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THE EASTERN OBLIQUE ARC OF THE UNITED STATES
OSCULATING SPHEROID

>

^TREASURY DEPARTMENT^

U. S. COAST AND GEODETIC SURVEY

m

O. H. TITTMANX

SUPERINTENDENT

GEODESY

THE EASTERN OBLIQUE ARC OF THE UNITED STATES
OSCULATING SPHEROID
By- CHAS. A.. SCHOTT, Assistant, Coast and Greodetio Survey

WASHINGTON GOVERNMENT PRINTING OFFICE
I 902

Treasi*ry Department, Document No. 2232.
Coast and Geodetic Survey.
His-
It) 03.

Treasury Department, Office of the Secretary,
Washington, July 16, igoi.
Sir: It affords me pleasure to approve the publication of the discussion of the
Eastern Oblique Arc of the United States, herewith presented to the public. It appears that the value of this arc to geodesy is very great, but that the results
are only incidental to the immediate purposes for which the triangulation was made. The results, however, could not have been obtained if the general plan of the Coast Survey had been less systematic or comprehensive'. Thus, in applied science, as well as
in many other things, the far-sighted wisdom of our earlier statesmen, who gave direc-
tion to our beloved country's policies, has borne fruit.
Respectfully,
L. J. Gage, Secretary. Mr. O. H. Tittmann,
Superintendent Coast and Geodetic Survey, Washington, D. C.

LETTER OF SUBMITTAL.

Treasury Department, Office of the Coast and Geodetic Survey,

Washington, D. C, July 16, 1901.

Sir: I have the honor to submit to you for publication the manuscript of Special Publication No. 7, giving the results of the completed measurements of the Eastern Oblique Arc of the United States.
This is the second of the publications intended to give the results of the principal
arc measurements made by this Service, and like the first, which relates to the Transcontinental Arc of the Thirty-ninth Parallel, it was prepared by Assistant Charles A. Schott, whose knowledge, mature experience, and ability fitted him especially for the task.
The Eastern Oblique Arc, though treated separately, intersects the Transcontinental Arc, and the two triangulations have several lines in common. The former extends from the Bay of Fundy to the Gulf of Mexico, and parallels the Appalachian mountain system, while the latter crosses the axes of the great mountain systems of this country, and extends from the Atlantic to the Pacific Ocean.

Invaluable as the Transcontinental Arc is as a contribution to geodesy and the geography of our country, it does not in itself contain the data for determining the figure
of the earth.

The Oblique Arc, however, contains within itself all that is necessary for determining the dimensions of a spheroid which corresponds most nearly with the existing geoid within the area covered by triangulation. It is unique in that it is the first one which utilizes on a grand scale a measurement oblique to the meridian. The peculiar power of an oblique arc for determining the compression of the earth was pointed out by Tobias Mayer (1 723-1 762), but the first practical application of such an arc to geodesy was made by Bessel. This was before the introduction of telegraphic longitudes had made
it possible to utilize such an arc to its fullest extent.
The results of previous discussions of parts of this arc led to the abandonment by
this Survey, in 1880, of Bessel's spheroid of reference and the adoption of Clarke's (of 1866), and the final discussion of the complete arc here presented sustains the grounds on which the change from one spheroid to the other was made.
Taken in connection with the Transcontinental Arc of the Thirty-ninth Parallel,

this discussion has enabled the Survey to decide upon the retention of the Clarke's spheroid and to adopt geographic coordinates for the whole extent of this country based on a uniform system. Further information as to these standard coordinates for geographic purposes, which differ slightly from those here published in connection with the Eastern Oblique Arc treated independently of other triangulations, will be published in due time.

Very respectfully,
The Secretary of the Treasury.

O. H. Tittmann, Superintendent.

7

CONTENTS.

Introduction

PART I. THE BASE LINES AND BASE NETS.

Page. 19

A. General remarks

25

B. The base lines of the eastern oblique arc, their measurement, resulting

length, probable error, and adjustment of base nets

27

1. Epping base line and base net.

Location, measurement, and length

27

Adjustment of the base net

28

Resulting angles and sides

35

Descriptions of stations

39

2. The Massachusetts base line.

Location, measurement, and length

41

Connection with the main triangulation

42

Descriptions of stations

42

3. The Fire Island base line and base net.

Location, measurement, and length

44

Adjustment of the base net

47

Resulting angles and sides

53

Descriptions of stations

54

4. The Kent Island base line, base net, and extension.

Location, measurement, and length

56

Adjustment of the base net

5S

Extension of the base net

63

Resulting angles and sides

68

Determination of probable error in the sides Osbornes Ruin Turkey Point, and

Tobacco Row Spear

72

5. The Atlanta base line and base net.

Location, measurement, and length

72

Adjustment of the base net

75

Resulting angles and sides

85

Descriptions of stations

87

6. The Dauphin Island base line and base net.

Location, measurement, and length

90

Adjustment of the base net

93

Resulting angles and sides

97

Descriptions of stations

97

C. Synopsis of the measurements and results of the base lines of the eastern

oblique arc

100

9

IO

CONTENTS.

PART II.

THE MAIN TRIANGULATION.

Page.

A. General treatment of the reduction of the main triangulation between

Calais, Maine, and New Orleans, Louisiana

103

B. The triangulation.

1. Northeastern terminus to Epping base net

105

Abstracts of horizontal directions

106

Figure adjustment

108

Resulting angles and sides

no

2. Epping base net to Massachusetts base and to Fire Island base net

1 11

Abstracts of horizontal directions

114

Figure adjustment

122

Resulting angles and sides

130

3. Fire Island base net to Kent Island base net extended

135

Abstracts of horizontal directions

137

Figure adjustment

142

Resulting angles and sides

145

4. First, or Virginia section, south of the transcontinental triangulation

148

Abstracts of horizontal directions

149

Figure adjustment

151

Resulting angles and sides

154

5. Second, or North Carolina section, south of the transcontinental triangulation

156

Abstracts of horizontal directions

158

Figure adjustment

1 62

Resulting angles and sides

163

6. Third, or South Carolina section, south of the transcontinental triangulation

164

Abstracts of horizontal directions

1 65

Figure adjustment

1 69

Resulting angles and sides

173

Adjustment of the position of Mount Mitchell, in North Carolina

176

7. First section west of the Atlanta base net

178

Abstracts of horizontal directions

179

Figure adjustment

182

Resulting angles and sides

185

8. Second section west of the Atlanta base net

187

Abstracts of horizontal directions

188

Figure adjustment

191

Resulting angles and sides

192

9. Third section west of the Atlanta base net

194

Abstracts of horizontal directions

195

Figure adjustment

,

1 96

Resulting angles and sides

.'

198

10. Fourth section west of the Atlanta base net

199

Abstracts of horizontal directions

200

Figure adjustment

204

Resulting angles and sides

206

11. Fifth section west of the Atlanta base net

209

Abstracts of horizontal directions

210

Figure adjustment

213

Resulting angles and sides

216

Remarks on the accord of the Atlanta and Dauphin Island bases

218

CONTENTS.

11

B. The triangulation continued.
12. First section west of the Dauphin Island base net
Abstracts of horizontal directions
Figure adjustment Resulting angles and sides 13. Second section west of the Dauphin Island base net
Figure adjustment Resulting angles and sides
14. Some statistics of the triangulation C. Resuming Geographic Positions of the Principal Stations of the Triangu-
lation, Calais, Maine, to New Orleans, Louisiana D. Additional Geographic Positions which were Derived Differentially and for
which Triangles are not Given in this Paper E. Additional Geodetic Azimuths Computed Directly from the Given Positions
of the Stations

Page. 219 219 222 224 226 228 232 234
237
247
248

PART III.

THE ASTRONOMIC MEASURES.

A. Results for latitude

. 1. General statement

251

2. Details at stations:

Agamenticus, Maine

276

Atlanta, Georgia

306

Atlanta Middle Base, Georgia

305

Aurora, Alabama

304

Bangor, Maine

'

257

Beacon Hill, New Jersey

289

Bull Run, Virginia

292

Calais, Maine

253

Cambridge, Massachusetts ( Cloverden Observatory)

282

Cape Henlopen, Delaware

292

Cape May, New Jersey

292

Cape Small, Maine

271

Causten, District of Columbia

292

Charlottesville, Virginia

292

Clark, Virginia

292

Coast and Geodetic Survey Office, District of Columbia

292

Coon, Alabama

310

Cooper, Maine

255

Currahee, Georgia

299

Dover, Delaware

292

Fast Pascagoula, Mississippi

312

Elliott Knob, Virginia

292

Farmington, Maine

258

Fort Morgan, Alabama

313

Gunstock, New Hampshire

274

Harvard College Observatory, Massachusetts (Cambridge)

281

Hill, Maryland

292

Howard, Maine

263

Humpback, Maine

256

Isles of Shoals, Maine

278

12

CONTENTS.

A. Results for latitude continued.

2. Details at stations continued.
Kahatchee, Alabama

King, North Carolina

Lavender, Georgia
Long Mountain, Virginia Lower Peach Tree, Alabama

Manomet, Massachusetts

Marriott, Maryland

Maryland Heights, Maryland Mobile, Alabama Montgomery, Alabama Moore, North Carolina Mount Desert, Maine Mount Harris, Maine
Mount Independence, Maine Mount Pleasant, Maine Mount Rose, New Jersey Mount Tom, Massachusetts Naval Observatory (new), District of Columbia Naval Observatory (old), District of Columbia New Orleans, Louisiana
New York, New York
Paris, South Carolina

Pooles Island, Maryland

Principio, Maryland Ragged Mountain, Maine

Rockville, Maryland Sabattus, Maine
Sandford, New York

Sawnee, Georgia Seaton, District of Columbia

Soper, Maryland

Strasburg, Virginia

Sugar Loaf, Maryland

:

Taylor, Maryland Thompson, Massachusetts
Unkonoonuc, New Hampshire
Wachusett, Massachusetts

Webb, Maryland
West Hills, New York

Yard, Pennsylvania Young, North Carolina
3. Summary of results for latitude B. Results for longitude.

1. General statement

2. Results for longitude at stations:

Atlanta, Georgia . Calais, Maine

Cambridge, Massachusetts
Cape May, New Jersey
Charleston, South Carolina

Charlottesville, Virginia Dover, Delaware

Page.
307 295 301 292 309 284 292 292 310 307 292 264 260 272 270 290 282
292 292 314 288
297 292 292 266
292 269 286 302 292 292 292 292 292 279 278 280
292 287 291 294 315
317
318 3 18 31S 318 318 318 318

t

CONTENTS.

B. Results for longitude continued.

2. Results for longitude at stations continued.
New Orleans, Louisiana
Washington, District of Columbia

Strasburg, Virginia

3. Details at stations:

Bangor, Maine

Charleston, South Carolina

.'

Columbia, South Carolina

Lower Peach Tree, Alabama . . . .-

Macon, Georgia Mobile, Alabama
Montgomery, Alabama
New Orleans, Louisiana

Petersburg, Virginia Raleigh, North Carolina Seaton, District of Columbia Statesville, North Carolina Wilmington, North Carolina
4. Summary of results for longitude C. Results for azimuth.

1 . General statement

2. Details at stations:
Agamenticus, Maine Atlanta Middle Base, Georgia Aurora, Alabama
Beacon Hill, New Jersey
Beaconpole, Rhode Island
Blue Hill, Massachusetts
Bull Run, Virginia Cape Henlopen Light-House, Delaware Cape Small, Maine Cat Island 1855, Mississippi Causten, District of Columbia

Clark, Virginia
Cooper, Maine Copecut, Massachusetts
Currahee, Georgia East Pascagoula, Mississippi
Elliott Knob, Virginia Ethridge, Alabama Fort Morgan, Alabama
Gunstock, New Hampshire
Harvard Observatory, Massachusetts

Hill, Maryland Howard, Maine Humpback, Maine Indian, Massachusetts Kahatchee, Alabama King, North Carolina

Lavender, Georgia
Long Mountain, Virginia Marriott, Maryland

13
Page.
318 318 318
318 321 321 322 322 323 322 323 320 320 319 319 321 326
327
334 359 361 345 341 339 351 347 332 366 350 351 328 341 357 365 352 363 364 335 338 348 328 329 340 362 355 360 351 348

14

CONTENTS.

C. Results for azimuth continued.
2. Details at stations continued.
Maryland Heights, Maryland Moore, North Carolina Mount Desert, Maine Mount Harris, Maine Mount Independence, Maine Mount Pleasant, Maine
Mount Rose, New Jersey
Mount Tom, Massachusetts Paris, South Carolina
Principio, Maryland Ragged Mountain, Maine Sabattus, Maine Sandford, Connecticut
Sawnee, Georgia Seaton, District of Columbia Shootflying, Massachusetts
Soper, Maryland Spencer, Rhode Island Sugarloaf , Maryland Thompson, Massachusetts
Unkonoonuc, New Hampshire
Wachusetts, Massachusetts
Webb, Maryland
West Hills, New York
Yard, Pennsylvania Young, North Carolina

Page.
350 352 330 330 333 334 345 343 356 347 33 1 332 343 35S 349 339 349 342 350 336 336 337 34S 344 346 354

PART IV.

DETERMINATION OF AN OSCULATING SPHEROID FOR THE REGION COVERED BY THE TRIANGULATION.

A. Comparison of the astronomic and geodetic results

369

1. The astronomic latitude stations.

Reduction to sea level

370

Reduction for variation of pole

370

Comparison of astronomic and geodetic latitudes

372

Review of latitudinal deflections

373

2. The astronomic longitude stations.

Comparison of astronomic and geodetic longitudes

374

Review of longitudinal deflections

374

3. The astronomic azimuth stations.

Comparison of astronomic and geodetic azimuths

375

Review of azimuthal deflections

376

B. Determination of an osculating spheroid for the region covered by the

TRIANGULATION

377

The method and formulae employed

377

Collection of constants and tabular quantities required in the computation for estab-

lishing the conditional equations

380

CONTENTS.

15

Page.
B. Determination of an osculating spheroid for the region covered by the

TriangulaTion continued.

Selection of stations for which data were admitted into the equations of condition

381

Conditional equations derived from latitude comparisons

385

Conditional equations derived from longitude comparisons

386

Conditional equations derived from azimuth comparisons

386

Formation of normal equations

387

The relative weights of the observation equations

387

Resulting normal equations

388

The precision of the adjusted or resulting values of the length of the equatorial radius

and of the compression as found from the measure of the arc

390

Resulting spheroid

391

Comparison with other spheroids

394

ILLUSTRATIONS.

Page,

i. United States Coast and Geodetic Survey Office

Frontispiece.

2. Epping base. View of line as graded for measurement

27

3. Epping base. Placing base apparatus over mark

27

4. Epping base net, Maine

29

5. Massachusetts base, and connection with the primary triangulation of Massachusetts

42

6. Diagram
7. Fire Island base net, New York

45

,

47

8. Diagram

_

57

9. Kent Island base net, Maryland

58

to. Kent Island base and extension of the triangulation to the westward and southward

64

1 1 . Ferdinand Rudolph Hassler

44

1 2. Atlanta base net, Georgia 13. Alexander Dallas Bache 14. Dauphin Island base net, Alabama

:

76

90

93

15. Diagram

1

94

16. Triangulation, Epping base net to northeastern terminus

105

1 7. Mount Desert, Maine

114

18. Mount Washington

116
_

19- 75-cni. or 30-inch theodolite. Troughton and Simms

....'.

135

20. 30-cm. or 12-inch theodolite. Designed and constructed in the Instrument Division, Coast

and Geodetic Survey Office

1 35

21 . Triangulation, Epping base net to Fire Island base net

112

22.

T
riangulation,

Fire

Island

base

net to

Kent

Island

base

net,

extended

135

23. Triangulation, first section south of the transcontinental arc

148

24. Triangulation, second or North Carolina section

156

25. Triangulation, third section, North Carolina to Atlanta base net

164

26. Mount Mitchell, North Carolina

176

27. Triangulation, adjustment of Mount Mitchell

176

2S. Triangulation, first section west of Atlanta base net

178

29. Triangulation, second section west of Atlanta base net

187

30. Triangulation, third section west of the Atlanta base net

194

31. Triangulation, fourth section west of the Atlanta base net

199

32. Triangulation, fifth section and junction with the Dauphin Island base

209

33. Gulf coast triangulation west of Dauphin Island base net

219

34. Gulf coast triangulation to New Orleans, Louisiana

226

35. Extended Lambert equivalent projection, showing the location of principal arc measures and

areas of osculating spheroids

369

36. Naval Observatory, Washington, D. C

377

37. Plan of Naval Observatory grounds

377

38. Subsidiary telegraphic longitude stations between Washington and New Orleans

320

MAPS.

A. Area covered by the eastern oblique arc of the United States triangulation from Maine to

Louisiana

In pocket.

B. Distribution of astronomic stations along the eastern oblique arc of the United States from

Maine to Louisiana

In pocket.

4192 Xo. 7 02

2

17

t

THE EASTERN' OBLIQUE ARC OF THE UNITED STATES, FROM MAINE TO
LOUISIANA, 1833-1898.

INTRODUCTION.

The general course of this inclined arc is indicated in the title, and is shown on a projection with elliptical outline * facing Part IV of this publication. The triangulation upon which it is based begins at Calais, Maine, on the St. Croix River, opposite the Canadian boundary, in latitude 45 11' oo" - 4, and in longitude 67 16' 57"'9 west of

Greenwich, and, following the trend of the Appalachian chain of mountains, reaches
the Gulf coast at Dauphin Island, near Mobile Bay, and terminates at New Orleans,

Louisiana, in latitude 29

57'

-
24" 4,

and

in

longitude

90

04' 24"'4 west of Greenwich.

The geodetic line covers 23 30' 57", and its total length is 2 6i2'3 kilometers, or
1 623^2 statute miles, with an azimuth of 57 3o'"7 at Calais and of 223 22 ,- 5 at New

Orleans, as counted from south around by west. Its extremes differ 15 13' 45" 'o in

latitude and 22 47' 26" "5 in longitude, and in its course it traverses sixteen States, f Near the middle of the arc the triangulation crosses the thirty-ninth parallel, and

for some distance in Maryland and Virginia the same triangulation is used in discussing

the oblique arc as was employed in the discussion of the arc of the thirty-ninth

parallel, an important feature, as will appear in the following pages.

Looking at the gradual development of this arc, extending over two-thirds of a

century-, it can be seen that in its historical aspect it is readily divisible into several well-defined groups, and as a whole it will appear that its existence must be ascribed to necessity rather than to any preconceived idea of measuring such an oblique arc.
Previous to the invention of the telegraphic method of determining differences of

longitude, first employed in October, 1846, by the U. S. Coast Survey, in determining the difference of longitude between Washington and Philadelphia, and up to a somewhat later epoch, when the great accuracy of the method had been fully demonstrated, oblique arcs as well as arcs of the parallel were held in small esteem by geodesists, for the reason that the earlier methods did not determine differences of longitude with a degree of

accuracy comparable with that obtained in observations for latitude. Consequently their attention was almost exclusively confined in practice to the measure of meridional arcs from which to deduce the earth's magnitude. Compared with an arc of the

parallel, an arc inclined to the meridian is less favorably conditioned for discussing the figure of the earth on account of the greater effect of any uncertainty in the measure of

A Lambert equivalent zenithal projection extended over a planisphere,

fSee Map A (in pocket).

19

20

THE EASTERN OBLIQUE ARC.

azimuths, and greater accuracy is demanded in the latter case than is required when
the arcs follow a meridian or parallel. Oblique arcs should no longer be regarded with any special disfavor, and while
they entail very much more labor, comparatively, when they are utilized in determining the figure of the earth, they are well adapted, when of sufficient extent, for the determination of an osculating spheroid for the region covered by them. _ The existence
of the arc discussed in this publication is the result of the necessity for a main triangulation binding together the detached surveys of the harbors on the Atlantic coast and forming a base upon which all subordinate triangulation along the coast could be brought
into accord.
The immediate object of the main triangulation was thus to secure uniformity and
systematic treatment for both the astronomic and geodetic measures in the preparation of the geographic position of the trigonometric stations. This was a leading idea from
the beginning of the Survey under its first Superintendent, and when fully developed resulted in the work under discussion.
There could be no doubt of the necessity of firmly binding together in this way the
small tertiary triangulation and traverse measures along the coast which wind, unbroken, following the indentations of the coast, from the Canadian boundary to Cape Florida and thence into the Gulf of Mexico, following the coast to the Mexican boundary.
The measurement of the oblique arc was thus identical with the progress of the
ordinary operations of the Survey in this portion of the country.
The first period, covering the years 1833 to 1844, witnessed the execution of the
work from central Long Island, New York, to the head-waters of Chesapeake Bay, uniting on the way the surveys at New York, New York, and Philadelphia, Pennsyl-
vania, and this work was nearly all completed under Superintendent Hassler. During the second period Superintendent Bache, pursuing the same general plan,
had the work carried from Rhode Island to the Canadian boundary, at Calais, Maine, on the St. Croix River, and this work was completed in 1859.
In 1865 the branch primary triangulation across the State of Connecticut, connecting the main scheme with some older work in this region, was completed. This period
closed in 187 1, when the Potomac River was reached and crossed. In the third period, covering the years 1873-1877, the work was extended to the
Atlanta base, in Georgia.
The fourth period begins in 1885 and extends to 1898, and during this time the work was extended to Mobile, Alabama.
The triangulation between Mobile and New Orleans, Louisiana, was done between
1846 and 1874. While the field work, as completed, apparently covers a very long period, the first
measures dating back to the year 1833 and the last measures being made in 1898, as has been stated, this interval contained many years when no work was done upon this arc. The slow rate of progress was thus only apparent, as it depended upon and was subordinate to the ordinary requirements of the Survey on this part of the coast, and of the general operations of which it was only an incidental feature.
Part I deals mainly with the base lines and Part II with the intervening triangu-
lation.
The astronomic determinations of latitude, longitude, and azimuths are numerous

INTRODUCTION.

21

and well distributed over the whole arc. There are available, for the computation and comparison of geodetic and astronomic positions, results at 71 latitude stations, at 17 longitude, and at 55 azimuth stations. The latitudes depend almost exclusively on observations with zenith telescopes, and the longitudes on telegraphic transmission of time. The azimuths depend upon a variety of methods, using the pole star most frequently. Abstracts of the individual and final results of the astronomic measures are presented in Part III of this publication. The distribution ,of the astronomic
stations over the region covered by the arc is shown on Map B (in pocket), and the
A two maps and B have the same scale as the similar maps accompanying U. S. Coast
and Geodetic Survey Special Publication No. 4, containing the discussion of the trans-
continental arc of the parallel in latitude 39 N.
Part IV contains the comparison of the geodetic and astronomic measures and the
determination of an osculating spheroid for the region covered by the arc. Preliminary publication of the greater portion of this arc has already been made in
the following reports of the Survey: Report for 1865, Appendix No. 21, pp. 187-203,
' ' Results of the primary triangulation of the coast of New England from the northeastern boundary to the vicinity of New York;" Report for 1866, Appendix No. 8, pp. 49-54, "Report on the geodetic connection of the primary base lines in New York
and Maryland, their degree of accordance and accuracy of the primary triangulation intervening, with the resulting angles and distances as finally adjusted," and Report for
1878, Appendix No. 8, pp. 92-120, "On the adjustment of the primary triangulation
between the Kent Island and the Atlanta base lines." These reports contain also more or less complete accounts of the six base lines located in the arc.
Other references will be given in their proper place. The present publication is complete in itself, and while no important facts or statements are omitted, much simplification has been effected by referring to the publication above mentioned, covering the transcontinental arc of the parallel, the same general treatment and method of reduction
of the triangulation having been employed in reducing that arc as is used in the
following discussion of the oblique arc.

>
PART I.
THE BASE LINES AND BASE NETS.
23

>
THE BASE LINES AND BASE NETS.
A. GENERAL REMARKS.
The unit of length is the same as that used from the beginning of the Survey until
1889, viz, an iron bar, 1 meter long, standardized at Paris in 1799 and brought to this country by Mr. F. R. Hassler in 1805. Its use was discontinued after the receipt of the
new prototype platinum meters in November, 1889. This meter, known on the Survey as the Committee Meter, is an end measure and is represented by an iron bar with square end surfaces, now slightly defaced by corrosion and perhaps by use. It will suffice to
refer the reader to the full account given of this meter in Part I of the ' ' Transcontinental Triangulation and the American Arc of the Parallel ' ' across the United States in the vicinity of latitude 39 , published by the Coast and Geodetic Survey in 1900. In that publication, after some historical notes, the results of the numerous comparisons, direct and indirect, by different observers, by different methods and at different times, are completely set forth, and the final conclusion is reached that this bar at o C. represents so nearly the length of the prototype meter that no reliable value of the difference
can be stated. The weighted mean of all comparisons gave the result i"'+o'2yuzho'6/u, and in all computations depending upon this standard it has been taken as equal in
length to the prototype meter with a probable error of about three-quarters of a micron. There are six base lines irregularly distributed along the arc, and they are described
in the order of location, beginning in the extreme northeast and ending on the Gulf coast. For each line all needful information is given in connection therewith, such as position, physical features, elevation above sea level, apparatus used for the measure, name of observer, computation of length and final result, with its probable error.
A sketch of each base net is presented, and it is followed by the abstracts of horizon-
tal directions, observed and adjusted, for each station forming part of the net. These abstracts contain the following information: County and State, date of measure, instrument used and observer's name, and also, in the first column, the number of each direction. These numbers, when in parentheses, indicate the corresponding corrections as given by the net adjustment. In the great majority of cases direction theodolites were
employed, and for these Bessel's method* of reduction at the station was used. When
repeating theodolites were used the station adjustment followed the ordinary method t of combination with the introduction of relative weights. Below the abstracts of directions resulting from station adjustment there is given the probable error of a single observa-
* See T. W. Wright's " Treatise on the Adjustment of Observations." New York, 1884, pp. 315-322.
tlbid., p. 139 and foil.; also p. 217 and foil.

26

THE EASTERN OBLIQUE ARC.

^ tion of

a direction

(mean

of

the direct

and reversed

series) deduced

from

e'= 1

o'4<*;s n5

^'
,
a-\-\

= = = where n number of observations, 5 number of series, d number of directions, and

= A differences of observed and adjusted values.

The figure adjustment of the triangulation generally proceeds on the supposition of

equal weights to all directions used in the adjustment, except, as in the case of the Epping
base net adjustment, where special weights are introduced.* To carry weight equations

from the station adjustment into the figure adjustment is not practiced or favored in the

Survey on account of the increased complexity and the doubtful advantage of the pro-

ceeding. The errors brought to light by geometrical conditions, and which have been

called triangle-combination errors, are of a different character from those developed
by a comparison of the measures made at a station, where defects of centering at

observing and observed stations, effects of large local deflections of the vertical at a sta-

tion, persistent lateral refraction along a line, etc., do not show; that is to say, weights

pertaining to one operation are not those proper for the next operation. Further par-
ticulars of figure adjustment with statement of formulae may be found in "The Trans-

continental Triangulation," Part I.

Fo* the computation of the sides of the triangles Legendre's theorem was used,

and since none of the lines of the oblique arc are very long the spherical excess was

computed by the simple formula

ab sin C

2pm pn sin l"

= where C the plane angle included by the sides a and b and the subscripts to p refer

to the radius of curvature in the meridian and in the prime vertical. Appendix No. 9,

Coast and Geodetic Survey Report for 1894, page 291, contains a table to facilitate the

computation of the spherical excess, the argument being the latitude of the center of the
triangle. The computation of the geodetic positions along the oblique arc is made

according to the formulae and tables in the same appendix, the differences in latitude,

longitude, and azimuth for two points of known distance and azimuth being given by

where

Dh E A<p=s cos a. B-\-s* sin2 a. C-\-(S<py

5" sin8 a.

A\ A a s sin sec q>' .

-Aa ^ % F = A\ sin (<p+<p') sec

3
(4<p)+ (^A.)

<p'=<p-\-A<p

\' = X+AX

+ a' =

J-)-i8o <:

R and 6cp=s cos a. B+s* sin" a. Chs* sin8 a.
= also A s cos a. B.

The factors A, B, C, D, E, and /"are tabulated and refer to Clarke's spheroid of 1866.

Their logarithmic values are given for every minute of angle between latitudes of 18

and 72 .
A description of each station used in the base nets is given.

The description of the

other stations of the triangulation can be obtained upon application to the Coast and

Geodetic Survey, Washington, District of Columbia.

When special weights are introduced for the several directions at a station, they are deduced from the rough exprreessssiioonn of the square of the prroo!l>Kai'ble error given bj fvt = /_ , where [xx] represents the diagonal coefficient cf
the direction in the normal equation.

t

BASE LINES AND BASE NETS.

2J

B. THE BASE LINES OF THE EASTERN OBLIQUE ARC, THEIR MEAS-
UREMENT, RESULTING LENGTH, PROBABLE ERROR,
AND ADJUSTMENT OF BASE NETS.

I. THE EPPING BASE LINE AND BASE NET, MAINE, 1857.

Locatioti, measurement, and resultiyig length of the Eppiny baseline, Maine, 185J.

The site of this base is on Epping Plains, near Cherryfield, Washington County,

A Maine.

reconnaissance of the locality was made in 1853, and the measurement of

the base followed in July and August, 1857, under the immediate direction of Superin-

tendent A. D. Bache. The Annual Report for 1865, Appendix No. 21, pages 189-191,

contains a full account of the measure and of the result. It will therefore suffice to

present herex only the salient points of the operation.
The measure was made with the Bache-Wiirdemanu contact-level compensating apparatus, and is the sixth primary line where this apparatus was employed, the Dauphin Island base, Alabama, being the first, an account of which is given further on (q. v.). The apparatus is fully described with illustrations in Coast Survey Report for 1854, Appendix No. 35, and reprinted in Coast Survey Report for 1873, Appendix No. 12. The essential part of the apparatus consists of two 6-meter bars, one of brass and one of iron, placed parallel to each other, one being above the other and firmly connected at one end. At the opposite or free end is the lever of compensation, so proportioned in its arms with respect to the actual and differential expansion and contraction with changes

of temperature that the end of the apparatus remains at a constant distance from the
opposite end. The spirit-level contact piece terminates in an agate, ground to a knife edge, whereas the agate at the opposite presents a slightly convex surface. The apparatus was standardized by means of a standard 6-meter iron bar, the length of which

was determined at different times in terms of the Committee Meter.

The length of this base is about 8*72 kilometers (or 5^42 statute miles), its middle point is in latitude 44 40' "8 and in longitude 67 53'" 1, with a mean azimuth of 106 54'. Much labor had to be spent preparing the ground for the measure by leveling it,
removing bowlders, and overcoming other obstacles, the handling of the apparatus demanding a wide and fairly smooth roadway. The average height of the tubes above the mean tide level of the Atlantic was 76'45 meters. The 6-meter base bars or tubes were compared with the standard 6-meter bar just before and immediatel}- after the base measure. Taking the length of the latter and its coefficient of expansion as determined in

i860 and published by Assistant J. E. Hilgard in CoastSurvey Report for 1862, Appendix

on No. 26, viz, 5 '999 941 meters, and o'ooo

54 for the centigrade scale, the following

2

4

results for the length of the tubes were obtained: Three sets of 23 comparisons, made

with Saxton's reflecting comparator* on July 16th and 17th, gave tube No. 1 shorter than

the standard (at i8'3C.) 1 300^4 divisions of the comparator and tube No. 2shorter 1 0887

2'0

2"2

* The instrument is known as Saxton's pyrometer, and it is described in detail, with illustrations, in the Report of the Superintendent of Weights and Measures for 1856. and the Report of the same bureau for 1862 contains, on page 249, a general description of it. One turn of the screw equals 357-11 scale divisions and one scale division equals 136 microns.
The head is divided into 100 divisions.

28

THE EASTERN OBLIQUE ARC.

divisions; again, after the base measure, on August 6th and 7th, from 4 sets of 27 comparisons, tube No. 1 shorter than the standard (at 2i'oC. ) 1 411 '8 divisions and from
3'3
4 sets of 23 comparisons tube No. 2 shorter 1 195 '3 divisions. Having regard to the
-
2g
weights, the above comparisons give the values for length of tubes,

for No. i a , 5 '999 459 o meters,*
49
for No. 2, 5 '999 750 6 meters.
49

Although the comparisons of the tubes with the standard bar were made with rising and

falling temperatures, there remained an uncertainty respecting the indication of the

y thermometers in air giving the temperature of the metallic bar even within x . Further,
some allowance had to be made for any defect in the mechanical compensation, for pos-

sible error in making contacts and transfers to the ground, and for other small uncertain-

ties in connection with the base measure, and this was arbitrarily fixed as =fc 9'7 M- The

+ probable error of the length of a tube during the measure was taken as V(4'9) 2

8
(9'7)

=

= = io'9 n, hence that for the whole length

1 453 X 109 /*

o'oi58'", which

equals T j TVjs part of the length. In this case, as in that of the other bases of this arc,

except the Atlanta base, the single measure fails to provide proper means for a more

We reliable value of the probable error of the length.

have for the length of the Epping

base:

1 452 tubes of mean length,

8 7ii n"4262

One odd tube, No. 1,

+5'9994

Correction for inclination of tubes,

2 -So4o

Defect of last tube at East Base,

+ 1 '4250

Reduction to half-tide level of ocean,

0^1044

Resulting length of base,
And its logarithm, 394031434

8

m 7i5

9422

0-00000079

o"'oi58

The Eppiiuj base net and results of its adjustment.
As shown on the following sketch, this net of triangles is included within the primary quadrilateral Humpback, Mount Desert, Howard, and Cooper, and involves 6 geodetic points. The figure is a very strong one and demands that 35 geometric conditions lie satisfied. The reduction of this base net is complicated on account of the employment of both direction and repeating theodolites, five of the stations having l>een
occupied with the latter instruments.
An account of the adjustment of this base net iscon.ained in Coast Survey Report for 1864, Appendix No. 14, and may be referred to for particulars; the results are here
transcribed, except that the notation has been changed for one more convenient. I11 connection with the station abstracts there is added a column containing the approxi-
Comparing these values with the corresponding values of 1847 (Dauphin Island base) and of 1872-73 (Atlanta base), it will be seen that the lengths are not invariable, but it should l>e noted that one of the agates of tube 1 was accidentally broken in 1S55, and after the new agate was substituted the tube was found to be 0430 millimeter shorter than
before.

BASE LINES AND BASE NETS.

29

mate value of the probable error of a resulting direction, depending on the formula

= 0-455 ^d* .

e'

FT-

ffTT^ in case of direction observations.

In case of repetitions the prob-

able error will depend upon the comparison of a resulting angle with each of its

20 measures (each of 3 repetitions direct and 3 repetitions reversed), from which an

average and approximate value of the probable error of a single measure of an angle

and of a direction has been derived, as well as the probable error 'of a resulting direc-

We tion.

have approximately

N

from the 20 measures of each angle the probable error of a

Co op era

single observation of an angle

^5 f = e~

n { n- -.V) * hence

.
the probable error of a single

observation ( 3 D. and 3 R. ) of a

= direction e s

e L /J2, also ap-

proximately for a resulting

= direction e,

eJ^2o. The last

column of the abstracts con-

Humpback

tains the final adjusted directions, the first direction having
again been made zero by sub-
tracting the correction to the initial direction from each of

the corrections to the other

directions, as given in the

preceding column, f

In the adjustment of the

base net special weights were assigned to the directions, as explained at length in Coast

10

20

Statute Miles

Survey Report for 1864. If
we deduce the probable error of a direction from the closing errors in the sum of the angles of the 46 triangles, we find from the sum of the squares of these errors the mean

= closing error of a triangle -Jf54'49_
46

i"'09, hence the probable error of a direc-

= = tion o'674 X 1 "09/76

:0"- 30.

On the other hand, the average value of the probable error of observation of the

116 directions in the net is about o"'24, whence the triangle combination error

= = e c

s
V{o"3o)

2
(o'24)

o"'i7 (nearly), and the square of this was added as a

We constant to each of the previously deduced squares of the observing errors.

then

= + have f

," *,* and the weight to any direction p

1 The values of p thus have

"The half bracket indicates sum of similar quantities, disregarding their signs. tThe mean of the 4 values of fi derived from a single measure (D. and A*. ) with the 75cm theodolite is i"'04 and 'he mean of the 5 values of et derived from a single measure (3D. and 3^.) with the 25cm repeating theodolite is
l"*i6, or one measure with the first instrument is about equal in accuracy to three with the latter.

30

THE EASTERN OBLIQUE ARC.

smaller range than they would have had without the addition of the constant; still
the maximum weight is to the minimum weight as 5 "4 to 1 . The effect of the intro-
duction of weights is small in cases like the present, a base net of great complexity and fair measures.
There was no special necessity for a reduction of the horizontal measures to sea level on account of the elevation of the signals sighted. The following table gives the approximate heights of the ground at the stations:

BASE LINES AND BASE NETS.

31

Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net,
/8$6-rS^g continued.
Burke, Washington County, Maine, September 30 to October 10, 1859. 25"' repeating theodolite No. 43. C. O. Boutelle, observer.

No. of directions.

32

THK EASTERN OBLIQUE ARC.

Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net, 1856-1850 con ti 11 ue< 1 .

Humpback, Hancock County, Maine.

July 19 to September 6, 1858.

cm 75

direction

theodolite

No.

1.

A. D. Bache and G. \V. Dean, observers.

No. of directions.

BASE LINES AND BASE NETS.

63

Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net,
1856-1850 continued.

Howard, Washington County, Maine. July 15 to August 8, 1859. 75' direction theodolite No. 1. A. D. Bache and G. W. Dean, observers.

No. of directions.

34
VI

THE EASTERN OBLIQUE ARC.

h

BASE LINES AND BASE NETS.

35

The reciprocals of the weights introduced for the several directions are as follows:
Dir's

36

THE EASTERN OBLIQUE ARC.

Resulting angles and sides ofthe lipping base net, Maine continued,

No.

Stations.

Tunk Epping West Base
Burke
Tunk Epping East Base
Burke

observed angles.
50 45 II '850 49 ' 45 33 80 13 02 '640
34 4o 37 '840 25 46 43 060 119 3 2 3 8 '49

Correction.

Spher-
ical
angles.

Spher
ical

o 039 1 o 300
203

II "8l I
45 630 02 -843

OO94 OO94 OO95

-o '945
+1-591
+0 283

36 "895 44-651 38 -773

o 106 o -106 0-107

I,og. distances.

Distances in meters.

4 -032 670 78 4-021 66233 4-137 328 24
4"'38 343 64
4021 66233
4 -322 778 80

IO 781 291 i<>5" '443
13 7>9>83
'3 751 296
105" '443
21 027 -072

Pigeon Epping West Base Epping East Base

19

56560

64 55 08 -300

96 03 55 -500

-i-i8o 55-380 0178 +0-951 09-251 0-178
+0 -402 55 -902 0-177

3 "940 314 34 4 '384 324 57 4 -424 896 92

8 715 -942 24 228 391 26 600 -936

Pigeon Burke Epping East Base
Pigeon
Tunk Epping East Base
Pigeon Burke Epping West Base
Pigeon
Tunk Epping West Base
Pigeon
Tunk
Burke

33 44 59 '30
101 48 19 "820 44 26 42 '6oo

0-174 58-856 0-197 1-005 18-815 0-197
+0 -322 42 922 0-198

49

08

-
34 3i

60 37 58 '620

70 13 25 660

+0 -629 +0 -084
-f-i'9'3

34 939 58 -704 27-573

0-405 0-405 o -406

14 44 02 470 141 07 55 -670
24 08 03. 450

+ 1 -006 03 476 o 099
-0 -925 54 745 O "IOO
-1-373 02-077 099

30 07 37750
76 42 32 '630
73 09 48 780

+ 1-809
+0 -990
-i'o73

39 '559 33 '620 47 707

0-295 o -296
0295

15 23 35 '280
25 57 20 780 138 39 01 690

+0 -803
+ 1 -029
+0 -723

36 083 21 809 02 -413

O'lOI O "I02 O "I02

4 138 343 64 4 '384 324 56 4 -238 847 61
4 322 778 80 4 '384 324 57 4 -417 660 18
4 -032 670 78 4 -424 896 91 4 238 847 61
4-13732824 4 -424 896 91 4 -417 660 18
4 021 662 33 4 -238 847 61 4 -417 660 18

13 751 -296 24 228 -390 17 33' '957
21 027 -072 24 228 391 26 161 352
10 781 291 26 600 936 '733' '957
13 719 '183 26 600 -936 26 161 352
10 511 -443 '733' "957 26 161 352

Humpback Epping East Base Epping West Base
Humpback Epping East Base
Burke

9 55 37 '650 27 41 01 -oio 142 23 21 940

M 25 3'

'879

79 18 13-910

75 10 31 '480

-0-051 +0-320
0551

37599
01-330 21/389

0-I05 o -106 o -106

0-220 14 659 0352
1^0-400 14-310 o-352
+0 -609 32 089 "353

3 "94o 3'4 34 4 -370 860 02 4 "489 329 42
4 138 343 64 4 496 419 39 4 '489 329 43

8715-942 23 488 -756 30 855 275
13 751 296 31 363 129 30 855 276

Humpback 13 Epping East Base
Tunk
Humpback 14 Epping East Base
Pigeon

42 39 01 097 53 3 1 3 '850 83 49 30 54o
24 26 46 698
123 44 56510
31 48 17 670

o -042 01 -055 0-441

1 192 29-658 0-441
+0 -070 30 6lO 0-441

-o 358 +0 72I +0 -335

46 -340 57-231 18 -005

0525
o'525
0526

4 322 778 80 4-397 '74 17 4 '489 329 43
4 '384 324 57 4 -687 346 90 4 489 329 42

21 027 072 24 955 '954 30 855 -276 24 228 -391 48 679 590 30 855 -275

BASE LINES AND BASE NETS.

37

Resulting

No.

15

16

17 18

19

23 24 25 26

38

THE EASTERN OBLIQUE ARC.

Resulting angles and sides of the Epping base net, Maine continued.

Xo.

Stations.

27

28

29

3 31
32 33 34 35 36 37 38

BASE LINES AND BASE NETS.

39

Resulting i les and .

Stations

Howard
39 Pigeon
Mount Deser
Howard 4" Mount Desert
Humpback
Cooper 4i Burke
Humpback
Cooper 42 Mount Desert
Burke
Cooper 43 Howard
Burke
Cooper 44 Mount Desert
Humpback
Cooper 45 Howard
Humpback
Cooper 46 Howard
Mount Desert

40

THE EASTERN OBLIQUE ARC.

A perpendicular to the base at the center of the monument passes through the intersec-
tions of cross lines in copper bolts in tops of two granite reference monuments, 3 '5 feet long and 1 foot square, set at distance of 36 and 72 meters north of station.
When the station was visited in 1884, these reference monuments were found

undisturbed, also a third, not described, with a hole drilled in top, 108 meters north of
the station. The marble monument was then found overturned and broken, but the granite surface mark remained undisturbed, except that the head of the copper bolt had been hammered so that the cross lines were no longer visible.
Epping West Base. This station is about 2 miles west of Schoodiac Hill, and has no subsurface mark.
The surface mark is the intersection of cross lines on a copper bolt in a monument 3 feet square, made from the solid ledge by cutting away the rock to a depth of 6 or 8
inches around it.

Similar marks 1 foot square were made north and south of the center in a line per-
pendicular to the base, with copper bolts and cross lines placed in position.
Over the surface mark was placed the monument of marble of same dimensions as

that described for Epping East Base.
When visited in 1884 the marble monument was found overthrown and broken,
while the copper bolt had been hammered so that no cross lines were visible. The mark south of the center was in perfect condition. The one to the north had been destroyed by vandals, but the remains of the hole in which the copper bolt had been placed could be distinguished. The distance from the station to these marks is about 10 meters.

Burke. This station is on the southernmost one of a range of rocky hills about 3 miles west of Cherryfield village and about 20 rods north of the line between Mount Steuben and Cherryfield. It is tnarked hy hole in a granite ledge at the north end of a small hollow on the summit of the hill, and it is about 3 feet below highest part of ledge,

which is too narrow for a signal. Tunk. This station is on a mountain of the same name, the most commanding
mountain (except Mount Desert) east of the Penobscot River. It is about 1 mile north

of the stage road from Ellicott to Cherryfield and about 3 miles west of the nearest house

in Cherryfield. It is marked hy & hole drilled in a granite ledge about 150 feet south-

west of the highest part of the summit and about 4 feet below it.

Pigeon. This station is on the highest part of a hill close to the ocean on the

western side of the outlet of Narraguagus River. It commands the coast from French-

mans Bay to Head

Harbor Island,

and

is

9

miles

from

-
Cherr3

field.

It is marked by a

hole drilled in a flat rock. In range to Mount Desert, 53'25 feet distant; to Saunders,

56'25 feet distant; to Humpback, 3533 feet distant, and to Mitten Mountain, 36'83
feet distant, there are holes and piles of stone.
Humpback. This station is on the mountain of the same name, near the western line of Brewster Township. The highest point of the mountain is about 400 feet northeast of the station and is 4 or 5 feet above it. It is marked by a hole drilled in the rock. Range marks, consisting of holes drilled in the rock and heaps of stones, were made toward Harris, Saunders, and Mount Desert, distant 14, 1742, and i3'5o feet, respectively.
Mount Desert.. This station is marked by a copper bolt in a ledge which is in the
% center of a small depression in the large bare rock and 22 inches easterly from the

southeast corner of a crevice.

BASE LINES AND BASE NETS.

41

Single range marks, consisting of a hole in the rock, were made toward Peaked, Blue, and Ragged mountains, distant from center 53'i7, 1752, and 2i'83 feet, respectively. Toward Saunders and Harris there were two such marks, distant, in the first instance,

3592 and i42"5o feet, while in the latter, i9'Q2 and i36'6o feet from the center of the

station.

Howard. This station is on a steep, precipitous hill, about 6 miles below Machias-

port and near Bucks Harbor. It is marked by a drill hole in a rock. Range marks

were established toward Mount Desert, Humpback, and Cooper, distant 33'67, 66'25,

When and 2 1 "30 feet, respectively.

visited in 1884, the station was recovered.

Cooper. This station is on the northern end of the summit of Western Ridge, about one-fourth mile west of the road running through the village of Cooper and about three-eighths of a mile northwest of Cooper Church. It is marked by a drill hole in a broad, fiat granite ledge. Range marks, consisting of drill holes in the rock, were made toward Mount Desert and Humpback, distant 22'8o and I9'65 feet, respectively.

2. THK MASSACHUSETTS BASE LINE, MASSACHUSETTS, 1844.

Location, measurement, and resulting length of the Massachusetts base line, Massachusetts,
1844.

This base was the third and last one measured with the Hassler base apparatus and followed within a few months the measure of the Kent Island base. Its site is on the

Boston and Providence Railroad, in Bristol County, Massachusetts, and about 12 kilo-
meters (7^ statute miles) to the northward and eastward of Providence, Rhode Island. An account of this base is given in the Coast Survey Report for 1865, Appendix No. 21,
page 189, and little need be said here respecting the apparatus, a description of which can be found in the account of the measurement of the Fire Island and Kent Island bases.

Its middle point is in latitude 41 58'"9 and in longitude 71 is''3, the mean azimuth is
27 49''2, and its length 1754 kilometers (or nearly ioj^ statute miles). There are but
two bases in the United States (both in California) which exceed this length.
The line was measured by Assistant Edmund Blunt during September, October, and November, 1844. As in the case of the two bases previously measured by the Survey, but one measure was made. The length adopted for the compound 8-meter bar rests
w upon the comparisons of 1844-45, ' tri tne resulting length of 7*999 87 16 meters at o" C.

55
(see account of the Kent Island base). The mean temperature of the bar during the measurement was I4"92 C. (or 58'85 F. ); the average elevation of the apparatus above the half-tide level at Boston Harbor was 44'"'83. The record at this base is defi-

cient in details.

The resulting length of the base is as follows:

2 165 boxes Correction for excess of temperature Correction for inclination
Fractional part of a box at Northeast Base Correction for 10 difference of temperature for above Additional length measured by scale Reduction to half-tide level

m I7 3i9 '722i
-\- 3 "2383
C5629
-f- 3 9999 00003
4- 01012 01 220

Resulting length of base

17 326""3763

42

THE EASTERN OBLIQUE ARC.

To form an estimate of the accuracy of this measure, we find, from the probable error

assigned to the base bars, that of the base to be o'"'oi 19. With reference to tempera-

ture, 702 boxes were laid with rising and 579 with falling temperature, and for the rest

of the boxes the temperature was stationary. The assumed probable error from this con-

dition and probable lag, and from graduation error is o'"'o332, and the probable error

from instability of the microscopes is taken as

o'"'oo59. Combining these three

independent values, we get for the probable error of the base o""o358, which equals

We fBS^BTr of its length.

have, therefore, the final result for the length of the

Massachusetts base 17 3263763 meters, and its logarithm 4^238 70774.

L O358

90.

The connection of the Massachusetts base with the main triangulation.

The Massachusetts base is connected with the main triangulation in an unusual

way that is, with a base net so simple as to render a special adjustment of it unnecessary. The conditional equations, therefore, which subsist between the three northern base-

lines were extended to reach directly to the Massachusetts base without any interven-

Jilwc Hi,

No. 5.

tion of a special base net adjustment.
The diagram shows the direct con-
nection of the base with the triangula-
tion of the New England States, the

quadrilateral Beacon Pole, Copecut,

Manomet, and Blue Hill being an

integral part thereof. One advantage

which the base possesses over the

other two is its great length. The following table gives the ap-

proximate elevation above the Atlantic

of the stations adjacent to the base:

Massachusetts South Base Massachusetts North Base Beacon Pole
Great Meadow
Copecut
Manomet
Blue Hill

Meters.
33 70 1 67
S05 1075
1 20
194

Feet. 108
231 548 264 353 394 635

BASE LINES AND BASE NETS.

43

on the west side of the road in the line toward Beaconpole Hill, 6 inches being above ground, and distant 33 feet from the termination of the base. ' ' *

Massachusetts North Base, 1844.. The station is marked by a brick tower, stated by

G. Bradford to be 44 feet in height, when reoccupied October 18, 1884. The center of
+ the station is indicated by a brass bolt in the center of a stone, thus . It is central

with the tower. The capstone (of 1844) had a mean diameter of 0^32 meter.

Beaconpole, 1844. This station is located about 2 miles northeasterly from the village

of Cumberland Hill. The station was visited and reoccupied in September, 1884, by

Assistant G. Bradford, who remarks: ''Found here, guided by E. H. Pickering, an

old resident, a copper (brass?) bolt set in lead and filling a hole drilled in a ledge of

A rock some 30 feet in diameter, which occupies the summit of the elevation."

tripod

signal was built over the station in '1884. There is also a description of 1896 by H. B..

Wood, of the "Survey of the Commonwealth of Massachusetts."

Copecut, 1844. Station on Copecut Hill between Fall River and New Bedford. Assist-

ant G. Bradford found here in November, 1884, a copper bolt in a rock, presumably

A the center of the station.

large pile of stones was found about the bolt, covering it.

The place is surrounded with bushes and small trees, and is difficult to find without a

A guide. The road to it through the woods is extremely rough.

tripod signal was

built here in 1884.

Great Meadow, 1843. This is one of the Borden Survey stations; about 3 miles north

of west of Rehoboth village, 7 miles from Taunton, and 12 from Providence, Rhode

Island. Assistant G. Bradford, in September, 1884, found here a hole in the rock,

where, an old resident says, the signal once stood. The trees have grown up, and are

now to the northward and westward some 40 to 50 feet high. The following description is by Assistant C. H. Van Orden, in 1889: "The hill is well known and is called Great Meadow Hill by the people about North Rehoboth. It is best approached from the

south side. It is a large flat hill, with a growth of timber on the east and west sides.

Directly north of the station is an open lot or meadow, noticeable from a distance."

Manomet, 184.5. Near Plymouth, Massachusetts. Assistant C. O. Boutelle states, in his record of the latitude observations of July, 1867: " The triangulation station at

Manomet has been more permanently marked by drilling three holes, forming an equi-

lateral triangle around the copper bolt, and each hole is distant 6 inches from it. The

two holes south of the bolt are east and west from each other and the third hole is north

from the bolt. Each hole is five-eighths of an inch in diameter and 2 inches deep." In

September, 1877, Assistant G. A. Fairfield writes: "Visited this station and found it

undisturbed;

had

no difficulty

in

finding

the

rock with copper bolt and

three drill

''
holes.

Blue Hill, 1845. Near Dedham, Massachusetts. The Coast Survey station is

distant from the Borden survey station of Blue Hill 8 337 meters, and the azimuth of

the Borden station is 11 16', as deduced from computation of December, 1884. The

Borden station was located in the middle of a square inclosure of stones. In November,

1886, Assistant C. H. Van Orden visited the station and found the Coast Survey copper

bolt (outside the old Borden inclosure) in good order. Borden's "Blue Hill" is under

the stone tower of the "Blue Hill Observatory."

The private meteorological observatory at this place was established by Mr. A. L,.

Rotch in 1885. It is a two-story circular tower, 12 feet in diameter inside and 25 feet

high, built of the broken stone found on the hill. Extending southward from this

* I-'rom original record of the base measurement.

44

THE EASTERN OBLIQUE ARC.

tower is a one-story, hip-roof house, built of stone, with a wooden shed attached,

heliotype in Annals of the Astronomical Observatory of Harvard College, Volume XX,

Cambridge, 1896). There is also a description of 1896 by H. B. Wood of the "'Survey

A of the Commonwealth of Massachusetts. ' '

sketch shows the Coast Survey station

with reference to the tower.

3. THK KIKK ISLAND BASE LINE AND BASE NET, NEW YORK, 1834.

Location, measurement, and resulting length of the Fire Island Base Line, Neic York, 1834.

The site of this base is on the southern shore of Long Island, New York, on the

narrow Fire Island beach between the Great South Bay and the Atlantic Ocean, and

distant nearly 80 kilometers, or 50 statute miles, to the east from New York City. It

was the first and only primary base measured by Superintendent F. R. Hassler, and the

measurement was made with an apparatus of his own design. He has left a full descrip-

tion, with illustrations, in detail, of this apparatus in the Transactions of the American

Philosophical Society, Philadelphia, Pennsylvania, new series, 1825, Volume II, pages 273-286. The essential parts of the apparatus are enumerated in No. 12 of his cata-

logue of instruments, which probably dates back to the year 1816. These parts appear
to have been made by Troughton, of London, in 1813. Two other primary base lines

were measured with the same apparatus, viz, the Kent Island and the Massachusetts bases.

The beach over which the measure extended is sandy, interspersed with low hum-

mocks and ridges, and subject to changes from storms, which caused the west end of the

base to be finally lost, notwithstanding a strong timber protection surrounded the hillock.

The eastern terminal point was further removed from the beach, which caused a bend

in the line close to the monument, and necessitated the measure of an angle at the bend.

The insecurity of this exposed base and the danger of its loss caused the transfer of

its length, a few years later, to be made to a primary line located on the central hills

of Long Island. The base net, therefore, in this case consists simply of a quadrilateral.

8^ The length of the base is about 14 kilometers (or

statute miles). The central

point is in latitude 40 38' '9, and in longitude 73 o8'"i. The mean of the forward and

backward azimuths is 72 56''8. For convenience of reference, a brief description of

the Hassler base apparatus is repeated here from his description, and further remarks

on this subject will be found in connection with the Kent Island base. It makes use

of one measuring bar and of optical contact. The bar is 8 meters in length and is

composed of four 2-meter iron bars placed in contact lengthwise. These pieces are of square section * and are firmly held together by means of collars clamped over the bar

ends and bringing them together by means of screw bolts. The whole or compound bar

is supported on 15 rollers, resting on a wooden beam, itself adjustable upon another

similar support. The whole is placed in the bottom of a wooden trough. There are

eight thermometers, two placed on the upper surface of each of the single bars to

A ascertain their temperature.

sector for measuring the inclination is attached to one

end of the supporting beam, and all required mechanical appliances for the adjustment

and alignment of the bar, as well as for the manipulation of the micrometer micro-

scopes, are provided. The trough itself rests upon five trestles. The two microscopes

are likewise mounted upon trestles. For alignment of the base the trough or box

carries at one end a small telescope and at the opposite end a short vertical pin to

* The same as that of the Committee Meter.

FERDINAND RUDOLPH HASSLER (1770-1843).

3*

BASE LINES AND BASE NETS.

45

define the axis of the apparatus and the direction of the line of measure. The micro-

scopes admit of adjustment for verticality of axis. Their objectives are composed of

two half lenses of different foci, one for pointing on spider threads stretched across

small central half-circular notches cut vertically into the end faces of the protruding

measuring bar, the other focus serving for a verification of the steadiness of the optical

axis, the pointing being made upon cross lines ruled on an ivory plate resting on the

support below the microscope.

For the standardization of the measuring bar repeated comparisons were made at

different times by different observers and by different means. The Hassler double end-

meters,

known

as

bars

A,

B,

C,

and

D,

were

first

compared

in

February and

March,

8 1 1 7,

with the Committee Meter and a standardized iron a bout meter by Lenoir. In the same

year Hassler determined their coefficient of expansion and found it o'ooo 006 963 for

Fahrenheit's scale or o'ooo 012 534 for the Centigrade scale, a value somewhat large yet

probably applying to these particular bars, but this could not be verified, the bars having

long since been lost. In May, 1834, and March, 1835, in connection with the Fire Island

base, comparisons were made involving the Troughton brass scale and the Committee

Meter. The last comparisons date from 1 844-45 , and were made with a Bessel level-contact

comparator, using the Lenoir iron meter. The results were, for the combined length

at oC:

2 From comparisons of 1817

= 7"'999 9506

From comparisons of 1834-35

8'ooo 0414*

From comparisons of 1844-45

242 7'999 8716
55

When the comparisons in 1835 in connection with the Fire Island base had been
A made an examination of bars and B showed them to be rusty. After cleaning them

they were again com-

pared, and the new 1835

2= value

fn 'g9g 9764 re-

sulted. The last obser-

vations indicate a decided

apparent shortening, which has not been ac-
counted for satisfactorily except it be due to the manner in which the
8-meter bar was built up. Upon the whole, it has been thought best to adopt
the Hassler value of
1834-35 for the reduction of the Fire Island
base as representing the conditions then existing.
But one measure of the base was made, owing probably to the labor and time required to measure such a long line. The measure was made during the months of August, September, and October, 1834. The above diagram shows the condition at

The value found in connection with the Fire Island base.

46

THE EASTERN OBLIQUE ARC.

the eastern end. The distances 2 to 3, 3 to 4, and 4 to 5 were measured with the base apparatus, and the angular horizontal directions of the fine and heavy lines at the points 1, 2, 3, 4, and 5 were obtained by means of a theodolite. Calling West Base
No. 6, the points 6, 5, 4, and 3 were placed in line. For reduction of the measured length of the base to sea level, the average height of the bar above the half-tide level
of the Atlantic was taken as 275 meters. The mean temperature of the bar during measurement was 26'6o C. (or 79'90 F. '). The resulting length from West Base to East End was as follows:

1 725 boxes

,

oC Correction for excess of temperature over

Correction for inclination

Reduction to half-tide level of ocean

13 .Socyoyu
+ 4"6o3i
02055 o -oo6o

Resulting length
Similarly we have the short measures
Line measured
Number of boxes
Corresponding length Correction for expansion Correction for inclination Defect of last box at eastern end

BASE LINES AND BASE NETS.

47

The. Fire Island base net and results of its adjustment.

In this net we include the quadrilateral which transfers the measured base to the

so-called mountain base, and the two other quadrilaterals, one within the other, which

start from this derived base. The line Wooster to Sandford will be the connecting link

with the northeastern triangulation, and the line West
Hills to Bald Hill will form the link for the south-

No. 7.

western branch.

The elevations of the stations above the sea level

are very moderate and the horizontal directions needed
but very small corrections, the maximum being less than o"'o2, but no account of this was taken when less than o"oo3. The approximate heights of the
trigonometric stations are as follows:

Meters.

48

THE EASTERN OBLIQUE ARC.

= error

t* c

equals

2
(o'23)

2
(o'iq)

or

e c

o"'i3, that is, the combination error is but

slightly less than the observing error eo.

If <r" c

is

added

to

each value of

e^ we

get

= the weight of each direction p i/(e'c -\-e'o ). Among the values of e there was one

= exceptionally large, and, omitting it, we findf

o"'i8,

hence

e c

=V(' 2 33)

( -I 83)'

=

o' 144 and p

1 / f_(o" 144)*+ ef] , and in order to make the average sum of the recip-

rocals of the weights nearly unity, the values of i/p were multiplied by 13. The range

in these relative weights is still large, the ratio of the greatest to the least being as 16

to 1, but it would have been as 144 to 1 had not the equalizing device been introduced.

Comparing the old with the present results they are found to be nearly the same. For

the side Wooster to Sandford we have old log. distance (Coast Survey Report for

1865, pages 201-202) 4-669 171 1 and by the present adjustment 4-669 171 o, which

log. difference corresponds to a linear difference of but 2 centimeters. For the side Bald

Hill to West Hills we have old log. distance (Coast Survey Report for 1866, page 52)

4648 135 3,

and

by

the

present

adjustment

-
4 648 135 6, corresponding

to a

linear

difference of 4 centimeters.
A preliminary publication of results of the triangulation about this base and vicinity A was made in 185 1 in the Coast Survey Report of that date, pages 222 and following.

second publication will be found in the Coast Survey Report for 1865, pages 201-202.

These results are now superseded.

Abstracts of horizontal directions at stations forming the Fire Island Base Net. /83J-/865.
Fire Island Fast Base, Suffolk County, New York. October 1 to October 8, 1837. F. R. Hassler,
observer. 75' direction theodolite No. I. Circle used in VI positions.

&. directions.

Object observed.

Resulting directions from station
adjustment.

Fire Island West Base West Hills Ruland*

BASE LINES AND BASE NETS.

49

Abstracts of horizontal directions at stations forming the Fire Island base net, /8jj-/86^ continued.

Ruland, Suffolk County, New York. August 19 to September 16, 1837. F. R. Hassler, observer.

cm 75

direction

theodolite

No.

1.

Circle used in VI positions.

June 11 to July 27, 1865. G. W.

V Dean, observer. Same instrument. Circle used in positions.

Fire Island East Base Fire Island West Base
West Hills
West Hills Wooster
Tashua* Sandford *

Adopted results at Ruland:

No. of directions.

Object observed.

CO 00 000
-'7 17 02-651 +0-065
78 54 02221 +0-114
o 00 00 000 61 26 28-009
+0-047 73 59 43-262
+0-047 '9 14917
+0-047

0-14
0-09 0-08
007 009

Resulting directions from
station ad-
justment.

Ap-
proxi-
mate
probable
error.

Reduction to
sea level.

Seconds reduced
to sea
level.

Correction from
net ad-
just-
ment.

Final sec-
onds.

7

Fire Island East Base o 00 00000

0-14

8

Fire Island West Base 27 17 02 -716

o - 22

9

West Hills

78 54 02-335

0-35

o 020
0-310
+0 -266

59-980 02 -406 02 601

10

Bald Hill f

11

Wooster

12

Tashua

132 oS 56733
140 20 30-391 152 53 45 '644

0-27 o '08
007

0-012
0018 -0-008

56-721 3 373 45 '636

+0-131
+0 -040
-o. 134

56 -852
3 '413 45 "502

13

Sandford

180 13 17-299

009 +0-004 17 '303 +0-192 17 '495

West Hills, Suffolk County, New York. October 18 to December 1, 1836. F. R. Hassler, observer.
75"" direction theodolite No. 1. Circle used in VI positions. July 18 to August 15, 1865. G. W. Dean, observer. Same instrument. V Circle used in positions.

5

THE EASTERN OBLIQUE ARC.

Abstracts of horizontal directions at stations forming the Fire Island base net, /8jj-/86j continued.

No notice is taken of those measures of 1836, which are superseded by new measures of 1865. The corrections for eccentricity are indicated; instead of increasing the direction to Ruland by o// "i36 this amount is subtracted from the measures of the base ends.

Resulting directions at West Hills:

No. of directions.

Object observed.

Resulting directions from
station ad-
justment.

Approximate
probable error.

Reduction to
sea level.

Seconds reduced to sea
level.

Correction from
net ad-
just-
ment.

Final seconds.

//

Wooster Azimuth Mark

O CO OO'OOO 7 26 21 768

-06
o -o6

-0003 59997 to -169 00-166

16

Tashua

17

Sandford

21 35 06-476 33 58 36-531

0-05 0-08

+o -oo6 +0 -014

06 -482 36 -545

o -099 0-089

06-383 36 -456

18

Ruland

89 14 44 741

0-32

-f-O'226 44-967

19

Fire Island East Base 122 36 15 '675

"33

20

Fire Island West Base 143 58 00-808

0-38

Harrow*

269 17 04-256

016

0-400
+0 -406

15 275 OI -214

Round Hill*

33' 59 49 '2ii

0-33

14

Bald Hill*

359 21 01 -916

0-25

-0-003 01-913

0-I23 01-790

Tashua, Fairfield County, Connecticut. August 25 to September 16, 1833. F. R. Hassler, observer.

cm 75

direction

theodolite

No.

1.

Circle used in III positions.

September 2 to October 21, 1S63.

G. W. Dean, observer. Same instrument. V Circle used in positions.

30

BASE LINES AND BASE NETS.

51

Abstracts of horizontal directions at stations forming the Fire Island base net, f8jj-/86f continued.

Wooster, Fairfield County, Connecticut. July 14 to October 10, 1864. G. W. Dean, observer.

V cm
75

direction

theodolite

No.

1.

Circle used in

positions.

No. of directions.

Object observed.

Resulting directions from
station ad-
justment.

Ivy

25

Sandford

26

Tashua

27

Ruland

28

West Hills*

52

THE EASTERN OBLIQUE ARC.

I

2-
I

Reciprocals of the weights or values of r_3

o= +0-945 o= 0*158 0= +0-027
o=+o'462 0= -0988 0= +0-321 o= 0-236 0= +0-072
0= + 1-026 0= +0-093 0= + 1-432
9"5
0=+4'2
o=+3'0 . 0= -o-8 0= + r4

BASE LINES AND BASE NETS.

53

Resulting angles and sides of the Fire Island base net.

Observed angles.

Correction.

- 7+ 8 Ruland

27 17 02716

'

4+ -

6 Fire Island East Base 1 1 2 32 52 "425

- 2+ 3 Fire Island West Base 40 10 05 353

-19+20
- 4+ 5
-1+3

West Hills

21 21 45 133

Fire Island Fast Base 44 48 25 129

Fire Island West Base 1 13 49 5i '57'

-18+20
- 8+ 9
- i-r 2

West Hills

54 43 '6 '067

Ruland

51 36 59 '619

Fire Island West Base 73 39 46-2T8

-18+19
-7+9
5H 6

West Hills

33 21 30'934

Ruland

78 54 02 -335

Fire Island East Base 67 44 27 -296

-3^3< - 9-12

Tashua Ruland West Hills

38 20 42 -545 73 59 43 '30 1 67 39 38-259

-27-28 - 9+i> -15+18

Wooster Ruland West Hills

29 18 52 -587 61 26 2S '038
89 14 44 744

-26-27
-30+33
-n + 12

Wooster Tashua Ruland

28 53 58 -295 138 32 49-081
12 33 15 '263

-26-28
-3I-I-33
-15+16

Wooster Tashua West Hills

58 12 50-882
100 12 06536
21 35 06 485

-21+22
+ - 9 '3 + -17 18

Sand ford Ruland West Hills

23 24 4i '555
101 19 14968
55 16 oS 1 96

22 23 -16- 17
-29+31

Sandford West Hills Tashua

'9 12 16-869 12 23 30 -063 148 24 16 201

21 -23 -12+13 -29+30

Sandford Ruland Tashua

42 36 58 -424
27 19 31 667
no 03 33 '656

-22 24
-15+17
-25 28

Sandford West Hills Wooster

45 38 5' '567
33 58 36M8
100 22 39 -308

4

BASE LINES AND BASE NETS.

55

station for greater security. Four stone postswere placed to the north, south, east, and

west of the center stone post. On the upper surface of the center stone post the inter-

section of two lines marks the position of the center point of the Hassler crock of 1833.

Around each post concrete was placed to secure it firmly in position. Upon the

center stone was placed a stout stub of locust wood into the top of which, level with

A the ground, a copper tack was driven, marking the center point.

fuller description

is given in the record of 1865, when the station was reoccupied. ,

West Hills, Suffolk County, New York. This station was established by Superin-

tendent Hassler in 1836. It is marked by a red sandstone post, 4 feet high and 1

foot square, sunk in the ground, with stones well packed around it; the intersection of

A diagonal cross lines upon the top marks the station point.

crock, which had before

served as station mark, was placed upon the post and a nail in a wooden peg driven cen-

trally through it marks the station. Upon the side of the post facing Harrow were cut

the initials U. S. C. S.

The station was reoccupied in 1865, and again described. The place is 4 miles- from Huntington and 7 miles from Farmingdale railroad sta-
tion. The point is on the summit of a hill. An examination had been made in i860, when the stone post appeared not to have been disturbed, but the crock was broken and

the stub decayed.
To mark the point more securely, posts arranged about the center post, north, south,
A east, and west of the station, were sunk to a level with the surface of the ground.
stout wooden stub, with a nail driven into it, was placed over the center of the old post to mark the station. Some further remarks are given in the 1865 description.
Tashua, Fairfield County, Connecticut. This station is located in Trumbull town-

ship, Fairfield County, Connecticut. It was established and occupied by Superintendent Hassler in 1833. The station was reoccupied in 1863 by the party of Superintendent
Bache, by whom the following description is given:
" The station point is marked by a copper bolt inserted in the top of a granite post sunk 2 feet below the surface of the ground. Four similar posts, 8 inches square and
2j4 feet in length, were adjusted 6 feet distant to the north, east, south, and west of
the center point. The tops of the posts are marked by two lines intersecting at right angles and the letters U. S. C. S. Four directions to signals visible from the station
are marked by copper tacks driven into hickory stubs at distances 171 feet 3 inches toward Ruland, 121 feet 7 inches toward West Hills, 73 feet q inches toward Wooster,
and 70 feet 3 inches toward tower in Warren."
Sandford, New Haven County, Connecticut, 1862. This geodetic point is located
on the highest and most western summit of Sandford Mountain, 5 feet from a pile
of stones which marks the boundry line between New Haven and Bethany townships.
The point is marked by the center of a half-inch drill hole in the top of a granite post
which is 234 feet in length and 1 foot square at the upper surface. Two cross lines

and the letters U. S. C. S. are cut on its top, which is 1% feet below the general surface

of the ground.

For

greater

security

four granite

posts,

each

2

l
/i

feet

long

and

6

inches

square at the top, were sunk into the ground at points about 6 feet to the north, east, south, and west of the station. The tops of these posts were flush with the ground.
To this description Assistant G. W. Dean adds the following: " The top of the stone post
marking the station was sunk 20 inches below the plane of the four surrounding stones.

56

THE EASTERN OBLIQUE ARC.

A copper tolt was driven into the central stone and the center accurately marked by

A intersecting lines.

cedar stub was placed immediately over the center of the granite

post, the top of which was flush with the ground and firmly secured with earth. The

station point was further marked by a composition nail driven into the top of the cedar

''
stub.

Bald Hill, Fairfield County, Connecticut. This station was established in 1833 by Superintendent Hassler and occupied by him in that year.
The hill is situated in Wilton Township, about 4 miles south of Ridgefield. The station was visited by Assistant Farley in 1868, who found fragments of an earthenware crock (of the pattern of the Hassler crocks, or cones, as he called them), and marks cut on three rocks, but he was not able to identify the marks owing to the (apparent ) loss of
the original description of the station by Superintendent Hassler and by Assistant Blunt
in 1866. What made the search at the place more difficult was the fact that rock blasting had been going on there for some time. A second visit in 1869 elicited no certain information from want of application of proper means. The place was next examined .
by Assistant G. Bradford in 1882 and 1884, when, by means of the determination of a

temporary signal, the location of the crock (cone) placed by Assistant Blunt in 1866 was readily discovered. It is assumed that this crock occupies the position of the Hassler crock, because Assistant Blunt is said to have put it in the place of the fragments
of the older one. The station appears to have been recovered. Woostcr, Fairfield County, Connecticut. This station was established in 1864 by

the party of Superintendent Bache. It is located in Ridgefield Township, about 4 miles
southwest of Danbury, on Wooster Mountain, known to the residents in the vicinity as

Pine Hill.

The station point is marked by a copper bolt, and is located on the highest point of gneiss which crops out near the summit of the mountain. The top of the ledge is
quite limited, its length east and west being about 25 feet.

4. THK KENT ISLAND BASE LINE, BASE NET AND EXTENSION, MARYLAND, 1844.
Location, measurement, iind resulting length of the Kent Island base line, Maryland, 1844..
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 is nearly opposite Annapolis Harbor. Originally it was intended as a check on the main triangulation
which extended from the Fire Island base southward and westward, but its position near the latitude of 39 rendered it desirable to incorporate it in the eastern part of the
transcontinental triangulation.
An account of the measure and length of this base is contained in the Coast Survey
Report for the year 1866, supplement to Appendix No. 8, page 140, and again in
Special Publication No. 4, "The Transcontinental Triangulation." The middle point of the base is in latitude 3S 56'" 1 , and in longitude 76 2i'"2, the
mean azimuth is 14 35' '4, and the length 87 kilometers (or 5*4 statute miles). The
surface of this part of the island is slightly undulating, and the line crosses cultivated fields, with some portions covered by swamps and woods. The elevation is very little
alxjve the surface of the bay. The shore is subject to erosion, in consequence of which the terminal monuments, each consisting of an upright stone surface mark with a copper

BASE LINES AND BASE NETS.

57

bolt in a piece of slate below the surface, the whole being protected by rubble masonry, have disappeared.
The base was measured by Assistant J. Ferguson, in May and June, 1844, by
means of the same apparatus as was used for the measure of the Fire Island base ten years before. It is known as the Hassler base apparatus,* and consists of four rectangu-

H B lar iron bars each 2 meters long, put together endwise and aligned in a wooden trough.

The protruding ends of this 8-meter bar have semicircular notches '

across

which was stretched a spider thread; over this was mounted, f.

')

on 111

independent stand, an adjustable micrometer microscope, by means of which the measure was held while the bar was brought forward into a new position. All needed adjustments for the apparatus were provided for and the temperature of the bar was read from thermometers attached to the top of the 2-meter bars placed in the bottom of the trough, which is supposed to have been covered with canvas. At the end of a day's work or at other times when necessary, the end of the last bar laid was transferred to the ground, generally by a plummet. Only one measure was made, and the total time consumed was a little over one month.

The four 2-meter bars made by Troughton, of London, about 1813 were standardized

in 18 1 7 by Hassler, by using the Committee Meter, in 1834-35 by using the Troughton

brass scale, and finally, in 1844-45, by Superintendent Bache, J. Saxton, and \V.

Wiirdemann, by using a Bessel comparator, with the following results:

In 1817 1834-35 1835 1844-45

2=7"'-999 9506 at o C. 8-ooo 0414
t7"999 9764 7-999 8716 55

This last value, after verification in July, 1854, was finally adopted for the two bases measured with this apparatus in 1844. The coefficient of expansion of the bar which was determined in 1817 by Hassler at Newark, viz, o'ooo 012 534 for the centigrade
scale, was adopted and, though somewhat large, may nevertheless be true for these particular bars, now lost. The mean temperature of the bar during measurement of the base was 25' 18 C. (or 77 '33 F. ). The deduced length of the base is as follows:

1086 boxes

8687"' 8606

Excess of last box over end mark at South Base, as measured by Bar D and scale

2 '0508

Correction for excess (25'44 C. ) of temperature of bars over o C. and graduation error of

thermometers (

-o0, 255C.)

127424

Correction for inclination of boxes
5o Reduction to half-tide level of bay for surface elevation and height of boxes

I 0007 o '0069

Resulting length of base'

S6S7""5446

The probable error of this value can only be estimated, since the base was meas-

ured but once. Supposing the combined length of the four 2-meter bars subject to

rfc 20^, the effect on the base will be o""o22; an assumed error of

j' part in the

* For a description, with

illustrations, of the apparatus, see the Transactions of

the American

Philosophical

Sock t\ ,

Philadelphia. Pennsylvania, for the year 1825, pp. 273-286. See also the preceding account of the Fire Island base

measurement.

t Result of comparisons made after cleaning two of the 2-meter bars which were found rusty when examined.

58

THE EASTERN OBLIQUE ARC.

coefficient of expansion would produce

-
o'" 055;

again, the effect for imperfect tempera-

ture correction, for inequality in number of boxes laid with" rising and with falling

temperatures, may be taken as o"'"034; other minor uncertainties may be omitted.
Combining the several values for probable error gives om 'o68, equal to ST J 00 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 Meter, taken as Yxr1 -

Resulting length of Kent Island base, 8 687*5446 meters and its logarithm,

0680

3-938 897 05

3 40

Kent Island base net and results of adjustment.

The following abstracts of observed and adjusted directions at the nine stations form-

ing the base net proper, as well as the conditional equations and results of its adjustment

with resulting length of triangle sides, were copied from Part I, Special Publication No. 4,
"The Transcontinental Triaugulation, " and from Part III of the same publication the.

results of

two

*
triangles

to

the

northward

of

the

net

and

of

35

triangles

to

the westward

and southward of the base.t The triangles of this last extension are shown on the follow-

ing sketch:

OsbornesRui

Finlay ,

Turkey 'Poini,^

Kent Island. North. Base

Marriott

Kent Island South Base
Kilometers Statute Miles

* Shown on the above sketch by dotted lines. t For adjustment of this work see Special Publication No. 4. " The Transcontinental TrianRUlation.'

>

BASE LINES AND BASE NETS.

59

The heights of the stations above the half-tide level of the ocean are small and
approximately as follows:

6o

THE EASTERN OBLIQUE ARC.

Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming lhe"J>ase
net, 1844-/897.

Kent Island South Base, Queen Anne County, Maryland. May 30 to June 4, 1847. 30" repeating

theodolite No.

E. Blunt, observer. (Observations in 1844 by J. Ferguson superseded by

above. )

Number of
directions.

Object observed.

Resulting directions from sta-
tion adjustment.

Corrections from
base net adjustment.

Final seconds.

Marriott

o

OO'OO

+0-03

Taylor

46-24

-)-o '06

Kent Island North Base

11 1

1825

-o'oo,

= Probable error of a single observation of a direction ( 6 I), and 6 A'. ), e,

00-03 46-30
1S16
0" 69.

Kent Island North Base, Queen Anne County, Maryland.

May 21 to 28, 1847.

cm
3o repeating

theodolite No. 11. E. Blunt, observer. (Observations in i844-'45 by J. Ferguson superseded by

above. )

4

BASE LINES AND BASE NETS.

61

Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming the base
net, 1844-iSgy continued.

Webb, Anne Arundel County, Maryland. July 10 to August 14, 1848. 6ocm direction theodolite No. 2.

A. D. Bache, observer. October 21 to December 2, 1850.

cm 75

direction

theodolite

No.

1.

A. D.

CO. Bache, observer.

September 18 to 25, 1868.

cm 75

direction

theodolite

No.

1.

Boutelle,

observer.

Number of
directions.

62

THE EASTERN OBLIQUE ARC.

Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming the base
net, /844-1897 continued.
Finlay, Baltimore County, Maryland. August 29 to September II, 1844. 60" direction theodolite No. 2. J. Ferguson, observer. October 15 to December 27, 1896. 30CI repeating theodolite No. 16. G. A. Fairfield, observer. Telescope above ground 1-5 meters.

Number of
directions.

Pinal seconds.

r#

BASE LINES AND BASE NETS.

63

The correlate and normal equations, when established and solved, gave the follow-
ing values of corrections to the angular directions:

(I)=

Results of local adjustment.

Coast and Geodetic Survey, J90J. The Eastern Oblique. Arc.
Maryland Heights

Wehb

No. 10

Ml. Marshall] Fork
THE KENT ISLAND BASE
Triaiiulation to tin; Westward and Southward

^

BASE LINES AND BASE NETS.

65

Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued.

Peach Grove, Fairfax County, Virginia. October 1 1 to November 8, 1869, ami July 28 to August 15,

1870.

cm 75

direction

theodolite

No.

1.

C. O. Boutelle, observer.

Telescope 1372 meters above

ground.

ObjJects observed.

Results of local adjustment.

Correction from

.

.

66

THE EASTERN OBLIQUE ARC.

Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued.

Bull Run, Fauquier County, Virginia. September 22 to November 28, 1.S71. 75'"- direction theodolite

CO. No. I.

Boutelle, observer.

Azimuth Mark

o

/

//

o 00 00 "oo

Clark

1 07 09 -35

Fork

33 03 17 -51

Mount Marshall

53 39 05-53

Maryland Heights

157 20 07 -15

Sugar Loaf

190 54 06 -98

Stabler

225 12 0395

Peach Grove

242 29 57 -85

D = Probable error of a single observation of a direction ( . and R. ) , f,

of circle, VII.

//

//

....

+o'ii
+0 -49
o '68

05-64 07 -64 06 -30

-j-o-oS

04-03

"
r 09.

o -co

57 S5

Number of positions

Maryland //eights, Washington County, Maryland.

September 16 to October 28, 1870.

cm 75

direc-

CO. tion theodolite No. 1.

Boutelle, observer.

Sugar Loaf

00

Azimuth Mark

Stabler Peach Grove
Bull Run Mount Marshall
R Probable error of a single observation of a direction ( D. and
of circle, VII.

Clark, Orange County, Virginia.

July 24 to September 5, "1871.

C. O. Boutelle, observer.

o

/

c,u
75

direction

theodolite No.

I.

//

//

//

Spear Peters

Humpback Azimuth Mark

Fork

Mount Marshall

Bull Run

= Probable

error

of

a single

observation of

a direction

D.
(

and

R. ),

*,

of circle, VII.

1 -03. Number of positions

BASE LINES AND BASE NETS.

67

Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued.

Fork, Madison County, Virginia. October 12 to December 24, 1874. 35^"' direction theodolite No. 10. A. T. Mosman, observer. July iS to August 6, 1879. 5ocm direction theodolite No. 114. Same

observer.

<*

asas*

r" jssl

Peaked

O

/

//

o 00 00 -oo

//

//

....

Slate Springs
Mount MarsnaU Bull Run

20 16 00 -96 136 25 13 '62
161 06 3764

Clark

224 16 58 -6S

Peters

270 56 24 '51

Spear

.

303 52 39-51

Humpback

322 58 40-96

Elliott Knob

353 33 11-50

= Probable

error

of

a

single

observation

of

a

direction

/).
(

and

R.

),

e,

tions of circle, XI in 1S74 and in 1879.

-)-o "98
+039
1 -oi
o \%

01 -94 14-01 36 '63 57 -82

....

o"io o -20

39-41
4076

-fo'So

12-30

i"-24. Number of posi-

Humpback, Nelson County, Virginia. June 8 to 29, 1S75. 35" direction theodolite No. 10. A. T.
Mosman, observer. May II to June 6, 1878. 50 direction theodolite No. 114. Same observer. August 18 to 28, 1879. 50cm direction theodolite No. 114. A. T. Mosman and W. B. Fairfield,

observers.

o

/

//

//

//

Jarman

o 00 00 'oo

....

Clark

24 30 20-46

+' '37

21-83

Peters

,

^

31 40 01 -24

Spear
Long Mountain
Tobacco Row
Bald Knob

126 14 25-02 154 41 57 'io 173 06 07-68 230 26 24-65

+0-44
....
0-87 +0-17

25-46
06 -8 1 24-82

Elliott Knob

265 35 01 13

1-03

00 -io

Slate Springs

300 08 53 -99

o 57

53 -42

Fork

357 28 32-18

+0-33

32-51

= Probable error of a single observation of a direction (D. and R. ),ez

//i 43.

Number of

positions of circle, XI.

Spear, Buckingham County, Virginia.

July 30 to August 29, 1875.

cm 35

direction

theodolite

No.

10.

A. T. Mosman, observer.

o

/

//

//

//

Willis

o 00 00 -oo

....

Long Mountain

1 13 14 26 -50

....

Flat Top
Tobacco Row

150 15 15-49 160 17 43-42

....
+022

43 -64

Humpback

233 59 02-50

0-44

02-06

Fork

266 07 14-11

+0-05

14-16

Peters

283 15 22 -59

Clark

288 05 31-91

Probable error of a single observation of a direction (D. and R.), e, positions of circle, XI.

....
+017
//i 37.

32-08
Number of

68

THE EASTERN OBLIQUE ARC.

Abstracts of resulting horizontal directions observed and adjusted at the stations forming the extension of the Kent /stand base net to the westward and sonthivard continued.
Tobacco Row, Amherst County, Virginia. September 14 to 23, 1875. 35"" direction theodolite No. 10. A. T. Mosman, observer. September 6 to 9, 1879. 50"" direction theodolite No. 114. Same
observer.

Objects observed.

Results of local adjustment.

Flat Top Bald Knob
Humpback
Spear
Long Mountain Smith Cahas
Probable error of a single observation of a direction (D.a.m\R.),e,= of circle in 1875, XI.

i"'43. Number of positions

BASE LINES AND BASE NETS.

69

Resulting a

13 19

70

THE EASTERN OBLIQUE ARC.

Wetern and southern extension of Kent

No.

23 24 25 26 27 28 29 30 31 32

BASE LINES AND BASE NETS.

71

Western
.

No.

33

34

35

36

37

38

39

40

4i

42

43

44

45

72

THE EASTERN OBLIQUE ARC.

Western and southern

46 47 48 49

BASE LINES AND BASE NETS.

73

is given in Coast Survey Report for 1854, Appendix No. 35, and in Coast Survey Report for 1873, Appendix No. 12. Further remarks will be found in the account of the Dauphin Island and the Epping bases in this publication. It will also appear from the seven values collected on page 131 of the Report for T873 that the average accuracy reached with this apparatus is about s^'iotf part of the length measured. In view of

the complete publication already made, it will suffice to give the present account in an

abbreviated form.

The middle point of the base is in latitude 33 54' '4 and longitude 84 16' '5, with a

mean azimuth 52

-
o8' 2.

The measurements were made by Assistant C. O. Boutelle.

The first and second measures were made in opposite directions in November and

December, 1872, and in January, 1873, and the third was made in Jul}' and August,

1873. The three measures were accomplished in 17, 13, and 14 working days, respec-

tively. In connection with these several measures the tubes* were frequently compared

for length with the standard bar, which was immersed in glycerin during the July and

September comparisons.

The summit of the ridge is narrow and crooked, but the slope of the measurement
was confined within the maximum inclination the tubes would bear, namely, 5 . A

gulch near the southwest end was crossed on trestlework consisting of two separate

structures. The approximate elevation above sea level is 320 meters. The terminals

are marked by granite monuments and the subdivisions of the line by small granite posts.

The length of the 6-meter standard bar is 5"'"999 941 at

C.,and its coefficient of

2

expansion o'ooooii 54. The numerous comparisons made for standardization of the

4

tubes and for testing their compensation showed that the latter was still close; that is,

about 2 1 parts of 22 remained compensated between the range of temperature o

to 22

C. ,

but between the temperatures from 22 to 38 C. the tubes compensated only about 10

parts inn.

The comparisons were made with the Saxton reflecting comparator No.

r ,

for which we have for the period November, 1872, to January, 1873, one division at

4 "4 C. equal i'384 microns and at 19 C. i'378 microns, values answering for the case

3

3

of the first and second base measures In connection with the third measure, observa-

We tions in July and September, 1873, gave 1 div.= 1*376 ft.

have also 1 turn of the

screw at

the

temperatures

4

,

19

and
,

28

C. equal to 35o'9, 352"3, and 353'o6 scale

18

divisions, respectively.
As the result from the above comparisons we have the following values forthe length
of the tubes, in which the uncertainty from the length of the standard is included:

For first and second measures:

= + Tube I]

5""999 999 7

o'odo 003 37 (/

u'2 C.)

144

~ Tube 2 =5 999 647 8 +o'ooooo4 84 (/ 1 1'2 C. )

'9 3

and fcr third measure

= Tube i 3

6""ooo 084 6 4" o'ooo 009 54 {t

112

2=5 Tube

999 730 3 r 0000 008 01 (/

11 6

27'6 C. )

27

S- C. )

Before making the comparisons tube No. i was supplied with a new agate. The Borda scale or differential thermometer as applied to the tubes is shown on plate No. 18 in the Coast Survey Report for 1873.

74

THE EASTERN OBLIQUE ARC.

The minimum temperature at which the tubes were used was 7"7 C, and many

were laid with temperatures below the freezing point; the maximum temperature at

which the tubes were used was 4i"7 C, and many were laid with temperatures above

38 C. The three thermometers attached to each tube were read and the mean values

were corrected for graduation errors. The maximum inclination of a tube laid was 4'7,

and there were a great many with inclinations of 4 . The ruggedness of the ground

caused

the

sum of

the

inclination corrections

for

the whole

base

to mount

up to

n
io'

'22i2

in the first and to io'""o375 in the last measure. Fractional parts of a tube at the base monuments and intermediate marks were measured with the brass Lenoir meter of the

Survey, which is of standard length at i3'6 C. The following table shows the temperature of the tubes during the measures of the
several parts of the base, their lengths as measured, corrected for inclination, but not reduced to sea level, and exhibits the difference of the individual measures from the
mean of the three measures:

Subdivisions of base.

BASE LINES AND BASE NETS.

75

afford a check on the measure. Starting with the first or shorter distance and using

the adjusted angular measures, the length of the base thus trigonometrically deduced

comes

out

9

n
338 '"502,

or

22"""

in

excess

of

the

direct

linear

measure.

For the probable error of the measure of the base we have the following data:

= Probable error from uncertainty in length of tubes in 1 556 tubes, 1 556 X 14'oyu

2 2 om '02i 78. For mere measuring error we have, after forming the values

3' tt

8*,

22 <? 3,

etc.,

where

the S's

are taken

from

the

preceding

table

of

differences

from

the

mean of three measures, assumed of equal weight, the probable error of the base from

.tuhese measures =

2 3*+2 3*+2 fV o

<:
674

(

'

=
(

3*+ .\% ..

= *

!

/

.
where

n

)

J 1)

3,

.
hence

At.he

= result

o'"'oo3 85, which includes errors arising from defective compensation, errors

of contact, of transfer to ground or to monuments, of alignment and inclination, etc.

Supposing an uncertainty in // of 1 meter, the reduction to sea level changes

i"""-46.
Combining the values we get the probable error of the base

2
V(2i-78)

+(3-8 5 )'+(r 46) 2

=

=fc

222,

which equals jjt (ftrtr Part of the length.

The resulting length of the base is 9 338'477 8 meters, and its logarithm 3^970 276 09

22 2

1 03

Adjustment of the Atlanta base net.
The base is connected with the principal triangulation by a rather complex system of triangles, which made the placing of the boundary of the net to some extent an arbitrary act, except in so far as the labor involved set a limit to it. The net as it had been selected and adjusted in 1876 is here retained as satisfactory. The only change that could be made would be the introduction of the small corrections to the horizontal directions for height of object observed upon, which it was not customary to introduce
at that time.
The heights of the 10 stations involved are as follows:

Approximate heights of stations above the Atlantic Ocean.

Atlanta Southwest Base Atlanta Northeast Base

Meters.
318 -5

Feet.
1 045

76

THE EASTERN OBLIQUE ARC.

This reduction of the directions to sea level, a maximum in the case of line Pine

Log to Grassy, is less than o"o7, and in general it is less than one-half of this amount.

It is therefore fully covered by the observing error of the directions which on the aver-
age amounts to ^ * or o"'i9; besides, a number of directions require corrections in the
77

figure adjustment of more than i".

As shown in the diagram, the net comprises 10 stations which were occupied between 1872 and 1874; two observers were engaged in the work and three different instruments

jo Grassy

no is

were employed, one being a
repeating theodolite. The ad-
justment of the observations

of directions at a station was

made by Bessel's method, and

the results are presented in the abstracts, where, for con-

venience, the resulting cor-
rections due to the figure or net adj ustment have been add-
ed. The latter computation
involved 29 conditions which had to be satisfied. Here

weights to the directions were

introduced, depending upon the same principle as ex-
plained in the case of the ad-
justment of the Epping base net. In accordance with the

method of application of weights to the directions in a net adjustment, we derive the mean error of a triangle from the sum of the squares of the closing errors of the 30 triangles involved and find

fiTt

y

=i"'74; hence also

the probable error of a direc-

BASE LINES AND BASE NETS.

77

Abstracts of horizontal directions at stations forming the Atlanta base net, 1873-/874.

n Atlanta Middle Base* De Kalb County, Georgia. January to 30, 1873. C. O. Boutelle, observer.

cm 75

direction

theodolite

No.

1.

Circle used in VII positions.

Number of
directions.

( )bjects observed.

7

THE EASTERN OBLIQUE ARC.

Abstracts of horizontal directions at stations forming the Atlanta base net, /8/J-/S/4 continued.
A'enesa?i\ Cobb County, Georgia. June 25 to July 18, 1873. F. P. Webber, observer. Instrument as before. Circle used in VII positions.
Number of
directions.

BASE LINES AND BASE NETS.

79

Abstracts of horizontal directions at stations forming the Atlanta base net, 1873-/874 continued.

Sawnee, Forsyth County, Georgia. October 7 to November 12, 1873. C. O. Boutelle, observer.

cm 75

direction

theodolite

No.

1.

November 26 to December 4, 1873.

Same observer.

5ocm direc-

tion theodolite No. 3. Circle used in VII and IV positions, respectively.

Number of
directions.

8o

THE EASTERN OBLIQUE ARC.

.Abstracts of horizontal directions at stations forming the Atlanta base net, 1X73-/874 continued.

Pine Log, Bartow County, Georgia. July 29 to September 17, 1874. F. P. Webber, observer. 3ocm repeating theodolite No. 32.

Number of
directions.

Objects observed.

Resulting directions from station
adjustment.

Approximate Correction

probable

from figure

error.

adjustment.

Final seconds

Carnes

O OO OO OOO

10

....

Indian Coosa Lavender Gulf

Johns Cohutta

49

Grassy

48

Sawnee

47

Sweat Mountain

46

Kenesaw

Lost Mountain

Pine Mountain

22 30 38597

36 '7 34 507

46

35 508

70

50 280

84

43 143

141

1 2 849

193

40 009

238

36-125

285

n -88o

308 19 38-586

323 54 52 071

347 ,59 1 > 443

013 012
o 08
012
O "12 o '14
0-13
on
Q-I2
OIO 015
0-14

......
o '600 +0-598
054I +0542

Mean correction o "ooo

Observations made in sets of 3 D. and 3 R. measures.

=1' Probable error of a single observation of a direction (6 repetitions), e,

23-

leaden

39'4o9 36 723
' 1 -339 39 '28

%
XI

BASE LINES AND BASE NETS.

8l

Observation equations continued.

33i-(38)+(4o)-(3 f)+(a9)-(i7)+(i&)
+ + + 971- (9) (ii)-(28) (29 )--(i7) (i5) + . 35 i-(ii) + (i3)-(5o)4-(52)-(34) (28) + + !-296-(l0) (lI)-(28)-f(30)-(23) (2l)
i 54 -(48) + (47)-(26) + (23)-(3o) + (33) 83i-(33) + (32)-(44) + (45)-(49) + (48) + + 3 i3-(26) (25 )-(43) + (45)-(49) (47) + 3oi-(22) + (26)-(47) (46)-(i9) -|-(i6)
152-0 -095(4) +0 -095(7 )-o-o26(8)+o -026(12)- 1 -505(35)+o-8i4(36)+o -691(37)

, -124-0 -n6(4)+o -021(6) -(-0-095(7)4-0 -531 (ao)+o 795(21)- 1 -326(24) +0-344(36)

'499(37) -0-843(39)
( -9420 -226(8)+o -199(9) -i-o -027( 12) -7 -676( 14)4-0 7g8( i5)-f-6 -878( 18)

I -941(36)4-0 -344(37)4-4 -596(38)

4364-0 -140(8) o -199(9)4-0 -o6o( io)4-o -6g9( 14) -o 798( 15)4-0 -o99< 16)

+0 1 -565(20)4-0 -531(21)

-034(22)

1-004 4- 1 -883(21) ! '3 26(24) -0-557(27) 4-0 -9i7(37)--o-843(39)-o -074 (41)

>726(5o)-o -496(51 )-o -230(53)

1 -915-0 "9i6( I5)4-o -207( 17)4-0 709( 18)- 1 -128(28)4-0 -237(29)4-0 -892(31 )

'692(37)4-0-311(38)^0-380(40) i '359+ '628(28)-o -892(31 )4-o -264(34)-(-o -306(37) o -380(40)4-0 -074(41 )

'305(50)4-0-075(52)4-0-230(53)

7924-0 -403( 9 )-o -500(10)4-0 -097(1 1 )4-o-i76( 15)4-2 '439(i6)-2 -616(17) 220(28) -5 -705(29) 4 5 "485(30)
463 ( o -223(23) -0-238(25)4-0 -016(26) 0-222(43)4-0 -2ro( 44)4-0 -012(45)

1 -194(47 )-o -404(48)4-0 -210(49)

619-2 7557( r6)4-2 '6l57( 17)4-0 -i4oo( 19)4-5 7048(29) 5 -9022(30)4-0 -1974(33)

1-5032(46)---0-6971(47)4-0 -1939(48)

[491 --2 -6157(16) 4-2 -6157(17) -0-4212(22)4-0 -4212(25)4-5 7048(29) 5-6861(30)

0187(32)4-1 -8885(42)-2 -1104(43)4-0 -2219(44)

liquations of correlatives.

= (i) i-o(4-C) (2) = i-o(-C,-C2 )

(3)=i -0(4-0

C) = (4) i -o(C,4-Cs 0-095 C o-ii6

= -C (5) i-o(4-C6 8 )

C) = -C (6) i -o(-C4 5 4-C8 4-o-o2i

O) = (7) 1 -C -o(4-C34-C4 6 +o-o95 04-0-095

O-o = (S)

i -o(4-Ca 4-C,

C 5

0-026

'226 04o-i4oO)

= (9) l o(-( C7 -C, 2 + o-i99Ca ,-o-i99C 4-0-403 C26 )

O = -
(lo) l o( 4-Cs C,

+ O '6o

0-500 Cat)

-O+O+o (ii)=i -o( t-C,2

-097 O)

4192 No. 7 02

6

82

THE EASTERN OBLIQUE ARC.

Equations of correlatives -continued.

i
'
:

P
(i2)==i o(-C-C3 -C7 +CIO+o-026 C+o-o27 C)

(i3) = i-o(+C,-C,fC>

c) = (i4) i -2( C6 +C8-7 '676 C-po -699

C C-o C-o = 3 (i 5 ) i ( C,+C+o 798

798

CO -916 4 +o -176

C+2 = (i6) i -i (-C8+C,8-o -099

-4394 C0-2 7557 Cs-a 6157 C,)

= C (i 7 ) i -i( Ca+o-ao7 C-a-6i57 0,6+2-6157 C8+26157 C,)

C+o (i8) = i-2(+C+C7 +C,+6 -878

709 c,,)

= (i9) i 7( Cn+o -1400 Cs)

= (2o) i o(+C4 +C5 -C8 +o-53i 0,0-0-565 C)

= (2i) i 2(-C5 +C,+C+o795 0,0+0-531 C+i -883 C3)

=
(22)

i

-o(+C8-Cl8 +o-034

Q-o-42i2

C,9 )

= +o C ( 23 ) 1 1 ( -C, 4 +C, 5

-2230 7 )

= (24) i o(-C,-i'326C-i -3260,3)

= ( 25 ) I -0(+C, 7 -0-23S5 C^+O'4212 Co)
= C -C (26) i -i(-C I5 I7 +C8+o-oi55 7 )

(27 ) = i-2(-C-o'557C3 )

+C-C = (28) I i(-C,3

4 -i-i28C4+o-628C5+o-22oC6)

C = (29) i 2(^-C+C,1,+o-237 4 -5 7048 Cs+5 7048 Cs+5 7048 C)

= ( 30) i -i(+C^-C+5 '4851 C.-5 '922 Cs-5 -686i C)

C = (31) 1 i(-C+o-892 4 -o-892Cs )

= C ( 3 2) i i(+C l6 -o-oi87 9 )

-C = ( 33 ) i o(-C,5

6 +o-i974 Cs)

= (34) i 2(-C I3 +o-264C5 )

= (35) I-

(- c

I

'55Co)

C = ( 36) i i(-C3 -C4 +C+o-8i4Co+o-344CM -4-94iC.)
= ( 37 ) i -o( +C,+C3 +C7 -C,o +0-691 C,o+o-499 C+o'344 ,,+0-917 0,3-0-692 4 +o'3o6 C,5 )

C (38) = i-2(-C-C7 -C+4-596C.+o-3iiC4)

= < 39 ) i -2(+C4 - o -843

-o -843 C)

C = (40) i o(+C,+o -380 4 0-3800,5)

= C (40 1 -i(+C IO -o-o74 3 +o-074 C,5 )

= ( 4 2) i-i (+1-8885 Co)

= C C) (43) i -o( C, 7 -o-22i9

-2
7

-1104

= C C) +o +o C (44) 1 -o(

l6

-2097 7

-2219

= (45) ' o(+C,+C,,+o-oi22 C?)

= (46) i -o( +0,8+0-5032 C,8 )

= , (47) i o(+C,s +C, 7 -C,8+o -1939 C -0-6971 C,8)

(48) = 1 -(-Cs+Cs-o-^osg Cj+o-1939 Cs)

= (49 ) i -o(-C,6-C 7 +o -2100 c,)

o(-C+C-C = ( 50) i

3 +o726 0,3-0-305 C,5 )

(5i) = i-o(+C+o-496C,3)

(52) = i-i(+C+o-o75C5)

= (53) ' -o(-C,o-o -230 C3+0 -230 C,5 )

BASE LINES AND BASE NETS.

83

Normal equations.

i

84

THE EASTERN OBLIQUE ARC.

C, = 0-115 09

Ca =+0-193 18

C 3

=-0-071

44

C, = +o - iio 00

C s

=-0-378

51

C = -o -337 23

C, =4-0-050 86

= Ce

O -362 70

C, = +0-411 93

C, = +0-255 74

Resulfaig Correlates.
C =+o-o83 78
=- C,a 0-350 90

C= 305 71

=- C,5

0-851 29

C, 6 =- 0-234 29

C,,= +0-978 52

C,g= -0-131 58

C,9 =+o-o8o 01

0,0= 1 726 74

and resulting corrections to observed directions:

C=-o-i37 98

C=-i-i32 88

C= +0-952 70

C = +0-383 71

C =5

i 046 58

C*+o7S5 58

C=+ 0-689 15

= + Cs8

1 "339 4o

C= -0-677 99

(1) = -01151

(2)

0-0781

(3) +0-1932

(4)

0-1144

(5) +0 -0255

(6)

0-1304

(7) +0-2194
(8) +0 -3708 (9) +0 -9042

(10) +0-0695

(II). : O '60I0
(12) +0 -oS25 (13) -o ;8262

(14) +0-2901

(15) +0-2258
(16) +0 -0491

(17) (18) (19) (20)

+0-II02 -I 0555
+0 ^427
-0-I826

()
(22) (23) (24) (25) (26) (27) (28) (29) (30)

-0-8348
+0 -OI59
+ -6689
+0-9164
+0 -5286
0-2729
I I3II
-o -2745 -o -8561 -o -3963

+ (31)= : I -3II2
(32) -o -2437 (33) -o -3526
(34) +0 -8473 (35) -o -3136 (36) -o 2452

(37) (38)

o 6491
-o '3747

(39) +0-9150
(40) *o -6273

(4i) =+o-u86

(48) = +0-5984

(42) -1 -4084

(49) -o -5995

(43) +0 -2994

+ (50)

1-8370

(44) +0 -2284

(50 00606

(45) +0 -7526

(52) -1-1669

(46) +0 -5424

(53) -0-7156

(47) -o -5413

We y _ have the probable error of a direction of unit weight C674 [^w]

o"674

24 /

4

or

V 29

o"'62 nearly, and since the average reciprocal of the weights is

1 '07, the probable error of an observed direction is nearly o"'65.

BASE LINES AND BASE NETS.

85

Resulting angles and sides of the Allan la base net.

No.

Stations.

8

86

THE EASTERN OBLIQUE ARC.

Resulting angles and sides of ike Atlanta base net -continued.

No.

Stations.

3

16 17 18 19

23 24

BASE LINES AND BASE NETS.

87

Resulting angles and sides 0/ the Atlanta base net continued.

Station.

25

26

27 28

29 30 31 32 33

88

THE EASTERN OBLIQUE ARC.

cross lines, in a copper 1x>lt driven into the center of the top of the upper block, marks

the station. Over the upper monument is placed a granite shaft bearing the usual

inscriptions on its faces. The station is further defined as the center of a square whose

side

is

m-
24 75,

each angular point of the square being a drill hole

at

the

intersection of

cross lines in a copper bolt driven into the top of a stone post 3 feet long and 6 inches

square at top. The center of each reference mark is 18 meters from the station, and

diagonal grooves are cut in top of each, with an arrowhead pointing to the station.

Atlanta Northeast Base. This station is at a road crossing on the Southern Rail-

way, near Norcross, Gwinnett County, Georgia. It is on the west side of the road and

the west side of the railroad, on the place of J. H. Maloney. The station is marked

exactly as described at Atlanta Southwest Base.

Atlanta Middle Base. The station is in De Kalb County, Georgia, upon a small knoll

in edge of woods 65 feet northwest of the Southern Railway and about a quarter of

a mile northeast of the railroad station at Doraville. The underground mark is the

center of the mouth of a short-necked bottle. The surface mark is a drill hole at the '

intersection of cross lines in the head of a copper bolt driven into a granite post. 1 foot square and 3 feet long, with diagonal grooves cut in the top, one in line with
the base and the other perpendicular to it. The copper bolt with the cross lines and drill hole is placed at the intersection of the grooves. Around this central monument are buried four reference marks, two in line with the base and two in a line perpendicular to it. Each of the granite posts is 7 inches square and 3 feet long, and has in its top a diagonal groove with an arrowhead pointing to the station, from which the center of each reference mark is 5 feet distant.
Stone Mountain. This station is in De Kalb County, Georgia, on the well-known
mountain of that name, about 15 miles N. 76 E. from Atlanta, and about 1 mile from
the post-office, Stone Mountain, on the Georgia Railroad, De Kalb County, Georgia. The station is marked by a copper bolt in the solid granite of the mountain.
Around the bolt the rock is cut down to a level in a circle of 3>4 feet radius, the bolt

3^ being the center. In the periphery of this circle are six equidistant holes

feet apart

and 2 inches deep.
Academy. This station is on the highest point of Academy Hill, in Lavvrenceville,
the county seat of Gwinnett County, Georgia.
The underground mark is the mouth of a bottle 3 feet below the surface. Over
this is a granite post 30 inches long and 7 inches square, with the letters U. S. C. S.
cut in top. Around the central monument are placed four reference marks aboift 30 W. of S., 30 N. of W., 30 E. of N., and 30 S. of E. The center of the SW. reference mark is 4 feet 6 inches from the center of the station, and the center of the other marks is 5 feet distant from station. In the top of each reference mark is a
diagonal groove with an arrowhead pointing toward the station. Kenesaw. This station is on the highest part of Kenesaw Mountain, about 3 miles
northwest of Marietta, Cobb County, Georgia. The station is reached by following the Marietta and Cartersville road for about 2j4 miles from the Kenesaw House, in
Marietta, and then following the road which turns to the left, near a covered well, and
finally along the spur of the mountain to the summit. The underground mark is a
% cross in the head of a copper bolt driven into a hole drilled in the solid rock 2 feet 1
inches below the surface. Above this is planted a granite post 5 inches square, with

BASE LINES AND BASE NETS.

89

the top projecting 2 inches above the ground. The intersection of two cross lines in the top of the post marks the station. The letters U. S. C. S. were also cut in top of

post. The station has three reference marks A, B, and C these being the intersec-

tions of cross lines cut in the heads of copper bolts driven into holes drilled in the rock.

n The distances of these points from the station are 6'65 feet, 11 '35 feet, and

19 feet,

A respectively. The angles subtended at the station by lines from to B, B to C, and

A C to are 170 59', 47 06', and 141 55', respectively.

Sweat Mountain. This station is in Cobb County, Georgia, the nearest post-office

being Woodstock, almost 4 miles distant in a direct line on the Atlanta, Knoxville

and Northern Railroad. The station is on top of the mountain, about ij^ miles from

Mr. Dial's house, and is reached by following the Marietta and Gumming road to a

point <)Y\ miles from Marietta, near Mr. Garrison's, and then taking the road along the

southeast ridge of the mountain.

The station is marked by a copper bolt driven in a hole drilled in the rock very near

the edge, and has three reference marks, A, B, and C, which are copper bolts driven in

drill holes in the most solid rocks available. These points are 6*2 feet, 7 '67 feet, and

i2'3 feet, respectively, from the station. Taking the line to Kenesaw, S. 4833' W., as

the initial or zero direction, and measuring angles counter-clock- wise, the directions of

A, B, and C are 3 19' 30", 83 44' 30", and 231 12' 30", respectively.

Sawnee. This station is on the most prominent or central peak of Sawnee Moun-

tain, in Cumming Township, Forsyth County, Georgia, about 2 miles NTJ. of dimming

and 12 miles from Buford, on the Southern Railway.

The station was marked temporarily by a copper tack driven in a stub, with similar stubs for reference marks. The permanent marks are supposed to be the usual central

marks with four reference marks.

Pine Log. This station is on Pine Log Mountain, Cherokee County, Georgia, about 7 miles north of Wolf Pen. The station is reached by going east from Cartersville, to Wolf Pen; thence 9 miles to Moore's Iron Furnace; thence 3 miles to Mr. Lewis' house: thence to the station on top of the mountain.
The underground mark is the neck of a jug 2 feet 6 inches beneath the surface. The surface mark is the intersection of cross lines on the top of a granite post 5 inches square, planted above the jug, the top of post projecting above the ground. The letters U. S. C. S. were cut in the angles of the cross lines. Around the station are four granite reference marks similar to the central monument, to the north, east, south, and west,
each distant 6 feet from the station. In the top of each is cut an arrowhead pointing to

the station.

Grassy. This station is on top of Grassy Mountain, 3,290 feet high, in Pickens County, Georgia, about 6 miles in a direct line east of Jasper, the county seat, on the
Atlanta, Knoxville and Northern Railroad. The station marks are supposed to be the usual central monument, and four reference marks to the north, east, south, and west,

each 5 feet distant from the station.