~39
|
|
|
|
( 23)
|
|
|
|
·333
|
|
|
|
(:q.J + ·4S3
|
|
|
|
II
|
|
|
|
(25)=+0·390
|
|
|
|
(26) - I ·Sou
|
|
|
|
(27) + ·749 ( 2S) + ·72S (29) + ·950 (30) -1 ·017
|
|
|
|
(31) + 771
|
|
(32) -1 ·401
|
|
|
|
(33) '(34) (35). (36)
|
|
|
|
-L
|
|
I
|
|
|
|
·630
|
|
|
|
+ -·577
|
|
|
|
763
|
|
|
|
+ ·186
|
|
|
|
++ 1 Checks: Sum of all +corrections 12·217 and :SP<«' = 23 ·648 Suni of all - corrections 12·217 and -:S<i'C= 23·615
|
|
|
|
= Mean
|
|
|
|
error
|
|
|
|
of
|
|
|
|
an. observed
|
|
|
|
di,-..ctio11
|
|
|
|
111,
|
|
|
|
=
|
|
|
|
y f
|
|
|
|
[P<'<']
|
|
II
|
|
|
|
± i "· 22
|
|
|
|
where n =number of conditions.
|
|
|
|
Mean error of an ang/e
|
|
|
|
111L=111,,/2= ± 1"·72 and probable error of same ± 111·16.
|
|
|
|
74
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
TRl_ANGLF;S OF TH~~ AMERICAN BOTTOlI BASE NET, ILLINOIS AND l\1ISSOURl, rS71 to rSSo.
|
|
|
|
No. Stations.
|
|
|
|
Observerl angles.
|
|
|
|
J Minoma
|
|
lI Am. B0t. Up. Base Am.Bot.Low.Base
|
|
|
|
!I
|
|
18 II 39·00 75 09 ·13 ·5s S6 39 IO :57
|
|
|
|
JInsane Asylum
|
|
l2. Minoma Am. Bot. Up. Base
|
|
|
|
03 "JS 7.3 46 19 ·17 So I5 30·38 ;i5 58 15 "IO
|
|
|
|
JI1isane Asylum
|
|
|
|
04·65 89 50 07·S1
|
|
|
|
l3 Minoma .
|
|
|
|
62 03_ SI ·38
|
|
|
|
Am.Bot.Low.Base 28 06 02·46
|
|
|
|
Jl1~sane Asylum
|
|
|
|
or ·65 16 03 48·64
|
|
|
|
l4 Am. Bot. Up. Base 49 10 58·48 Am.Bot.Low.Base II4 45 13 ·03
|
|
|
|
00 ·15
|
|
r Sugar Loaf Mound 46 q 05 ·40
|
|
l5 Am.Bot.Low.Bas~ 109 r6 57 79
|
|
Insane Asylum 24 28 61 ·18
|
|
|
|
04 ·37
|
|
JSugar Loaf Mound jO 18 25·37
|
|
l6 Am.Bot.Low1 Base Sr IO SS ·33
|
|
|
|
Minoma
|
|
|
|
28 30 3$·95
|
|
|
|
s9·65
|
|
|
|
{ S'W"' Lo'fl\!oond :1-1 04 19 ·97
|
|
|
|
7 Insane Asylum
|
|
|
|
65 2r o6·63
|
|
|
|
Minoma
|
|
|
|
9C> 3.J. 30·33
|
|
|
|
[ Cl~k•M®od 8 Insane Asylum
|
|
J.Vlinorna
|
|
|
|
56·9:; "27 42 09·6o
|
|
98 JI 40 ·,:;2
|
|
53 46 oS·So
|
|
|
|
5S"i2
|
|
|
|
[ CWk• Mound w3 17 07 ·a
|
|
|
|
9 Insane Asylum
|
|
|
|
33 IO 33 ·69
|
|
|
|
Sugar Loaf Mound 43 _·,~ _ ::?074
|
|
|
|
JClarks Mound
|
|
l10 Insane Asylum
|
|
|
|
01 ·54 rnS oS 04·So :q 45 2r ·rs
|
|
|
|
Am. Bot. Up. Base 47 06 3s·o7
|
|
|
|
01 ·o~
|
|
|
|
Correc- Spher- Spher-
|
|
|
|
,, ti0 115 "
|
|
|
|
1cal 1cal angles..excess.
|
|
|
|
"
|
|
-I ·oS
|
|
|
|
"
|
|
37·92
|
|
|
|
o·q
|
|
|
|
-I ·53 12 ·05 o·q
|
|
|
|
-o·r3 ro·44 0·13
|
|
|
|
-0·61 - l ·44 - r "<}'>
|
|
|
|
IS ·s6 28·94 13 "12
|
|
|
|
0 ·41
|
|
0"2I 0·20
|
|
0 ·21
|
|
|
|
-07,:; -0·36 -0·02
|
|
|
|
07·oS 5I "02 02·44
|
|
|
|
0·62
|
|
o "IS o ·rs · o ·rs
|
|
|
|
-0·12
|
|
+0·45 -o·r5
|
|
|
|
4S ·52 5S·93 r2·ss
|
|
|
|
0·54 o "II
|
|
O"II O "II
|
|
|
|
-o ·42 -r·q -2 ·27
|
|
|
|
o4·9S 56 ·6s sS ·9r
|
|
|
|
o·33 o "IS o ·rs o ·rs
|
|
|
|
+o ·40
|
|
- I "12
|
|
+r "jI
|
|
|
|
2S ·77 54 "2I 40·66
|
|
|
|
O"S4
|
|
0·21 0·22 0 ·21
|
|
|
|
+0·82 +r ·s.i +r ·3s
|
|
|
|
2079 08·17 ,:;I "68
|
|
|
|
0·64 0"2I o ·2r 0"2:?
|
|
|
|
-0·02
|
|
+o·s5 +r ·2.i
|
|
|
|
09·s8 4o·S7 IO "O.j.
|
|
|
|
0·64 0 ·16 0 ·17 0 "16
|
|
|
|
+o ·20 • 07 ·31 -0·99 32·70 -0·09 20'65
|
|
|
|
0·49 0 ·22 0'22 0·22
|
|
|
|
0"66
|
|
|
|
-I"ji
|
|
+1 ·17 +0·05
|
|
|
|
03 ·03 22 ·32 35 ·12
|
|
|
|
0 ·rs 0 ·16 0 ·16
|
|
|
|
0 ·47
|
|
|
|
Logs.
|
|
|
|
Distances in metres.
|
|
|
|
3·S6r 348 2 4·352 12,:; 5 4·366 12S 5
|
|
|
|
7 266"S84 22 496 ·94
|
|
_.,_., 234·24
|
|
|
|
4·366 12S s 4 "37i 47S 4 4·025 166 I
|
|
|
|
2..,. 234 ·24 23 849 ·45 IO S96 ·59
|
|
|
|
4·352 123 5 4 ·298 ,FS 3 4·025 166 I
|
|
|
|
22 496·94 19 875 ·51 IO 596"S9
|
|
|
|
3 ·S6I 348 2 4·298 318 3 4 ·377 478 3
|
|
|
|
7 266"884 19 87s"SI 23 849 "4S
|
|
|
|
4 ·298 31S .:; 4 ·414 600 7 4·057 !Ii 2
|
|
|
|
19 875 ·51 25 977 70 II 4os·57
|
|
|
|
4·3s:i 123 s 4·373 1."._""I.) ._•'I 4·057 II7 2
|
|
|
|
22 496·94 23 612 ·03 II 40S "57
|
|
|
|
4·02s 166 I 4 ·,:;73 133 2 4 ·414 6oo 7
|
|
|
|
IO 596"S9 23 612 ·02 25 977 70
|
|
|
|
4·025 166 l 4 ·,:;52 994 4 4·264 sos 3
|
|
|
|
IO 596"S9 22 542 ·ro IS 386 76
|
|
|
|
4 ·414 6oo 7 4 ·16.j. 534 3 4·264 505 3
|
|
|
|
2s 977 "70 I4 606 "IO 18 386 ·76
|
|
|
|
4·377 478 3 4·02r 566 I 4 ·264 sos 2
|
|
|
|
23 849 ·.is IO 509 "II rs 386 76
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-EASE LINES.
|
|
|
|
75
|
|
|
|
'rRJANGLES OF 'rHE AMER,ICAN BO'rTOl\I B.~SE NE'r, II.LINOIS AND MISSOURI, 1871 T_O 1880-cont'd.
|
|
|
|
No. Stations.
|
|
lCla.bM~od
|
|
II Minoma
|
|
Sugar Loaf, Mr!.
|
|
|
|
Observecl angles.-
|
|
,,
|
|
iS 34 Si ·sr
|
|
36 48 21 "S3 67 36 40 71
|
|
|
|
( Cloclra Moonol 12 Minona
|
|
Am. Rot. Up. Base
|
|
|
|
59 75 So 25 55 ".?O 26 29 21 ·58
|
|
73 04 so ·17
|
|
|
|
Dreyer
|
|
nJ Insane Asylum ' l Clarks Mound
|
|
|
|
06·95
|
|
84 03 50·44
|
|
49 47 08·94
|
|
46 oS s8 ·.w
|
|
|
|
lr Kleinschmidt
|
|
14 Insane Asylum Clarks Mound
|
|
|
|
57·72 :..~ 49 29 59".)8 IOI 44 32 ·32 28 45 27"99
|
|
|
|
JKleinschmidt l·rs Insane Asylum
|
|
Drey"r
|
|
|
|
s9·69 71 S7 57 ·90 5i: 57 23·JS 56 04 42·32
|
|
|
|
( Kl<i=hmidt 16 Clarks Mound
|
|
Dreyer
|
|
|
|
03 ·6o ::?::? 27 58·52 17 23 30·3s 140 oS 32 76
|
|
|
|
OI ·63
|
|
|
|
Correc- Spher- SJ?her-
|
|
|
|
tions · 1cal 1cal.
|
|
|
|
· angles. excess.
|
|
|
|
•. II
|
|
|
|
,,
|
|
|
|
II
|
|
|
|
+0·22 s7"73 0·27
|
|
|
|
+o·r2 21 ·6s 0·27
|
|
|
|
+072 41 ·43 .0 ·27
|
|
|
|
o·8r -I '75 S3 ·4s O"I9 -2·68 18·90 0·20 - I ·93 48 ·24 0·20
|
|
|
|
+2'03 +0·37 +0·36
|
|
|
|
52 ·47 09"3I ·58·70
|
|
|
|
0·59 0·16 0·16 0 'I6
|
|
|
|
-I ·34 -0·36 +2"54
|
|
|
|
58·04 31 ·96 30 "S3
|
|
|
|
0·48 0·18 0·17 0·18
|
|
|
|
-0·39 -0·73 -:!"IT
|
|
|
|
57 "5I 22 ·65 40 "I5
|
|
|
|
0·53 0 "JI 0 "IO 0'10
|
|
|
|
+0·95 -2 ·19 -o·q
|
|
|
|
59·47 28 ·16 32 ·62
|
|
|
|
0"3I o·og o·os o·oS
|
|
|
|
0·25
|
|
|
|
Logs..
|
|
,., 4 ·373 I...,. ., ....,..
|
|
4 ·164 S34 3 4·352 994 4
|
|
4 ·366 128 s . 4 ·021 56/.) I
|
|
4·352 994 3
|
|
4·264 505 3 4 ·149 726 7 4 ·1.24 866 r
|
|
4·264 50s 3 4·374 278 9
|
|
4·065 715 r
|
|
4 "124 866 I 4·043 OI6 7 . 4 ·o65 7I5 2
|
|
4 ·149 726 7 4 "04J 016 6 4·374 278 9
|
|
|
|
Distances in metres.
|
|
23 612 ·03 14 6o6 ·10 22 S42 ·10
|
|
23 234·24 IO 509 "II 22 S42 "IO
|
|
rs 386•76
|
|
14 116 ·49 13 33I "IO
|
|
r8 386 76 2.) 674 ·40 II 633 ·63
|
|
IJ 331 "IO II 041 "2I II 633·63
|
|
14 II6"49 II 04I ":!I 23 674·40
|
|
|
|
l'ROBABJ,E ERRORS.
|
|
|
|
Dd.:r111i1111tio11 •?i Ille' probabk ,,rrvrs of tlie ft>11gtl1 <?f Ifie sides co111111011 to !11<? 11d a11d tilt? adfaff11l cliai11s of tria11g11latio11.
|
|
|
|
For the side Sugar Loaf Mound to Clarks Mound, as adjusted, we make use of the expression-
|
|
|
|
Sugar Loaf Mound to Clarks Mound_ si11 ( S - 5) sin (3 - 2) sin ( I 2 - 9)
|
|
|
|
Alllerican Bottom Base
|
|
|
|
- sin (II - IO) sin ( 24 - 21) sin ( 29 - 28)
|
|
|
|
hence the function
|
|
|
|
F= log sin (8-S) +log sin (3- 2) +log sin {I2 - 9) - log sin (11 - IO) - log sin ( 24 - 21) - log sin (29- 28)
|
|
|
|
Establishing and solving the transfer equations, we fit~d the reciprocal of the
|
|
|
|
weight~= 46·04, also the mean error 111F and the probable error rF, both expr~ssed in
|
|
|
|
units of the sixth place of decimals in their logarithms, viz: ± S ·25 and ± 5 ·56,
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.-
|
|
|
|
respectively, hence log distance Sugar Loaf Mound to Clarks Mound 4·r64 534 3 and
|
|
|
|
.
|
|
|
|
± 56
|
|
|
|
the distance q 606 ·10 metres. The probable error is .about '!Ttruu part of the length.
|
|
|
|
± 0·19
|
|
|
|
To this must be added the proportional error depending upon that of the base measure,
|
|
|
|
or.±
|
|
|
|
0·0206
|
|
|
|
X
|
|
|
|
14 606
|
|
-7 -2 6-7 =
|
|
|
|
±
|
|
|
|
0·04 r
|
|
|
|
metre;
|
|
|
|
hence
|
|
|
|
. probable error m
|
|
|
|
length
|
|
|
|
of
|
|
|
|
side Sugar
|
|
|
|
Loaf Mound to Clarks Mound ~<.0·19-Y+ (0·041)2 = ±0·19111etre.
|
|
|
|
For the side Clarks Mound to Dreyer we use the expression-
|
|
|
|
Clarks Mound to Dreyer sin (4- 1) sin (7 - 6) sin ( 19- 18) American Bottom Base = sin ( l 7 -· 16) sin (30 -- 27 ) sin (33 - 32)
|
|
F= log s·n (4- 1) +log sin (7 - 6) +log sin ( 19 - 18) - log sin ( 17 -'16) - log sin (30- 27) - l()g sm (33 -- 32)
|
|
Establishing and solving the transfer equations, we get pI = 40·94, also m ~· = ±
|
|
|
|
7·78 and rF= ±5"25, hence log distance Clarks Mound to Dreyer.4·149 726 7 and ±, 5 2
|
|
d.istance 14 116·49 metres. 1'he probable error is about ~-g·bii·ii part of the length. . ±. 0·17
|
|
Adding to this the proportional error due to that of the base measure, or <Yo206 /'. 1 ~ ~~~
|
|
= ± 0·040 metre, we have probable error of length of side Clarks Mound to Dreyer
|
|
+ ~(o·I7)2 (0·040)2 = ± 0·17 metre.
|
|
For the side Minoma to Insane Asylum we use the expressi.on-
|
|
|
|
. Minoma to Insane Asylum sin (8-5) sin (2-1) -American Bottom Base =sin (II - 10) sin ( 17 - 14)
|
|
|
|
F=.log sin (8 - 5) +log sin ( 2 - 1) - log sin (II - 10 l -- log sin (I7 - 14)
|
|
|
|
Establishing and solving the transfer equations, we find the reciprocal of the
|
|
= = weight ~ 41 ·4s, a_lso the mean error m.~· ± 7·s3 and probable error rp == ± 5 ·2s;
|
|
|
|
hence log distance. Minoma to Insane Asylum 4·025 I66 I and distance Io 596·59
|
|
|
|
± 53
|
|
|
|
± 0·13
|
|
|
|
metres. The probable error is about -s 2 huu part of the length. Adding to this the
|
|
|
|
Proportional error dt1e to that of_ the base measure, c_,r 0·0206 X -I-O7-"2'-i69--77 = ± o·o:';o
|
|
|
|
metre, we have probable error of length Minoma to Insane Asylum J(o· 13)2 + (0·030)"
|
|
|
|
= ± 0·13 metre. .
|
|
|
|
For the side Insane Asylum to Kleinschmidt we use the expression-
|
|
|
|
Insane Asylum to Klein!>chmidt sin (4 - r) sin ( 7 - 6) sin ( 27 - 26) American Bottom Base =sin ( 17 - i6) sin ( 30 - 27) sin (35 - 34)
|
|
F=log sit1 (4-1)+log sin (7-6)+log sin (27-26)-log sin (17-16)-log sin (30-27) - log sin (35 -- 34)
|
|
|
|
Establishing and solving the transfer equations, we find the reciprocal of the
|
|
|
|
weight];= 47"36, als_o the mean error mp= ± 8"42 and the probable error rF = ± 5 "68,
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE -·LINES.
|
|
|
|
77
|
|
|
|
hence log distance Insane Asylum to Kleinschmidt 4·065 7I5 I ai~d distance II 633·63
|
|
|
|
± 57
|
|
|
|
± 'IS
|
|
|
|
metres. The probable error is about 77 ho part of the length. Adding_ to this the
|
|
|
|
Pro1Jortional
|
|
|
|
error
|
|
|
|
clue
|
|
|
|
to
|
|
|
|
that
|
|
|
|
of
|
|
|
|
the
|
|
|
|
base
|
|
|
|
measure,
|
|
|
|
.or
|
|
|
|
0·0:?06
|
|
|
|
:<
|
|
|
|
-I I7' - ,62,30-74
|
|
|
|
=
|
|
|
|
0.03-:. v
|
|
|
|
metre,
|
|
|
|
we have probable error of length Insane Asylum to Kleinschmidt J-(o___I_5_)2__,+,---(,_o-·o-3_3_)_"
|
|
|
|
= ± o'I5 metre.
|
|
|
|
DESCRIPTION OF STATIONS FORMING THE AMERICAN BOTTOM BASE NET-ILLINOIS AND MISSOl.TRI.
|
|
,../.mcricau B<1fto111 L£l7:(10' Base, St. Clair County, Illinois; established in I872 by
|
|
c;. H. Boyd. This station is situated on th~ west slope of the I11inois bluffs on the east
|
|
side of the American bottom, opposite St. Louis, Missouri, on land belonging to Mr. Francis Simoin. The geodetic point is on the west side of the road running north from the Belleville rock road along the foot of the bluffs through the small settlement of ~rench Village. It is about I mile from the rock road and one-fourth mile from the village, 4 metres west of the fence at the side of the road, and about I93 metres north of Mr. Davenroi's house. The center is marked by a cross cut on a copper bolt set in the toiJ of a limestone mom1me11t 12 by 14 by 40 inches, having the letters U.S.C.S. cut on the side facing the base, 1872 on one side and BASE on another. An earthenware pyramid is buried 4 feet below the surface of the ground, under the cross on the copper bolt. Two reference stones were set, one in prolongation of the base, distant 39·37 feet, and the other at right angles to the eastward, distant 63 feet from the center.
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,-/11wican Bottom Upper Bast·, Madison County, Illinois; established in I872 by C. H. Boyd. This station is situated on the west slope of the Illinois bluffs on the east side of the American bottom, opposite St. Louis, Missouri, on land belonging to Mr. A. Smnner. The geodetic point is about one-fourth mile north of the road from East St. Louis to Collinsville and a short distance east of the road running n'orth from the Collinsville road along. the foot of the bluffs. The center is marked by a cross cut on a copper bolt set in the top of a limestone monument 12 by 14 by 40 inches, inscribed in a similar manner as the monument at Lower Base. An earthenware pyramid is buried 4 feet below the surface of the ground directly under the cross on the copper bolt. Two reference posts were set, one in prolongation of the base and one at right angles to the eastward, ~ach 5 by 5 by 30 inches and distant 24 feet from the center.
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. 1lfino111a., St. Louis County, Missouri; established in 1872 by C. H. Boyd. This station is on the cupola of the residence of Mr. Jefferson Clark, situated about one-half inile north of the Natural Bridge road and about 7 miles from St. Louis. The geodetic . point is the center of the flagstaff on. top of the .cupola.
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lnsmzt' .-lsy/11111, St. Louis County, Missouri: established in rS7r by R. E. Halter. This asylum, also known as the "County Lunatic Asylm11," is situated on the "County farm forming part of a larger tract of land known as the ••Gratiot League Square.'' It is about 5 ·miles southwesterly from the court-house at St. Louis and about 500 feet south of the Arsenal street road, at ·a point about one-half mile westerly from its intersection with the Kings Highway. 'fhe geodetic point. is the finial of the cupola of the building. Eccentric points were occupied on the main floor of the cupola.
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Sugar Lo1~l Jlfouud, Madison County, Illinois; established in rS]I by R. E. Halter. This station is situated near the middle of the north line of the northeast quarter of section
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UNITED STATES COAST AND GEODETIC SURVEY. ·
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2o, township 3 north, range S west, about 3 miles northwest of Collinsville on the Vandalia Railroad. It is on a very prominent mound on the edge o~ the bluffs, with a steep slope in all directions falling off about 50 feet to the level ground· to the eastward and 150 to 200 feet to the westward down to the American bottom. A small private graveyard is just south of the mound. The geodetic point is a little to the north of the center of the mound and is marked with the usual earthenware pyramid, the apex being 3 ·1 feet below· the surface of the ground. The surface mark is a white marble post, 6 by 6' inches square and 2 feet apd 6 inches long, projecting about I inch above the ground, having cross lines cut on the top with the letters U.S.C.&G.S. cut in the four squares.
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Clarks llfou11d, St. Clair County, Illinois; established in 1871 by R. E. Halter. This station is situated near the middle of the south line of the northwest quarter of section 35, township 2 north, range 9 west, directly on the bluffs overlooking the American bottom, about three-fourths mile south of French Village and about 7.% miles northwest of Belleville. The mound is quite prominent, the property, in 1880, of Mr. "William Clark, of St. Louis. The underground mark is the center of .the bottom of a soda-water bottle buried, bottom up, 2 feet and 7 inches below the surface of the ground. The surface mark is (in 1880) a white marble post 6 inches square, 2 feet 6 inches long, projecting about 2 inches above the ground, the top cut and inscribed like the one at Sugar Loaf Mound. Two white marble posts, 4 inches square, 2 feet 6 inches long, with diagonal lines cut on the top, an arrowhead at the end of one of the lines pointing to the station, were set a~ reference marks; one in prolongation of the line to the Blind Asylum, St. Louis, and the other in prolongation of the line to Sugar Loaf l\found, each 50 .feet distant. Additional reference marks are nails in the centers of triangles cut on 3 trees, as follows:
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A hickory 64·3 feet distant,· bearing north 41° 3o' east; a white oak J9'3 feet distant, bearing south 57° JO' east, and a hickory 92·;i feet distant, bearing south 51° 3o' east-bearings magnetic.
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Drqer, St. Clair County, Illinois; established in 1871 by R. E. Halter. This station is situated in the southern part of section 27, township I north, range IO west, mi the bluffs, about 6 miles northwest of Centerville, about I j·f miles nearly south of Falling Springs, and nearly east of where the Carondelet rock road, which crosses the bottom, strikes the bluffs. It is on land belonging' to Friedrich Dreyer, about 370 metres west by north from his house and about 17 metres north of the road leading to the bluffs. The apex of an earthenware pyramid, 3 feet below the surface, marks the geodetic point. The surface mark is a spike in the center of a cedar stub, 4 by 4 by JO inches, projecting about 3 inches above the ground. A white marble post, 6 by 6 by 29 inches, with cross lines cut on top and the letters U.S.C.&G.S. cut in the four squares, was set south of the station in the fence line north of the road, a trifle below the surface, distant 64 ·4J feet from the geodetic point and l 210 feet from the northwest corner of Dreyer's corn house. Two other marble posts, 4 by 4 by JO inches: with diagonal lines (arrowhead at encl of one line pointing to the station) were set in the fence line, projecting about 2 inches above the surface, as reference marks-one west and one east of the larger post, the west one distant 107'95 feet and the east one 76·55 from the geodetic point. The following angles were measured at the center: East stone, o0 ·oo'; south stone, 45° ·09'; west stone, 90° · 18'.
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TRANSCONTINENT.'\L TRIANGULATION-PART 'I-BASE LINES.
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79
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Kld11sd1111idt, St. Louis County, Missouri; established in rS71 by R. E. Halter. This station is situated in township 44 north, range 6 east of the fifth principal meridian, on an eminence known as Terrills Hill in the sonthwest part of the commons of Carondelet, south of the River des Peres, on lot belonging to Henry Kleinschmidt, at northeast corner of intersection of Lemay Ferry and Sappington Barracks roads. The apex of an earthenware pyramid, set 2 feet and 4 inches below the surface of the ground, marks
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the geodetic point. The surface mark is a tenpenny nail in the center of a white pine
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stub 4 inches square: Two cedar stubs were set, 41 feet apart, within 1 foot of H1.e fence on the north side of the Sappington Barracks road. as reference marks--one due south of the geodetic point, 41 feet 4 inches distant, and 132 feet distant from the east corner of the lot, the other 37 feet 7 inches distant from the geodetic point and 225Yz feet from the west corner of the lot. Distance from geodetic point to southeast corner of rock foundation c•f Kleinsclunidt's house is 149 feet. and to northeast corner of rock foundation of Bauer's house, south of Sappington Barracks road, 165 feet and 3 inches. The angle at the station between the house corners is 75° 18'.
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(c) O/ue_v Base' Lilu, Illinois, I879.
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LOCATION, MEASUREllIENT, AND LENGTH.
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This base line is due to the labors of the United States Lake Survey, and, on account of its position with reference to· the transcontinental triangulation and its high accuracy, has been incorporated into the scheme of triangulation passing over this region between the American Bottom Base, Illinois, and the Holton Base, Indiana. A full account of the measure of this base is given in ··Report* upon the Primary Triangulation of the United States Lake Survey by Lieut. Col. C. B. Comstock, Corps of Engineers, brevet brigadier-general, United States Army, aided by the assistants of the Survey," to which the reader is referred who may desire more information than what is given here, viz, a brief abstract of a chapter (XII) in that publication.
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The Olney Base is situated on a prairie in the southern part of Jasper County, Illinois, about 13 kilometres (say 8 statute miles) fron~ Olney, about one-half "the length of the line being on cultivated ground and the other on unbroken prairie sod. The line is a straight one, and the greatest difference of elevation of its points is but 7 meters (23 feet); its length is approximately 6·59 kilometres (4·09 statute miles); its middle point is in latitude 38° 51'·s and in longitude 88° 03'·9 west. nearly. The azimuth of the line at the west encl is 268° 301 west of south, about. The ends of the base were marked by granite posts set in brickwork, ·and the terminals are agate hemispheres set in brass cylinders leaded into granite posts, and are 3 feet below the surface of the ground. 'rhe base was divided into 6 nearly equal sections by marks on stones, the mark beitig a drill hole in the top of a copper bol~ leaded into the stone. Each of these sections was measured in duplicate in opposite directions.
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The measurement was made with the Repsold apparatus by a party under the charge of Assistant Engineer E. S. \Vheeler, between July 9 and September 15, 1879. 'rhis apparatus arrived at the Survey office. Detroit, in November, 1876. With it the measurement is made with one tube, which is 4 meters long, and is a metallic thermometer consisting of a bar of zinc:: and a bar of steel joined at their middle points; the tube
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*Profe•sional Paper" of the Corps of Engineers, United States Army, No. 24, Washington, 1.S.S2, pp.J<O-J".5·
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So
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UNITED STATES COAST AND GEODETIC SURVEY.
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lengths are defined between microscopes provided with reading micrometersfor measuring
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interyals between successive tube ends and mounted on .stable iron stands, so constructed
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as to admit of all needed adjustments of the microscopes over the ends of the tube. A
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full description, with plates, of the apparatus and of the manner of using it will be found
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in
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Chapter
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VIII
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of
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the
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1 •
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Professional
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Papers,
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Corps
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of
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Engineers,
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United
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States .Army,
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No. 2+"
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.
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·when used in the field, the tube and microscopes are protected from heat radiation
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by awnings. The apparatus was accompanied by a steel meter designated 11 R. 1876."
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. A line of levels was run along the base lil\e and checked by the observed inclinations of
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the tubes. '!'he average height of these tubes above the mean tidal level of the ocean,
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as found by combinations of various levels, is given for the western part of the Olney
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base 489 ·7 ± 5 ·o feet ( 149 ·25 metres ± 1·5 2) and for the eastern part 480 ·5 ± 5 ·o feet
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{146·45 metres± 1·52). The resulting length and its probable error are given on
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pages 303-304 in terms of the Repsold Metre.
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Olney
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Base
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at
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sea
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level=
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6
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589·2
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(R
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1876
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at
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-1f.61o5
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0
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o
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."7->197Fc
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'. )
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-
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165·04mm ± 3·48mm.
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In order to obtain a reliable value for the length of this metre, it was sent to the International Bureau of Weights and Measures at Sevres, France, in April, 1882, for comparison with the standards of that Bureau. The results are given in Tome III, Travaux et Memoires du Bureau International des Poids et Mesures. Paris, x884. The expansion of R i876 for 1°C was 10·56311; at that time, however, the length of the
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± 'Oii
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Prototype Metre had not been finally adopted, though the uncertainty was supposed not to exceed a few tenths of a micron. The value given is R 1876 = 1111 + 9]·S1J.1 at o0 C.
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We hav.e next the result from direct comparisons of the Committee and the Repsold metres made by Ass~stant 0. H;. Tittmauu at \.Vashington, District of Columbia, between August, 1888, and March, 1S89, for which result see 11 The relation between· the metric standards of length of the United States Coast and Geodetic Survey and the United States I,ake Survey." A report by C. A. Schott and 0. H. Tittmann, Assistants.* From these elaborate observations we have the result (p. 185):
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R 1876 =Committee Metre+ 9S·19J1±0·70Jt at o°C.,
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a result almost identical with that obtained at Paris. In the same report ·we find a comparison of the several independently determined values for the expansion of R 1876, all in excellent agreement, and we therefore adopt the values a R1s76 = 10·606p and ac.,1r. = I 1·795µ (p. I 86); further we take the Committee Metre to represent in length the Iriternational or Prototype. Metre. In this connection see the discussion relating to the standard of length of the transcontinental triangulation; in fact relating to all
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distances determined by the Survey. Substituting the value of R m6 = 1111 + 98· 211 ± 0·7 JI at o0 C. into .the equation given
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above for length of base, we find it to be 6 590·780 4 metres, and if we take± 1Jt for the probable error of the length of the Repsold bar, t that of the base becomes
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...j(6'6f + (3•5)"mm. Or± 7'51111/l. which is about i!HISliu part of the length of the base.
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*Appendix No. 6, Coast and G<:odetic Snn•ey Report for 1889.
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t This can not be cous1dered too l:irge if lVe i-emen1ber that the direct con1parison of line and end 111easnres offers
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special difficulty, part1c11larly when the rcyic·.•· method is applied to the end surface.
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lio.5
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0
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&
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~ 3
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0
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Statute Miles
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..3
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~
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A
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6
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Eilome"tres
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10
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8
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9
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10
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.
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20
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OLNEY BASE NET. ILL. 1879 TO 188'±.
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TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES.· 81
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This may be taken to represent the measuring error, combining it with the probable
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error due to our practical unit of length, the Committee Metre, taken as± ~-~µwe get
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.J<fs)"+q·9)° = ± s·9mm., or about n1looo part of the length. We therefore have
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the final value for length of base 6 590·780 4m., and its logarithm 3·818 936 84
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± 89
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± 59
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ABSTRACT OF RESULTING HORIZONTAL DIRECTIONS OBSERVED AND ADJUSTED AT THE STATIONS FORMING THE OLNEY BASE NET I879, 1883-84. .
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0/11ey East Base, Jasper County, Illinois. November, 1879. 35-centimetre theodolite, T. & S., No. 4. Telescope above ground 11·43 metres. J. H. Darling, observer..
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No. of direction.
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Objects observed.
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Resulting direc- Corrections Final seconds
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tions from station from base-net
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in
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adjustment.
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adjustment. triangulation.
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39
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Claremont
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40
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Check Base
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41
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Onion Hill
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42 Olney Middle Base
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43
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Olney \Vest Base
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44
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Buffalo l\'.Iound
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0
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II
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0 00 oo·oo
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IS 20 42 "II
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Sr 38 03 ·54
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IOI 56 20·04
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IOI 56 23 ·oo
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162 57 14 ·89
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II
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-0·43 +0·35 +0·35 -0·10 -o·o6 -0·12
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II
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59·57 42·46 03·89 I9"94 22·94 I4"77
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Ol11q West Ease', Jasper County, Illinois. October and November, 1879. 35-centimetre theodolites, T. & S., Nos. 3 and 4. Telescope above ground 15·70 metres. R. S. Woodward and J. H. Darling, observers.
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45
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Buffalo l\'.Iound
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46
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Olney East I!::.:::
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47
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Olney Middle Base
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4S
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Check Base
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49
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Claremont
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50 Denver
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51
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Onion Hill
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·o
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II
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0 00 cio ·oo
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47 46 00·53
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47 46 03 ·17
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94 31 34 "7I 99 54 21 ·74 IS3 I6 48·00
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I90 4S 14 ·04
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II
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-0·30 +0·04 +0·40 +0·29 +0·03 +0·15 -0·61
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II
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|
59·70 00·57 03·57 35·00 21 ·77 4S ·15 13·43
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Ol11e_y lJliddlt? Base, Jasper County, Illinois. October, I879. 25-centimetre theodolite, R., No. I. Telescope above ground I ·9S metres. E. S. \Vheeler, observer.
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58
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Olney West Base
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·I 59
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Buffalo Mound
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6o
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Olney East Base
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0
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II
|
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0 00 oo·oo
|
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100 04 09 ·23
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I79 59 53 ·52
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II
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-0·43 +0·3S +0·05
|
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II
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59 ·57 09·6I 53·57
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C/1cck· Base, Richland County, Illinois. November and December, 1879. 35-centimetre theodolite,
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T. and S., No. 4. Tdescope above ground t~:9~....metres. J. H. Darling, observer.
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,,
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0
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II
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II
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34 Claremoilt
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0 00 oo·oo
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+0·60
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oo·6o
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35
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Onion Hill
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127 15 17 ·17
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-0·17
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17 ·oo
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36 Olney West Base
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167 12 31 "73
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-0 "O'J
|
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31 ·66
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. 37 Buffalo Mound
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200 59 15 ·44
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-0·39
|
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15·05
|
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3S Olney East Base
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216 SI 16·S2
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+0·03
|
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I6"85
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18732-No. 4--6
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UNITED STATES COAST AND GEODETIC SURVEY.
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ABSTRACT OF RESUT.TING HORIZONT.U. DIRECTIONS OBSERVED AND ADJUSTED AT THE STATIONS . FORMING THE or.NE\" BASE NET 1879, ~883-84-continued.
|
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011io11 I-fill, Richland County, Illinois. November, I8i9· 35-centimetre theodolite, T. and S., No. 3. Tele~cope above ground I ·83 metres. R. S. \XJ'oodward, observer.
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No. of direction.
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Obj~ct~ observed.
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|
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Resulting directions from station
|
|
adjustment.
|
|
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Corrections from base-net adjustment.
|
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Final seconds in
|
|
triangulation.
|
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|
.52
|
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Buffalo Mound
|
|
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53
|
|
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Olney West .Base
|
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54
|
|
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Olney East Base
|
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55
|
|
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|
Check Base
|
|
|
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56
|
|
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|
Claremont
|
|
|
|
5Z
|
|
|
|
Denver
|
|
|
|
0
|
|
|
|
II
|
|
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|
.o 00 oo·oo
|
|
|
|
4 40 27·96 21 19 56·39
|
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|
48. 26 34 ·48.
|
|
|
|
65 34 23 ·07 I66 59 J2 ·21
|
|
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II
|
|
+0·2I -O'o8 -0·34 +0·49 +0·07 - 0 ·-~5
|
|
|
|
II OO":=?J
|
|
27·88 56·05
|
|
~4"97
|
|
23 ·q II 086
|
|
|
|
Oblo11g, Crawford County. Illinois. October and November, 1879. 35-centimetre theodolite, P. a11d M., No. 2. Telescope above ground 30·94 metres. G. Y. \Visner, observer.
|
|
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22
|
|
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|
Claremont
|
|
|
|
23
|
|
|
|
Buffalo Mound
|
|
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|
24
|
|
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|
Hunt City
|
|
|
|
Casey
|
|
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|
Belle Air
|
|
|
|
0
|
|
|
|
II
|
|
|
|
0 00 oo·oo
|
|
|
|
34 36 "'~I "20 JOO 27 20·78 I32 34 08·03 r6o IO 26·65
|
|
|
|
II
|
|
+0·37 -0·38 +0·02
|
|
|
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II
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00·37 jo·82 20·80
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Buffalo .llfo1111d, Jasper County. Illinois. October and November, I879. -~5-centimetre theodolite, T. and S., No. 1. Telescope above ground 31·24 metres. A. R. Flint, observer.
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25
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Olney East Base
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0
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II
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0 00 oo·oo
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I/
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+o·os
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II
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oo·oS
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26
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Claremont
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27
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Check Base
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:is
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Olney :Middle Base
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29
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Olney .west Base
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30
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Denver
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3I
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·onion Hill
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32
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Hunt City
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II 54 58 ·16 I9 3I 25·93
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39 o_•, 2I 0 6I
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71 I.'J 07·72 73 29 29·29 77 20 53·39 2::?1 26 33·58
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+0·36 +0·09 -0·27 -0°::?6 +0·38 '+o"I7 -0'62
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58·52 26·02 21 ·34 07·46 29·67 53·56 32·g6
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33
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Oblong
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:i66 I5 21:90
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+0·07
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21 ·97
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N,wto11, Jasper ·county, Illinois. October 3 to October 16, I883. 30-centimetre the~dolite,'No. 135. Telescope above ground I::? 065 metres. G. A. Fairfield, observer.
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:3
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Denver
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. I Lucas
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'' Island Creek
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I Hunt City
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2
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I
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!
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Claremont
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0
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II
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0 00 00'00
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79 44 I3"0l
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129 23 45·69
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205 20 35 ·47
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307 38 00·83
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II
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-0·13
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+0·46 -0·32
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/I
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59·87
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35·93 _00·51
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Probable error of a single observation of a direction (D. and R.) = ± 111·00.
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. TRANSCONTINENTAL TRIA.NGULATION-PART I-BASE LINES. S3
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ABSTRACT OF RESULTING HORIZONTAL DIRECTIONS OBSERVED AND .ADJUSTED AT THE STATIOl"S FORMING THE OLNEY BASE NET 1879, I883-84-contihued.
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De11vo-,. Richland County. Illinois. November, I879. 35-centimetre theodolite, T. & S., No. 3.
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Telescope above ground 23·16 metres. R. S. "Woodward, observer. -November r2 to December:!.
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r883. 30-centimetre theodolite, No. 135· Telescope above ground 23 ·16 "metres. G. A. Fairfield.
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observer.
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'
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No. of direction.
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Objects observed.
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Resulting directions from station
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adjustment.
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Corrections from base-net adjustment.
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Final second~ in
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triangulation.
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4
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Newton
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5
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Onion Hill
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6
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Buffalo Mound
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7
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Olney West Base
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8
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Claremont
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Parkershurg
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0
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II
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0 00
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19 57 29 06
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30 07
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So 43 r29 20
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26o 42
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300 I,")
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I/
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+070 +0·09 -0·16 -0·19 -0·44
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II
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00 "jO 16·36 40·87 07 ·14 I3'27
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H1e11t Ci(v, Jasper County, Illinois. October, 1879. 35-centimetre. theodolite, T. & S.. No. 3. Tele-
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scope above ground 23 ·32 metres. R. S. ·woodward, observer.-September 5 to September 17, r8S4. 30-centimetre theodolite, No. 107. Telescope above ground 23 ·32 metres. G. A. Fairfield, observer.
|
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0
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I
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II
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II
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/I
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Belle Air
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0 00 00'00
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Honey Creek
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74 41 37·75
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18
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Oblong
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19
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Claremont
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20
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Buffalo Mound
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21
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Newton
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Island Creek
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75 44 47 ·03 131 OI 27 ·19
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145 05 08'9I 173 22 02 ·r9 232 34 09·67
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+0·12 -0·07 -o·r2 +0·07
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47 ·15 27·12
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o8 ·79 02·26
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Casey
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313 18 25·33
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= Probable error of a single observation of a direction (D. and R.) ± I11'25 in I884.
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Clart'111011t, Richland County, Illinois. November, 1879. 35-centimetre theodolite, P. & M., No. 2.
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Telescope above ground 24·84 metres. G. Y. \Visner, observer.-July 26 to August 22, 1884.
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30-centimetre theodolite, No. 107. Telescope above ground 24·84 metres. G. A. Fairfield, observer.
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9
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Denver
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IO
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Onion Hill
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lI · Olney West Base
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0
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II
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0 00 00'00
|
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17 49 15'39 46 01 29·05
|
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"
|
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+0·65 -0·12 -0·41
|
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N
|
|
00·65 I~ '27 28·64
|
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12
|
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Newton
|
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13
|
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Check Base
|
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14
|
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Buffalo Mound
|
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|
46 54 49·55
|
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53 26 l I '<Y]
|
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66 48 58 ·rs
|
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-0·01 -0·21 -0·30
|
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49·54 m·S6
|
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57·85
|
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15
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Olney East Base
|
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16 Hunt City
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71 56 44·50 82 16 50·46
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-0·23 +0·56
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44 ·27 51 ·02
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17
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Oblong
|
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106 32. 51 ·56
|
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+0·07
|
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51 ·63
|
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Honey Creek
|
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138" 23 II ·73
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Summit
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174 40 19·45
|
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Parkersburg
|
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2i4 17 40·86
|
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|
Probable error of a single observation of a dir~ction ( D. and R.) = ± 111·03 in r884.
|
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|
,UNITED STATES COAST AND GEODETIC SURVEY,
|
|
FIGURE ADJUSTMENT.
|
|
Obsn<'<llio11 t'q11atio11s. *
|
|
+ ( I 0 = + I'6o + ( 12) - ( 9) 8) - (4) -f- (3) - ( 2)
|
|
2 o=+o·oS+(2r)-(19)+(16)-(c2J+ (2)- (r)
|
|
·' O= + 1"2I-!- (30)- (26) T (14) - (9) + (8) - (6)
|
|
+ + ( + ( 4 o= + r·oi (24) - (22) 17)- (I6) 19) - ( rS) + + ( + ( S o = - 0·85 24) - ( 23) (33) - (32) 20) - ( rS) + ( 6 = ll -t- 0·09 + ( 26) -- (33) + ( 23) - ( 22) 17) - ( 14)
|
|
7 0=+1·72+(57)-(56)+(ro)- (9)+ (8)- (S) 8 O= -f-0·51 -j- (56) - (52) + (31) - (26) -j- ( q) - (IO)
|
|
9 o=+nS-!-(50)-(49)+(11)- (9)--i- (8)- (7)
|
|
IO 0 = -f- O" I 8 -f- (49) - (45) -j- ( 29) - ( 26) -f- ( I4) - ( II)
|
|
II O= -j-0·77 -j- (SI) - (49) + (II) - (lo) -j- (56) - (53)
|
|
12 O= - ro8 + (41) - (39) -f- (IS) - (IO)+ (56) - (54)
|
|
13 O= - 0·53 + (43) - (39)-t- ( 15) - (II)+ (49) - (46) 14 O= - 1"03 + (38)·- (35) + (55) - (54)-!- (4r) - (40) rs o = + n8 + (35) - ( 34 l + ( 13) - ( ro) + (56) - (55) 16 O= + 0"06-!- (43) ·~ (40)-!- (38) - (36) :f- (48) - (46) I7 O= +0·04+ (44) - (40) + (38) - (37) + (::!7) - (25)
|
|
I 8 I 0 = _, 1 •53 -f- (59) - (58) -f- (47) - (45 ) + (29) -- ( 28)
|
|
19. 0=+0·71+(6o)-(59)+(28)-(25)-j-(44)-(42) 20 o= -o·ss+ (60)-(58) + (47)-(46) + (43) -(42)
|
|
21 O= -f- 0·32 + (43) - (42) - (47) + (46)
|
|
22 o=- 3·0+·46(1) + n6(2)- r·62(3) -·34(4\ + 1·67(6)- r·33(8)-6·m(19) +s·41(20)
|
|
- 2·31(2!) + 2·58(26) + r14(30) -372(32) 23 O= -j- 3·2 + 5·07(14) - 7"61( 16) + 2·54( I7) +·79(18) - S·4r( r9+ 7"62( 20) + 3·05( 22) - 3·99( 23)
|
|
+·94( 24)
|
|
24 O= - 0·4 - 2·60( 25) -f- 5'95( 28) - 3"35( 29) + l ·17(42) --1'17(44) -I ·91(45) + l '91(47)
|
|
25 o= - r666- 1·1744(5) + 11·975(6) - m·Soo6(7) -3·3447(29) +5·3054(30) -1·96o7(31)
|
|
+ -2·5751(52) r9149(53) +·66o2(57)
|
|
26 0 = + 5;45 -- II ·744( 5) + 13·473( 7) - r729(S) - 2·032(9) + 3·926( IO) - I •&)4( r I) - 7"774( 53)
|
|
+ + 1· 172( 56) 6·602157)
|
|
27 O= + 18·65 - 3·926(IO) -f- 9·471( II) - 5"545(14) - 1"250(26) + 20·$57(29) - 19·607(3r)
|
|
-25·75r(52) + 26·923(53) - n72(56)
|
|
+ + 28 o= +qr - 3·926( 10) 8·258( u) -4·332( 15) +·445(39) 5·69(41) -6·135(43) -5·865(53)
|
|
+ ro37(54) -1·172(56)
|
|
+ + 29 o = + 3·76 - JI"S54( II l 16·186( 13 l - 4·332( 15) - 9·273( 34 l + r4S4(36 l 1..789(38) + ·445( 39)
|
|
+ ·236(40) - ·681(43")
|
|
30 O= -f- 0·77 - 2·513(35) -j- .rJ02(36) - q89(38) -·236(40) -f- 5·69(41) -5·454( 43) - 4·839(53)
|
|
+ ro37(54) - n98(55) + 31 o = - 0·26 - r·213( r 1) 5·545( 14 l - 4·332( 15) -·7r6( 25) + 1"25( 26) - ·534( 29) + ·445( 39)
|
|
+·72r(43) -1·166(44)
|
|
+ 32 o= + o·SS-·716( 25) + 1·663(27) -·947( 29) - 1'359(36) 3·148(37) - qS9(3S) -·236(40)
|
|
+ qo2(43) - 1:166(44)
|
|
*Number of angle equations oi and of side. equations u; in establishing the latter either 7 or S places in the logarith1ns are used and the logarithtnic differences for 1'' are gh~eu in units of the siXth place, with one exception.
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES. 85
|
|
|
|
Correc'tions.
|
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|
C,
|
|
|
|
Corrdatc t'lJllalio11s.
|
|
c. C3 C4 Cs c6 C1 Cs C9 Cro c.. C,. .C,3 C,4 C15
|
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(I)
|
|
(2) -I
|
|
(3) +x
|
|
(4) -I Is.> (6) (7)
|
|
(8) +x
|
|
(9) -I
|
|
( 10)
|
|
(Tl)
|
|
( 12) +x
|
|
( 13)
|
|
( 14)
|
|
(15) (16) (17) ( 18)
|
|
(19) (20) (21) (22) (23) (24) (25) . (26)
|
|
(27) (28)
|
|
(29)
|
|
(30) (31) (32) (33) (34) (35) (36) (37) (38)
|
|
<.w>
|
|
(40) (41) (42)
|
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-I
|
|
+x
|
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-I
|
|
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|
-I
|
|
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|
+r
|
|
-I
|
|
.......
|
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-I
|
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-I
|
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+1
|
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-t-1
|
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|
-I
|
|
|
|
-I
|
|
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|
+1 -I
|
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|
-I
|
|
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|
-I
|
|
|
|
··I
|
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|
|
-t-r -I +r
|
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|
···I
|
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|
|
t I
|
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|
+x
|
|
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|
-I
|
|
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|
-t-r
|
|
|
|
I I
|
|
|
|
·+·r t I .
|
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|
+r
|
|
|
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-I
|
|
|
|
+r
|
|
|
|
+r
|
|
|
|
-I -I
|
|
|
|
-I
|
|
|
|
+1
|
|
|
|
+r
|
|
|
|
+r
|
|
|
|
-I
|
|
|
|
--I
|
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|
|
-I +1·
|
|
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|
+r +1
|
|
|
|
-I
|
|
|
|
+1
|
|
|
|
-I
|
|
|
|
·-I
|
|
|
|
+r
|
|
-I
|
|
-t I -I
|
|
|
|
t·1
|
|
t [
|
|
|
|
·-l
|
|
-I +r
|
|
|
|
+1
|
|
|
|
. -I -I
|
|
|
|
-I
|
|
|
|
+r
|
|
|
|
+r
|
|
|
|
TRANSCONTINENTAL· TR~ANG ULATION-PART I-BASE LINES.
|
|
|
|
87·
|
|
|
|
Li>rrdate ,-q11,1tiv11s-Continued.
|
|
|
|
Corrections.
|
|
|
|
C,6
|
|
|
|
C,1
|
|
|
|
C,s
|
|
|
|
C,9
|
|
|
|
Coo Cor
|
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|
c ••
|
|
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c.3
|
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|
|
Co,
|
|
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|
~25
|
|
|
|
(24) (25) (26) (27) (2S.) .. ( 29) (30) (31) (32) (33.) .. (34) (35) (36) -I (37) (38) +1 (39) (40) -I (41) (42) (43.).: .+r (44) (45.l (46) -I (47) ·(4!l) +1 (49) (50). (51) (52) (53.) ... (54) (55) (56) (57) .(58.).. (59) (6o)
|
|
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-I
|
|
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|
-I
|
|
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|
+1 . -I +1 +1
|
|
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|
+2 ·5S
|
|
+1 ·q -3·72
|
|
|
|
...
|
|
-I
|
|
+1
|
|
|
|
-I
|
|
|
|
...
|
|
|
|
-I
|
|
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|
-·I -I
|
|
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|
+r .. +1 ..
|
|
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|
+r
|
|
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|
+1
|
|
|
|
-I
|
|
-r +r
|
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|
+r
|
|
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|
+r -I
|
|
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|
......
|
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|
···.···
|
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|
-I
|
|
|
|
-I
|
|
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|
+1 -I
|
|
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|
+1 +r
|
|
|
|
+0·94
|
|
|
|
2·60
|
|
|
|
··''······
|
|
|
|
· +5 ·95 . ··3 ·35
|
|
|
|
- 3 ·344 7
|
|
+ 5 ·305 4
|
|
I ·¢o 7
|
|
|
|
••!••····
|
|
i
|
|
|
|
+1 ·17
|
|
- I ·17 -I '9I
|
|
+1 ·91
|
|
|
|
.... ·....
|
|
|
|
-- ~·575 I
|
|
. .... + I '914 'i>
|
|
+ o·66o 2
|
|
|
|
88
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
C1_.rrections.
|
|
|
|
co(i
|
|
|
|
Con-elate t'qualhws-Continued.
|
|
|
|
c.7
|
|
|
|
c.s
|
|
|
|
c.o
|
|
|
|
C:io
|
|
|
|
c ..
|
|
|
|
c3'>
|
|
|
|
(I) (2) (3) \4) (5) -TI °744 (6) (7) +13 ·473 (8) - I ·729 (9) - 2 ·032 (IO) + 3 ·926
|
|
(II) - I •894
|
|
(12) ( r3) (14) (rs) (r6) (r7) (r8) (19) (20) (21) (22) (23) (24) ( 25) (26) (27) (28) (29) (30) (31) (32)
|
|
(33) (34) (35) (36) (37) (38) (39) (40) (4I) (42)
|
|
|
|
- 3 ·926 + 9 ·47r - 5·545
|
|
- I '250 . +20·857
|
|
.....:19 ·6o7
|
|
|
|
-:; 9:6 +8·.58 -4·332
|
|
.. ..
|
|
+0·445 +s·69
|
|
|
|
- p :854 +rG-·186 - 4·332
|
|
|
|
........
|
|
|
|
- 9·273
|
|
+ 7 ·484
|
|
+I 789 + 0·445 + 0·236
|
|
|
|
-2 ·5r3 -f-4·302
|
|
-I •789
|
|
--o ·236 +s·69
|
|
|
|
........
|
|
|
|
- I "2I3
|
|
+s ·545 -4 ·332
|
|
|
|
. ········
|
|
|
|
-0·7r6 +r ·25
|
|
-0·534
|
|
|
|
-0·7r6 +r ·663 -0·947
|
|
|
|
+o·M.s
|
|
|
|
- I ·359 +3 ·148 -I ·789
|
|
-0·236
|
|
|
|
Corrections.
|
|
|
|
TRANSCONTINENTAL TRIANGULATIQN-PART I-BASE LINES.
|
|
|
|
lorrdali' ,·q1111tio11s~Completecl.
|
|
|
|
c.6
|
|
|
|
. c.1
|
|
|
|
C.s
|
|
|
|
C29
|
|
|
|
·c,.,
|
|
|
|
c.,
|
|
|
|
89
|
|
C31
|
|
|
|
(43) (44) '(45) (46) (4i) (48) (49) (50) (51) (52)
|
|
·. (53) (54) (55) (56) (57)
|
|
|
|
- 7 ·774
|
|
+ l "172 + 6·6o2
|
|
|
|
-25 ·751 +26 ·923
|
|
- I. ·172
|
|
|
|
-6 ·135
|
|
-5 •865 +7 ·0.,7 -1 ·172
|
|
|
|
- 0·681
|
|
|
|
-5 ·454
|
|
|
|
+0·721 -1 '166
|
|
|
|
--4·S39 +7 ·037. -2·198
|
|
|
|
-tr ·402 - I '166
|
|
|
|
90
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
A'ormal e·qm1tio11s.
|
|
|
|
C,
|
|
-----
|
|
|
|
c.
|
|
|
|
C3
|
|
|
|
c• Cs
|
|
|
|
c6
|
|
|
|
C;
|
|
|
|
Cs
|
|
|
|
Cg
|
|
|
|
C10 C,.
|
|
|
|
C,.
|
|
|
|
C,3
|
|
|
|
c,.
|
|
|
|
C,s
|
|
|
|
O=+ I "00 +6 -:? +:?
|
|
|
|
+2
|
|
|
|
+2
|
|
|
|
+o·oS
|
|
|
|
+6
|
|
|
|
-2
|
|
|
|
-f- I "21
|
|
|
|
+6
|
|
|
|
-2 +2 +2 +2 +2
|
|
|
|
+I "02 -0·85
|
|
|
|
+l? +2 +2
|
|
-t-6 -2
|
|
|
|
+0·09
|
|
|
|
-t-6
|
|
|
|
-2
|
|
|
|
-2
|
|
|
|
+I ·72
|
|
|
|
+6 -2 +2
|
|
|
|
-2 -2
|
|
|
|
-2
|
|
|
|
+ o·.5r
|
|
·+I "18
|
|
|
|
+6
|
|
|
|
+2 +2 +2
|
|
|
|
+2
|
|
|
|
+6 ·-2 +2
|
|
|
|
--2
|
|
|
|
+o·r8
|
|
|
|
+6 -2
|
|
|
|
+2
|
|
|
|
+0·77
|
|
|
|
+6 +2 :-2
|
|
|
|
+2
|
|
|
|
- I "o8
|
|
|
|
-t-6 +2 +2 +2
|
|
|
|
-0·53 - l "03
|
|
|
|
-t-6 ··+6 -2
|
|
|
|
-f- I "28
|
|
|
|
+6
|
|
|
|
Normal eq11alio?1S-:-Conti11ued.
|
|
|
|
C,6 C,1 C,s C,9 Coo C.,
|
|
|
|
c ••
|
|
|
|
c •.•
|
|
|
|
c.,
|
|
|
|
c.s
|
|
|
|
+ I '00
|
|
+ 0·08 + I "21
|
|
+ I '02 0·85
|
|
+ 0·09 + J 72
|
|
+ o·sr + 1·rs
|
|
+ 0·1S + 0·77
|
|
r ·as
|
|
0·53 +2
|
|
I "03 +2
|
|
+ I "28
|
|
o=+ 0·06 +6 + 0·04 I ·53
|
|
+ 0 "71 o·ss
|
|
+ 0·32
|
|
3·0
|
|
+ 3·2
|
|
0·4
|
|
- .[ '666
|
|
|
|
3 'i7
|
|
+· 4·49 + o·So
|
|
|
|
4·44 + 5 ·07
|
|
|
|
6"!0
|
|
|
|
I "I6
|
|
|
|
+ 12 ·13
|
|
+ 2·58
|
|
|
|
+ I I ·76
|
|
9 ·57
|
|
|
|
1 ·33
|
|
|
|
2·58 + s ·07
|
|
|
|
I '33
|
|
|
|
+z
|
|
|
|
2·58 + 5 '07
|
|
|
|
-t-2 +2
|
|
|
|
+2
|
|
|
|
+2
|
|
|
|
-t-6
|
|
|
|
+2
|
|
|
|
+6 -2 ·+2 -I
|
|
|
|
-t-6 +2 +r
|
|
|
|
+6
|
|
|
|
+4
|
|
|
|
+143·924 +us ·385
|
|
|
|
-t-245 ·59
|
|
|
|
6•6696
|
|
|
|
- I "44
|
|
|
|
+ I '8346 + 0 ·6144 + ro·Soo6
|
|
3·3447 I ·9149
|
|
|
|
+ 1·43 - 5·48 + 6"21
|
|
+ 074 - 3·oS
|
|
|
|
3·3447 + 26 ·046
|
|
|
|
+63 ·42 . + II ·205 +-'15 "J.l.5
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES.
|
|
|
|
91
|
|
|
|
Normal equatio11s-Completed.
|
|
|
|
c"6
|
|
|
|
c.,
|
|
|
|
C.s
|
|
|
|
c.9
|
|
|
|
C;.,
|
|
|
|
C3,
|
|
|
|
C3•
|
|
|
|
+ r·6o
|
|
+ o·oS + I '21 + I '02 - 0·85 + 0·09 + 1 ·72 - 0·51 + I '18 + 0·18 + q·77 - I ·oS
|
|
- 0·53 - I '03
|
|
+· i·2s
|
|
+ 0'06 + 0"·04
|
|
- l '53 + 071 - 0·88
|
|
+ 0·32
|
|
- 3·0 + 3·2 - 0·4
|
|
- J "666
|
|
o=+ S ·45 +18 ·65 + I 71
|
|
+ 3 76
|
|
+ 0·77
|
|
- 0·26 + 0·88
|
|
|
|
+ 0·303 + o.·303
|
|
|
|
+ 2I ·403
|
|
|
|
2·754
|
|
|
|
i5·064
|
|
|
|
I
|
|
T
|
|
|
|
r ·894
|
|
|
|
+ 3 ·126
|
|
|
|
2 '754
|
|
|
|
+ I 0894
|
|
|
|
2·754
|
|
|
|
+ 2·299
|
|
-142 ·251 +4so·95
|
|
|
|
4·295
|
|
|
|
+ 4 ·295
|
|
|
|
+ 4·295
|
|
|
|
2 '754
|
|
|
|
2·754
|
|
|
|
+ 4·603
|
|
+ 9·471
|
|
+ 7 ·091
|
|
l4 ·6gS
|
|
|
|
+ 2 '754 + 8·258
|
|
8. 258
|
|
+ 16·877
|
|
|
|
+ 2 '754
|
|
|
|
3·370
|
|
|
|
9·471
|
|
|
|
19 ·170
|
|
|
|
I '347
|
|
|
|
+ 2'754'. + 2 754
|
|
|
|
6 ·135
|
|
|
|
+ 20"·857·
|
|
|
|
·3 ·225 28 'll3
|
|
- 69 ·S74
|
|
+ 86'549
|
|
-244 ·025
|
|
+2346 '21
|
|
|
|
6 ·135 6 ·135
|
|
- II '231 + 13 ·167 - 62 ·905 +257 ·877
|
|
|
|
+ 4 ·295
|
|
|
|
Il ·854
|
|
+ II ·854 II ·854
|
|
4 777 + 6 ·39"i
|
|
+ [ ·553
|
|
+ 25 ·459 6·612
|
|
+ I '553
|
|
|
|
+ 4> ·839 l '347 5·454 2·585 0·3-15 JI '309. I '553
|
|
|
|
o·6Sr 0·681
|
|
|
|
5·454 5'454
|
|
|
|
- 9 ·267
|
|
|
|
+ 22 ·45~ +. 3~ '618
|
|
|
|
-Il2 '269 -130 ·28o
|
|
|
|
- · 74 748 · · +r4~nJ6
|
|
|
|
+ +s67 ·.19
|
|
|
|
32 ·658
|
|
|
|
. +167 ·967
|
|
|
|
+ 4 ·295
|
|
- I '213
|
|
+ 4 '974 - I '213 - 4 ·777 - 2·843
|
|
+ 0·721 - o. 450 - 0·534 - p·450
|
|
+ 0 '721
|
|
+ 0 ·721 + 3 ·225 +28 'II3
|
|
+ 5 ·015
|
|
+ I .'786 + ,2 ·29'3 -54 ·935
|
|
+ 4 ·524
|
|
+32 ·851 - ,; ·932· +5s ·422
|
|
|
|
- 0·947
|
|
+ I ·402 - l '553
|
|
+ i ·2o8
|
|
-: 3 ·488 - 0·947 - 0·450 + I ·402 + I ·402
|
|
+ 6·398 + 3·168
|
|
-19 ·752 - 8·601 -14 ·383 -IO '237
|
|
+ 3 ·389
|
|
+:?2 ·513
|
|
|
|
92
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
Res11ltint( ·values of corrdales a11d of corrcctio11s to a11g11lar directio11s,
|
|
|
|
CI=-o ·5C}S 2
|
|
|
|
c 9=+0·152 4
|
|
|
|
Cr7=to ·r95 o
|
|
|
|
C25=+0 ·059 44
|
|
|
|
2 -0·590 4
|
|
3 +0·390 3 4 -I ·745 2 5 +.r ·688 3 6 +1 ·618 0 7 -0·685 7 8 -j-0·003 5
|
|
|
|
IO +0·199 9 II -0 ·612 I I2 +r ·r33 6 13 -0·631 I I4 -0787 5 15 -1·r27 I 16 +0·288 0
|
|
|
|
rs +0·066 6 19 -0·314 5 20 +0·365 7 21 +0·065 9 22 -0·286 7 23 +0·078 6 24 +0·018 44
|
|
|
|
26 +0·044 86 27 -0·014 35 28 +o·o6S 6o 29 +o ·056 51 30 -0·067 75 3r -j-0·044 29 32 -0·062 67
|
|
|
|
Corrections:
|
|
|
|
(1)=+0·458 5
|
|
|
|
(2)
|
|
|
|
·324 s
|
|
|
|
(3)
|
|
|
|
·133 7·
|
|
|
|
(4) + ·695 7
|
|
|
|
(5) + ·o89 I
|
|
|
|
(6)
|
|
|
|
·157 3
|
|
|
|
(7)
|
|
|
|
·190 0
|
|
|
|
(8)
|
|
|
|
·437 5
|
|
|
|
(9) + ·650 0
|
|
|
|
(10)
|
|
|
|
'120 5
|
|
|
|
(II)
|
|
|
|
·4o6 5
|
|
|
|
(r2)
|
|
|
|
·007 8
|
|
|
|
(13)
|
|
|
|
'212 4
|
|
|
|
(14)
|
|
|
|
·300 6
|
|
|
|
(15)=-0"::!31 4
|
|
|
|
(16)=+0·556 7
|
|
|
|
(17) + ·072 4 (18) + 'II9 o·
|
|
(19) ·o66 9
|
|
|
|
(20)
|
|
|
|
'123 9
|
|
|
|
(21) + ·071 9 (22) + ·366 9
|
|
|
|
(23)
|
|
|
|
·383 9
|
|
|
|
(24) + ·017 0
|
|
|
|
(25) + "o84 8
|
|
|
|
(26) + ·357 9
|
|
(27) + ·090 s
|
|
|
|
(28)
|
|
|
|
·271 4.
|
|
|
|
. (29)
|
|
|
|
·2~7 7
|
|
|
|
(30)=+0·378 9
|
|
|
|
(31)=+0 ·168 4
|
|
|
|
(32)
|
|
|
|
·621 8
|
|
|
|
(33) + ·070 3·
|
|
|
|
+ (34)
|
|
|
|
'003 I
|
|
|
|
(35)
|
|
|
|
·169 3
|
|
|
|
(36)
|
|
|
|
·071 5
|
|
|
|
(37)
|
|
|
|
·392 3
|
|
|
|
(38) -\- ·029 9
|
|
|
|
(39)
|
|
|
|
·427 2
|
|
|
|
(40) + ·348 6
|
|
|
|
(41) + ·350 9
|
|
|
|
(42)
|
|
|
|
·095 5
|
|
|
|
(43)
|
|
|
|
·057 5
|
|
|
|
(44)
|
|
|
|
'II9 6
|
|
|
|
(45)=-o ·301 9
|
|
|
|
(46J=+o·043 3
|
|
|
|
(47) + ·401 8
|
|
|
|
(48) + ·288 0
|
|
|
|
(49) + ·028 5
|
|
|
|
(50) + ·152 4
|
|
|
|
(51)
|
|
|
|
·612 I
|
|
|
|
+ (52)
|
|
|
|
'212 9
|
|
|
|
(53)
|
|
|
|
·oS3 6
|
|
|
|
(54)
|
|
|
|
·340 2
|
|
|
|
+ (55)
|
|
|
|
·488 5
|
|
|
|
(56) + ·072 6
|
|
|
|
(57)
|
|
|
|
·350 3
|
|
|
|
(58)
|
|
|
|
·432 3
|
|
|
|
(59) + •381 I
|
|
|
|
(6ol=:'+o·o51 2
|
|
|
|
Check: .:s'f''''=+s ·¢4 3 -.:s'iuC=+5 ·¢3 S
|
|
|
|
:S+corrections=7 ·701 r .::s'-corrections=7 ·701 4
|
|
|
|
Letting n stand for the number of .conditions we have-
|
|
|
|
Mean error of an observed direction
|
|
|
|
1
|
|
11Z,= 1T:ifP.=±0 :43
|
|
1l
|
|
|
|
Mean error of an-angle
|
|
|
|
111L='11,../2 =±o ·61, also
|
|
|
|
Probable error of an angle
|
|
|
|
=±0·41
|
|
|
|
TRANSCONTINENTAL ·TRIANGULATION-PART I-BASE LINES.
|
|
|
|
93
|
|
|
|
TRIANGLES OF THE OLNEY BASE NET, ILLINOIS, 1879, 1883-84.
|
|
|
|
No. Stations.
|
|
IBuff•lo Mound Olney East Base
|
|
Olney West Base
|
|
|
|
Observed angles.
|
|
|
|
0
|
|
|
|
!I
|
|
|
|
71 13 07·72
|
|
|
|
6r 00 5r •Sc)
|
|
|
|
47 46 00·53
|
|
|
|
oo·q
|
|
•oo { Ol0<y Middlo B= 04 09·23
|
|
|
|
2 Olney West Base 47 46 03 'I7
|
|
|
|
Buffalo Mound
|
|
|
|
32 09 46 'II
|
|
|
|
C
|
|
|
|
Spher- Spher- ·
|
|
|
|
tfrrec- ical ical
|
|
|
|
Oils. angles. excess.
|
|
|
|
II
|
|
-0·34 -o·o6
|
|
+0·34
|
|
|
|
II
|
|
o7·3S 51 ·S3 00·87
|
|
|
|
II
|
|
0·03 0·03 0'02
|
|
|
|
o·o8 +o·Br 10'04 O'OI +0·70 03·87 O'Ol +0·02 46 ·13 0'02
|
|
|
|
Logarithms.
|
|
|
|
Distances in metres.
|
|
|
|
3 ·SrS 936 S 3·784 5i9 2 3\712 r75 5
|
|
|
|
6 590·7So 6 oS9·47 5 r54 ·37
|
|
|
|
3·784 579 2
|
|
3·660 So2 7
|
|
3·517 499 3
|
|
|
|
6 oS9·47 4 579·34 3 292·30
|
|
|
|
~ 58 ·5r { Olnoy Middlo Ba~ 79 55 44·29 3 Buffalo Mound 39 03 :n ·61
|
|
Olney East Base 61 00 54·85
|
|
|
|
-0·33 -0·36 -0·02
|
|
|
|
43 ·96 21 ·25 54·83
|
|
|
|
0·04 0·01 O'Ol 0·02
|
|
|
|
3 ·712 175 5 . 3·5r8 3r3 9 3·66o So2 6
|
|
|
|
5 I54 '37 3 298·48 4 579·34
|
|
|
|
I Check Rase l4 Olney West Base
|
|
Buffalo Munud
|
|
|
|
33 .46 94 31 5r 4r
|
|
|
|
00 '75 43 ·7r 34 '7I 4r '79
|
|
|
|
-0·32 +0·59 -0·35
|
|
|
|
0·04 43 ·39. 0·04 35 ·30 0·05 41 '44 0·04
|
|
|
|
3 784 579 l 4·038 158 0 3 ·934 229 7
|
|
|
|
. 6 089·47 ·IO 918 '37
|
|
8 594 '68
|
|
|
|
JCheck Base
|
|
l5 Olney West Base
|
|
Olney East Base
|
|
|
|
00 '21 49 38 45·09 46 45 34 ·rs 83 35 40·89
|
|
|
|
+0·10 +0·25 -0·41
|
|
|
|
45 ·19 34 '43 40·48
|
|
|
|
0·13 0·03 0·04 0·03
|
|
|
|
3·8r8 936 8 3'799 370 I 3·934 229 7
|
|
|
|
6 590 ·7So 6 300·43 8 594·68
|
|
|
|
(Chock"'~
|
|
6 Buffalo Mound Olney East Base
|
|
|
|
00'!6 IS .52 OI ·.~8 r9 .3r 25·93 144 .36 32 78
|
|
|
|
0·10 +0·42 OI ·So 0'02 +o·or 25 ·94 0'02 -0·47 32 ·31 0'01
|
|
|
|
3 ·712 r75 5 3 '799 370 I 4 ·038 158 0
|
|
|
|
5 154·37 6 300·43 IO 918·37
|
|
|
|
00·09
|
|
|
|
{Onion Hill 7 Buffalo Mound
|
|
|
|
4 40 27 ·96 6 07 45·67
|
|
|
|
Olney West Base 169 II 45'96
|
|
|
|
-0·30 +0·42 +0·31
|
|
|
|
27·66 46·09 46·27
|
|
|
|
0·05 O'OI o·oo 0·01
|
|
|
|
3 7!t1 579 2 3 ·901 934 2 4·146 340 6
|
|
|
|
6 o89•47 7 978 '74 14 006·85
|
|
|
|
JOnion Hill
|
|
l8 ~uffalo Mound
|
|
|
|
59·59 2I 19 56·39 77 20 53·39
|
|
|
|
Olney East Base . 81 19 11 ·35
|
|
|
|
-0·56 +o·oS -0·47
|
|
|
|
55 ·83 53·47 10·88
|
|
|
|
0·02 o·o6 o·o6 o·o6
|
|
|
|
3 ·712 175 5 4 ·140 668. 5 4 ·146 346 5
|
|
|
|
5 154 ·37 13 825 'II 14 oo6·S5
|
|
|
|
JOnion Hill
|
|
l9 Buffalo Mound
|
|
Check Base
|
|
|
|
OJ '13 48 26 34·48 57 49 27 ·46' 73 43 58·27
|
|
|
|
+0·27 +0·08 -0·23
|
|
|
|
34·75 27·54 5S·c4
|
|
|
|
0·18 0'11 O'II 0'11
|
|
|
|
4·038 158 0 4;'091 670 2 4 ·146 340 4
|
|
|
|
IO 918•37 12 ;;so ·09 14 006·85
|
|
|
|
00'21
|
|
|
|
0·33
|
|
|
|
94
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
TRIANGLES OF THE or.NEY BASE NET, II.LINOIS, 1879, 1883-84-continued.
|
|
|
|
No. Stations.
|
|
|
|
Obsen·erl angles.
|
|
|
|
Correc- Spher- Sphertions:· 1ca I 1cal
|
|
angles. excess.
|
|
|
|
.
|
|
Logarithms.
|
|
|
|
Distances in metres.
|
|
|
|
{ Onion Hill 10 Olney \Vest Base
|
|
Olney East Base
|
|
|
|
0
|
|
16 39 r43 Ol 20 18
|
|
|
|
II
|
|
28 "4., 13 ·51 19 ·46
|
|
|
|
II
|
|
-0·26 -0·65 -0·41
|
|
|
|
II
|
|
28 ·17 r2 "86 19·05
|
|
|
|
II
|
|
o ·02 0·03
|
|
0·03
|
|
|
|
3·S18 936 8 4·140 668 5 3·901 934 0
|
|
|
|
6 590·7So 13 825 "II 7 978·73
|
|
|
|
r.Onion Hill
|
|
lII Olney \Vest Base
|
|
Check Base
|
|
I Onion Hill
|
|
l12 Olney East Base
|
|
Check Base
|
|
|
|
01 ·40 43 46 06 ·52 96 16 39".B 39 57 LI ·56
|
|
00 ·,p 27 06 38·09 63 17 21 ·43 89 35 59 ·65
|
|
|
|
+0·57 -Cl ·go +0·09
|
|
|
|
07 ·09 38 "4.~ I4 ·65
|
|
|
|
o·os o·o6 I) •o6 0·05
|
|
|
|
+0·83 o·oo
|
|
+0·20
|
|
|
|
38·92 21 ·43 59·85
|
|
|
|
0 ·r7 0·07 o·o6 0·07
|
|
|
|
3·934 229 7 . 4 ·091 670 2
|
|
3 ·901 934· 0
|
|
|
|
8 59,i "68 I2 350·09 7 978·73
|
|
|
|
3·799 370 1 4·091 670 3 4 ·140 668 5
|
|
|
|
6 300·43 12 350·09 I3 825 "II
|
|
|
|
{ ci.~mont 13 Onion Hill
|
|
Olney \Vest Base
|
|
|
|
59 ·17 28 12 I,) ·66
|
|
6o 53 55 "II 90 53 52·30
|
|
|
|
-0·29 +0·16 -0·64
|
|
|
|
13 ·37 55 ·27 51 •66
|
|
|
|
O"::!O b "IO O"IO
|
|
0"10
|
|
|
|
3 ·901 934 l 4·1688260 4·227 3So 2
|
|
|
|
7 978·74 I4 751 ·rs r6 8So·30
|
|
|
|
, lClaremont Onion Hill
|
|
Check Base
|
|
!Cl•=>0nt
|
|
15 Onion Hill
|
|
Buffalo l\foun•l.
|
|
|
|
01 "07 35 36 "55"68 I7 Oj 48·59 127 15 17 ·17
|
|
or ·44 48 59 42 ·76 65 34 23·07 65 25 55·23
|
|
|
|
-0·09 -0·42 -0··77
|
|
|
|
55"59 48 ·17 16"40
|
|
|
|
0·30 0·05 0·05 0 ·06
|
|
|
|
--o ·18 -0·14 -0·19
|
|
|
|
42·58 2~ "9.) 55·04
|
|
|
|
o·r6 0·18 0 ·19 0 ·18
|
|
|
|
4 ·091 670 2. 3 ·795 6.)8 4 4·227 3So 2
|
|
|
|
I2 350·09 6 246·52 16 8So·30
|
|
|
|
4 ·r46 340 5 4·227 867 4 4·227 38o l
|
|
|
|
q oo6·85 16 899 ·25 16 88o ·30.
|
|
|
|
{ Cl•~ont 16 Onion Hill
|
|
01 ney East Base
|
|
lCfai<'mont
|
|
17 Olney West Base Check Base
|
|
I Claremont
|
|
l18 Olney West Base
|
|
Buffalo Mourid
|
|
|
|
or ·06
|
|
54 07 29 "II
|
|
44 I4 26"68
|
|
Sr 38 03·54
|
|
59·33 7 24 42 ·02 5 22 47·03 167 12 31 ·73
|
|
I
|
|
00·78 20 47 29 ·ro 99 54 2r ·74 59 18 09·56
|
|
|
|
00·40
|
|
|
|
-O"ll
|
|
+0·41 +078
|
|
|
|
29·00 27·09 0'.i-"32
|
|
|
|
0·55 0·14 0·13 o·14
|
|
|
|
4 ·140 668 5 4·075 679 3 4·227 38o 1
|
|
|
|
0·41 +0·19 42·21 O'OI -0·26 46·77 Cl "01 -Cl "68 31 ·05 o·or
|
|
|
|
3·934 229 7 3 ·795 638 7 4 "168 826· l
|
|
|
|
+o·n -1-0·33 -0·62
|
|
|
|
0·03 29 "21 0·07 22·07 o·os oS·94 ·0·07
|
|
|
|
0":22
|
|
|
|
3:784 579 2 4·227 867 5 4 ·168 826 0
|
|
·I
|
|
|
|
13 825 "II II 903 ·63 16 8So·30
|
|
s 594·68
|
|
6 246·53 I4 751 ·16
|
|
6 u89·47 16 899"·25 I4 751 ·15
|
|
|
|
TRANSCONTINENTAL TRIANGULATION-PART I-BASE LINES.
|
|
|
|
95
|
|
|
|
'fRIANGLES OF THE OLNEY BASE NET, ILLINOIS, J879, J883-84--continued.
|
|
|
|
No. Stations.
|
|
|
|
Observed angles.
|
|
|
|
( Cfa~•ont 19 Olney West Base
|
|
Olney East Base
|
|
|
|
0
|
|
|
|
II
|
|
|
|
2S ·ss IS "4S
|
|
|
|
s2 oS· 21 ·21
|
|
|
|
IOI 56 23·00
|
|
|
|
f Claremont
|
|
l20 - Check Base Buffalo Mound
|
|
|
|
I3 22 IS9 •00
|
|
7 36
|
|
|
|
s9·66 47 ·08 44·s6 27·77
|
|
|
|
Correc- Spher- Spher-
|
|
|
|
t" · 1cal 1cal
|
|
|
|
10118 "
|
|
|
|
angles.
|
|
|
|
excess.
|
|
|
|
II
|
|
+0·18 -0·02
|
|
+0·37
|
|
|
|
II
|
|
IS"63 2I ·r9 23·37
|
|
|
|
II
|
|
0·07 0·06 ci "(16
|
|
|
|
".
|
|
-0·09 46·99 +1 ·00 4S'56 -0·26 27"5I
|
|
|
|
O"I9 0'02 0'02 0'02
|
|
|
|
·L-0gari thms.
|
|
|
|
Distances in metres.
|
|
|
|
3 ·818 936 8. 4 ·075 679 4 4 '168 826 0
|
|
|
|
6 S90 780 II 9'J3 ·63 I4 751 ·1-s
|
|
|
|
4 ·o.:;8 158 o 4 ·227 867 4 3'79S 638 7
|
|
|
|
IO 918 '37 16 899 ·25 6 246·53
|
|
|
|
JClaremont
|
|
l2I Check Base Olney East Base
|
|
|
|
59·41 IS 30 33·43 143 oS 43 ·18 J8 20 42 "II
|
|
|
|
o·o6 -0'02 33 ·.p 0·02 +o·sS 43·76 0·02 +0·78 . 4~ ·s9 0'02
|
|
|
|
3·799 370 r 4·07s 679 4 3'79S 638 3
|
|
|
|
6 300·43 II go3·63 6 246·s2
|
|
|
|
·1Cla«moot
|
|
22 Buffalo Mound Olney East Base
|
|
ID""" 23 Onion Hill Buffalo Mound ID•n«< 24 Onion Hill · Olney West Base
|
|
|
|
s8 72
|
|
s 07 46:35 II 54 sS ·16 162 57 14 ·89
|
|
|
|
s9·40
|
|
9 09 24 76 I66 S9 ·12 ·2r
|
|
3 51 24·10
|
|
|
|
IO 09 162· I8
|
|
7 3I
|
|
|
|
01 '07 SI •o6 44·2s 26·04
|
|
|
|
+0·07 +0·27 +0·31
|
|
|
|
. 0'06
|
|
46 ·42 0·02 5-~ ·43 o·or 15 '20 0'02
|
|
|
|
-0·2s -0·56 - 0 '21
|
|
|
|
0·05 24 ·sr · o·or II "65 0·02
|
|
2.1 ·s9 0'02
|
|
|
|
.:._0·28 -0·27 -0·76
|
|
|
|
0·05 s?·7S O'OI 43 ·98 0"01 2s ·28. 0"02·
|
|
|
|
3·712 175 5 4·075 679 4 4·227 867 s
|
|
|
|
s 154 "37 II 903 ·63 I6 899·25
|
|
|
|
4 •146 340 5 4·297 098 3 3·772 326 8
|
|
...
|
|
3"gDI 934 I
|
|
4"I37 89-".l 6
|
|
J-'772 327 0
|
|
|
|
14 oo6·85 I9 8I9;75 5 920·07
|
|
7 978 74 I3 737 ·21. 5 920·07
|
|
|
|
· (Den~
|
|
2s Onion Hill · Claremont
|
|
|
|
oi ·35 6o 45 S7 ·44 IOI 24 49 ·r4 17 49 I5 ·39
|
|
|
|
-o·s3 -0·42 -077
|
|
|
|
0·04 s?·91 0 ·o.'l
|
|
48 72. 0 ·og.
|
|
I4 ·62 o·oS
|
|
|
|
4 ·227 38o 2 .4 '2i7 875 3 . 3·772 327 0
|
|
|
|
16 8So;30 I8. 961 ·62
|
|
5 920·07
|
|
|
|
r Denver
|
|
l26 Buffalo Mound
|
|
Olney West Base
|
|
|
|
I 00 2 16 I76· 43
|
|
|
|
01 ·97 26·30 2I ·57 I2'00
|
|
|
|
0·25 -0·036 26·264 0·004 +0·634 22·204 0·004 -0 ·456 I I "544 0 '004
|
|
|
|
3 ·784 579 2 4 "I37 Sg8 8 4·297 ogS I
|
|
|
|
6 089·47 I3 737 '22 19 ·SI9 7~.
|
|
|
|
lJ Denver
|
|
27 Buffalo Mound Claremont
|
|
|
|
59·87 5I 36 32·68 6I 34 31 "I3 66 48 58 ·15
|
|
|
|
....:.0·28 +0·02 -0·95
|
|
|
|
O"OI2 32·40 0·25 31 "IS 0·25 57·20 0·25
|
|
|
|
4·227 867 5 4·277 SiS 4 4·297 098 5
|
|
|
|
I6 899·25 18 961 ·62 19 819·76
|
|
|
|
01 ·96 I·
|
|
|
|
0 "75
|
|
|
|
96
|
|
|
|
UNITED STATES COAST AND GEODETIC SURVEY.
|
|
|
|
TRIANGLES OF THE OLNEY BASE NET, lLI.INQlS, 1879, 1883-84-continued.
|
|
|
|
No. Stations.
|
|
|
|
.Observed angles.
|
|
|
|
!Don~
|
|
28 ~llney West Base · Claremont
|
|
|
|
0
|
|
|
|
II
|
|
|
|
50 36 o6 ·38
|
|
|
|
83 22 26·26
|
|
|
|
46 01 29·05
|
|
|
|
Correc- Spher- Sphertion 1cal 1.cal
|
|
s. angles. excess.
|
|
|
|
II
|
|
-0·25 +0·13 -1·o6
|
|
|
|
II
|
|
o6 ·13 26·;:9 27·99
|
|
|
|
II
|
|
0 ·17 0 ·17 0 ·17
|
|
|
|
Logarithms.
|
|
|
|
Distances in metres.
|
|
|
|
4 ·168 826 0 4·277 875 3 4 ·137 898 5
|
|
|
|
14 751 ·15 18 961 °62 13 737 ·21
|
|
|
|
lr Newton
|
|
29 Claremont Denver
|
|
|
|
OI 0 69 52 21 59 ·17 46 54 49·55 So 43 13 '71
|
|
|
|
0·51 +0·19 59 ·36 0·28 -0·66 48·89 0·28 -r ·13 12·58 0·27
|
|
|
|
4 ·277 875 3 4·242 702 7 4'373 466 I
|
|
|
|
18 961 °62 17 486·49 23 630 ·13
|
|
|
|
r Hunt City
|
|
l30 Claremo11t
|
|
Buffalo Mound
|
|
!Hunt City
|
|
31 Claremont
|
|
Newton
|
|
|
|
02 ·43 14 03 41 ·72 15 27 52·31 150 28 24·58
|
|
58·61 42 20 35·00 35 22 00·91 102 17 25·36
|
|
|
|
-o"o6 +0·86 +0·98
|
|
|
|
41 •66 53·17 25·56
|
|
|
|
0·83 0·13 0·13 0·13
|
|
|
|
+o·q +0·56 -0·78
|
|
|
|
35·14 or ·47 24·58
|
|
|
|
0·39 0·40 0·40 0·39
|
|
|
|
4·227 867 5 4 ·268 259 5 4·535 016 4
|
|
|
|
16 899·25 18 546·39 34 '278 ·07
|
|
|
|
4·373 466 l 4·307 622 I 4·535 016 5
|
|
|
|
23 630 ·13 20 305·39 3.J. 278 ·08
|
|
|
|
J Oblong
|
|
l32 Claremont Buffalo Mound !Obl~g · 33 Claremont
|
|
Hunt City
|
|
!Oblong
|
|
34 Buffalo Mound
|
|
Hunt City
|
|
|
|
34 36 39· 43 105 39
|
|
|
|
01 ·27 31 ·20 53·41 36·26
|
|
|
|
00·87 100 27 20 78
|
|
24 16 01 'JO 55 16 40 ·16
|
|
|
|
02 ·04
|
|
65 50 49·58
|
|
44 4fl 48·32
|
|
69 20 21 ·ss
|
|
|
|
-0·75 +0·37 +0·29
|
|
|
|
30·45 53 78 36·55
|
|
|
|
l ·19 0·26 0·26 0·26
|
|
|
|
-0·35 -0·48 -0·19
|
|
|
|
20·4-~
|
|
00·62 39·97
|
|
|
|
0 78 0·34 0·34 0·34.
|
|
|
|
I '02 +0·40 49 '9''3 0'21 +0·69 49·01 0'21
|
|
-0·24 21 •64 0 ·21
|
|
|
|
4·227 867 5 4·279 177 2 4 ".J.57 IIS 7
|
|
|
|
16 899·25 19 018 ·54 28 6.j.9°61
|
|
|
|
4·535 or(i 4
|
|
4 ·156 lf4 3
|
|
4·457 us 7
|
|
|
|
34 278·07 14 325·65 28 649 °6! ·
|
|
|
|
4 ·268 259 5 4 ·156 Il4 2 4 '279 Iii 2
|
|
|
|
18 546·39 14 325·65 19 018·54
|
|
|
|
59·78
|
|
|
|
0·63
|
|
|
|
TRANSCONTINENTAL TRIANGUI~ATION-PART I-BASE LINES.
|
|
|
|
97
|
|
|
|
PROBABLE ERRORS.
|
|
Dele.rmilzalio11- of tilt' probable· errors of Ifie lmgtl1 of Ilic· sid,·s co111111t>n to Ilic net and 1,, tile adjace11t
|
|
d1ai11s of tria11g11la/i,111.
|
|
|
|
For the side Hunt City to Oblong, as adjusted, we make use of the expression
|
|
|
|
Hunt City to Oblong sin (43-39) sin (49-45) sin (17-14) sin (33-32).
|
|
|
|
Olney Base
|
|
|
|
.=sin ( 15- II) sin (29- 26) sin ( 23- 22) sin (20- 18) '
|
|
|
|
hence the function-
|
|
F= log sin (43-49) t log.sin (49-45) +log sin ( 17- 14) +log sin (33-32)
|
|
-log sin (15 - ll)-log sin (29-26)- log sin (23 - 22)-log sin (20-18).
|
|
|
|
Establishing and solving the transfer equations, we find the reciprocal of the
|
|
|
|
weight; =26'615, also the mean error mF, and the probable error rF, both expressed in
|
|
|
|
units of the sixth place of decimals in the logarithm, viz, ±2·227 and ± 1·502,
|
|
|
|
respectively; hence log distance Hunt City to Oblong 4·156 n4 2 and the distance
|
|
|
|
±I 5
|
|
|
|
.
|
|
|
|
I
|
|
|
|
14 325 '65 metres. The probable error is about
|
|
|
|
part of the length.
|
|
|
|
± 0·05"
|
|
|
|
287 000
|
|
|
|
To this must be added the proportional error depending upon that of the l?ase
|
|
|
|
measure,
|
|
|
|
or
|
|
|
|
±0·0089
|
|
|
|
X
|
|
|
|
r4 •?6
|
|
---->2..:....
|
|
|
|
=
|
|
|
|
±o·or9 metre;
|
|
|
|
hence probable error of length of side
|
|
|
|
6591
|
|
|
|
v Hunt City to Oblong, <_0·05)" + (0·019)2 = ± 0·05 metre.
|
|
|
|
For the side Hunt City to Newton, we use the expression
|
|
|
|
Hunt City to Newton= sin (43- 39) sin (50-49) sin (S-4) sin (16- 12)
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Olney Base
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sin (15 - II) sin ( S - 7 ) sin (3 - 2) sin ( 21:-19)
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F=log sin (43-39) +log sin (50-49) +log sin (S-4) +log sin (16-12) -log sin (r5-II)-logsin ( 8-7 )-logsfo (3-2)-logsin (21-19)
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Establishing and solving the transfer equations, we get
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-I p= 20·859,
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.
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also
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mF= ±
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1·97
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.
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and
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rF=
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±
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1-·33;
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hence
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log. distance Hunt City to Newton~- .j.·307 622 1 and distance= 20 305·89 metres. The
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±I· 3
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±0'06
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probable error is about 1 part of the length: adding to this"the proportional error 327 000
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ari.sing from
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the
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base
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measure,
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or
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±
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0·0089
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X
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20 6
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306 59r
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=
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±
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0·028 metre, the probable error
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of length of side Hunt City to Newton is v(o.06)"+ (0·028) 2 = ±0·07 metre.
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- We may also take without sensible error the probable error of the side Hunt City
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to Claremont as 1 part, or ±0·112, to which error must be added that propor306 000
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tional one due to the base measure, or ±0'0089 >: 34 278 = ±0·046; hence probable
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6591 error of si'de Hunt City to Claremont= ± o· 12 metre.
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18732-No. 4--7
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98
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UNITED STATES COAST AND GEODETIC SURVEY.
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GENERAT. DESCRIPTroN OF STATIONS FORMING THE 01.NEY BASE NET, 11.LINOIS.
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East BaSt', Jasper County, Illinois; established in I879 by the United States Lake
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Survey. This station, marking the east encl of the Olney Base Line, is situated. in
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section 19, township 5 north, fractional range l 1 east, St. Marie Township, about 3!
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miles east and one-half mile north of the railway station of West Liberty, on the Gray-
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ville and Mattoon Railroad. The geodetic point is marked by a brass cylinder leaded
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into the top of a stone post of the usual form, set 2! feet below the surface of the
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ground, and surrounded by brickwork 3 feet square and 3 feet deep. Two side stones
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are set on a line at right angles to the direction of the base line, and at a depth below the surface of the ground of about 2i feet; one bear~ north l 0 28' west, distant ]"91
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metres, and the other south 1° 28' east, distant 8°04 metres from the geodetic point.*
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Three stone reference posts are set as follows: One bearing north 49° 49' east, distant
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361 metres; one bearing south 58° 02' east, distant 322 metres, and one bearing south
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35° 5o' west, distant 208 metres from the geodetic point. The northwest corner of
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section 19, township 5 north, fractional range I I east, bears north 77° r2' west,_ and is
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distant about l 054 metres from the geodetic point.
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TVi•st.Base, Jasper County, Illinois; established in 1879 by·the United States Lake
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Survey. This station, marking the west encl of the Olney Base Line, is situated in the
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northwest quarter of the northeast quarter of section 2r, township 5 north, range IO
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east, Fox Township. The geodetic point is marked by a stone post of the usual form,
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set in a bed of brickwork 3 feet square, with its top 4 feet below the surface of t1 e
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ground. Two additional stones are set on a line through the geodetic point perpe1:-
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dicular to the direction of the base line and at a depth below the surface of the ground
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of about 4 feet, one bearing north 1° 30' west, distant 8 ·02 metres, and one bearing-
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south 1 ° 30' east, distant 8"06 metres from the geodetic point. Three stone reference
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posts are set as follows: Two on the south side of the road ·north Qf the station, one
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bearing north .2° 45' west, distant 246·7 metres, and one bearing north 45° 32' east,
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distant 356·0 metres, and one bearing south 6r 0 oo' east, distant 301·0 metres. An oak
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latitude post 17 inches in diameter, occupied in rSSo, bears south 88° 36' east, and is
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di~tant 16·19 metres. The northeast corner of section 21 bears north 67° 19' east, and
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is distant about 727 metres.
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.
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Buffalo 11Iou11d, Jasper County, Illinois; established in 1879 by the United States
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Lake· Survey. This station is situated in section r, near the line between sections 1 and
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2, township 5 north. range IO east. of the third principal meridian, Fox Tovvnship, on
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a hill known as Buffalo Mound, abo11t·2~-~ miles squthwest of the village of St. Marie.
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The geodetic point is inarkecl in the us11al manner by two stone posts set one above the other. Three stone reference posts are set on the west side of the section-line ~oad just
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west of the station, as follows: One bearing south 40° 46' west, distant 44.4 metres;
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one bearing north 87° 19' west, distant 28·9 metres, and one bearing north 38° 54' west,
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distant 45 ·3 metres. The c.orner of sections r, 2, r r, and l 2 bears south l 0 29' west,
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and is distant 966 metres from the geodetic point.
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llfiddle Base, Jasper County, Illinois; established in 1879 by the United States Lake
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Survey. 'fhis station, near the middle of the Olney Base Line, is si~uated in the north-
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west quarter of section 23, township 5 nort~. range IO east, Fox Township, about l · 1
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~All bearings in the Olney Base Net are true.
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