DEPARTMENT OF COMMERCE
U. S. COAST AND GEODETIC SURVEY
'I'
SUPERINTENDENT
GEODESY
PRIMARY TRIANGULATION ON THE ONE HUNDRED AND FOURTH MERIDIAN, AND ON THE THIRTY- NINTH PARALLEL IN COLORADO, UTAH, AND NEVADA
BY
WILLIAM BOWIK
Inspector of G-eodetio Work and Chief of the Computing Division
TJ. S. Coast and G-eodetio Survey
SPECIAL PUBLICATION ,'NO. 19
WASHINGTON GOVERNMENT PRINTING OFFICE
wu

DEPARTMENT OF COMMERCE
U. S. COAST AND GEODETIC SURVEY
SUPERINTENDENT
l GEODESY
PRIMARY TRIANGULATION ON THE ONE HUNDRED AND FOURTH MERIDIAN, AND ON THE THIRTY- NINTH PARALLEL IN COLORADO, UTAH, AND NEVADA
BY
WILLIAM BOWIK
Inspector of Geodetio 'Work and Chief of the Computing Division IT. S. Coast and Geodetic Survey
SPECIAL PUBLICATION No. 19
WASHINGTON GOVERNMENT PRINTING OFFICE
191*

ADDITIONAL COPIES O? THIS PUBLICATION MAT BE PROCURED FROM
THE SUPERINTENDENT OF DOCUMENTS GOVERNMENT PRINTING OFPICE WASHINGTON, D. C. AT
25 CENTS PER COPY
<2b
Has
'9M

CONTENTS.

General statement

Reconnoissance

General instructions for reconnoissance

Cost of reconnoissance

Measurement of bases on the one hundred and fourth meridian

Ambrose base

5

Provo base

El Paso base, discussion of old measurement Base measurements in 1913

El Paso base

Cheyenne base Conclusions from base measurements

Building signals and marking stations Instruments used on triangulation

Light keepers Signal code and instructions to light keepers
Observations for horizontal directions

General instructions to observers on primary triangulation

,

Methods of observing employed

Program of occupation of stations, one hundred and fourth meridian

Connections made between the one hundred and fourth meridian triangulation and stations and monuments of

other surveys
Connections made between the thirty-ninth parallel triangulation and stations and monuments of other surveys.
Statement of costs

Statement of adjustments

1

Abstract of horizontal directions and elevation of telescope above the station mark

Condition equations Accuracy as indicated by corrections to observed directions
Accuracy as indicated by corrections to angles and closures of triangles Accord of bases

Accord of azimuths

Study of errors Deviation of triangulation in azimuth
Effect of drag Accuracy of the primary triangulation in the United States
The North American datum

Explanation of tables of positions
Tables of positions ' One hundred and fourth meridian

Thirty-ninth parallel

Descriptions of stations

:

One hundred and fourth meridian

Th irty-ninth parallel

Vertical circle
Computation, adjustment, and accuracy of the elevations Table of elevations

Determination of astronomic longitude

Astronomic azimuths

Astronomic latitudes

Triangulation sketches Index to positions, descriptions, elevations, and sketches
General index

Page.
5 6 6 8 9 10 13 15 19 19 22 28 28 30 31 32 35 35 37 38
39 40 40 41 42 47 53 56 63 63 64 65 76 79 80 83 88 88 95 114 115 126 140 140 146 148 151 152 154 155 162

3

4

CONTENTS.

ILLUSTRATIONS.
No.
1. Reel for invar tape (two viewB) 2. Twelve-inch theodolite
3a. Vertical collimator (two views)
3b. Box heliotrope used on triangulation 3c. Large acetylene signal lamp used on triangulation
4. Standard triangulation station and reference marks 6. Vertical circle used in trigonometric leveling and for making time observations 6a. Zenith telescope used for latitude observations 6b. Portable wooden support with adjustable legs for the zenith telescope 6c. Motor truck used by latitude party
7. Index map showing areas covered by published triangulation which has been rigidly computed on the North American datum
8. Index map showing the main scheme of the triangulation published in this report and showing also the limits of each of the following sketches Nos. 9tol7
9. Triangulation, one hundred and fourth meridian, stations Pikes Peak and Divide to Ragged and Whitaker. 10. Triangulation, one hundred and fourth meridian, stations Ragged and Whitaker to Alkali and Elk 11. Triangulation, one hundred and fourth meridian, stations Alkali and Elk to Black and Rainy 12. Triangulation, one hundred and fourth meridian, stations Black and Rainy to Canada boundary 13. Triangulation, one hundred and fourth meridian, Missouri River connection 14. Triangulation, thirty-ninth parallel, Kansas-Colorado boundary to stations Divide, Pikes Peak, and Plateau. 15. Triangulation, thirty-ninth parallel, stations Divide, Pikes Peak, and Plateau to Patmos Head and Mount
Ellen
16. Triangulation, thirty-ninth parallel, stations Patmos Head and Mount Ellen to Diamond Peak and White
Pine
17. Triangulation, thirty-ninth parallel, stations Diamond Peak and White Pine to California-Nevada boundary.

l-age.
10 28 30 32 32 114 140 150 152 152
154
154 154 154 154 154 154 154
154
154 154

PRIMARY TRIANGULATION ON THE ONE HUNDRED AND FOURTH MERIDIAN, AND ON THE THIRTY-NINTH PARALLEL IN COLORADO, UTAH, AND NEVADA.

By William Bowie,
Inspector of Geodetic Work and Chief of the Computing Division, United States Coast and Geodetic Survey.

GENERAL STATEMENT.

The primary object of this publication is to give the geographic positions, elevations, and descriptions of the main scheme, subsidiary and intersection stations determined by primary triangulation in the State of Colorado and northward, from the line Pikes Peak-Divide of the

thirty-ninth parallel triangulation, approximately along the one hundred and fourth meridian

to the Canadian border, and also similar data for the various stations of the thirty-ninth parallel triangulation which He in the States of Colorado, Utah, and Nevada.

The geographic positions are on the North American datum, and,, as far as geographic purposes are concerned, they will probably not be changed. The geographic positions of

stations of the thirty-ninth parallel within the States mentioned above, as given in Special

Publication No. 4 (The Transcontinental Triangulation), are superseded by the positions contained herein. That publication was issued before the adoption of the North American datum.
The author desires to express his appreciation of the valuable services performed in the

field and in the office by members of the Survey in connection with the one hundred and fourth

meridian triangulation; also in the office work connected with the readjustment of the thirty-

ninth parallel triangulation in Colorado, Utah, and Nevada, and the preparation of the results

for

1
publication.

Especial mention should be made of E. H. Pagenhart and C. V. Hodgson, who were in

charge of the base measurements and triangulation observations; also of J. S. Bilby, who laid

out the scheme and selected the stations in the field and then prepared the stations for the

observing party. In the office A. L. Baldwin had direct supervision of the computations and
adjustments and prepared portions of the text. The heavy adjustments were made by W. P. Reynolds and O. S. Adams under Mr. Baldwin's direction. C. H. Swick prepared the descriptions of stations, assembled the tables, and edited the text. Of the others who assisted in the
work, including the preparation of this report, W. D. Lambert, H. R. Tolley, E. F. Church,

and E. M. Panopio should be mentioned. .

The engineer intent only on securing the necessary information to extend this triangula-

tion or to base other surveys on it will find the information he desires on pages 80 to 148, com-

mencing with the explanation of the table of positions, lengths, and azimuths. The index,

printed on pages 155 to 161, used in connection with the sketches at the end of this publication will enable him to find quickly the data for any given locality.

Illustration No. 7, at the back of this volume, shows graphically the area covered by each

of the publications of the United States Coast and Geodetic Survey and by one publication of

the United States Army Engineers, which give the results of triangulation, which has been

rigidly adjusted and computed on the North American datum.

In illustration No. 8 are shown the main scheme of the triangulation covered by this

report and the area covered by each of the illustrations Nos. 9 to 17, which give the details of

the triangulation nets.

1 Acknowledgments are made for the field and office work connected with the transcontinental triangulation in Special Publication No. 4. 5

6

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

There are also given in this publication descriptions of the methods employed in the triangulation and base measurements on the one hundred and fourth meridian arc and data necessary to show the accuracy of the results of that work.
The methods employed on the thirty-ninth parallel triangulation and the accuracy of the results are described in Special Publication No. 4 of the Coast and Geodetic Survey.

RECONNOISSANCE.

The reconnoissance for the triangulation on the one hundred and fourth meridian was
done by Signalman J. S. BUby in 1911. His party consisted of only one man besides himself;
his equipment was three mules, one wagon, one riding saddle, necessary tools for repairing the outfit, one tent, cots and bedding for two persons, and a few cooking utensils. The instruments he carried were a 4-inch surveyor's transit, a prismatic azimuth compass, a field telescope,
binoculars, and a set of drawing instruments. He also carried copies of all the available maps
covering all or parts of the area within which he operated. The new scheme began with the line Pikes Peak-Divide of the transcontinental triangula-
tion, with station Bison as the third and check point ; it was carried northward to the Colorado-
Wyoming boundary, thence northeastward just across the Wyoming-South Dakota boundary,
thence northward to the international boundary. Base lines were provided for at Provo, S. Dak. (approximate latitude 43 12'), and at
Ambrose, N. Dak., at the northern end of the scheme.
Provision was made for connecting with a number of triangulation stations of the United States Geological Survey, with monuments of each State boundary crossed, with the triangula-
tion stations of the Missouri River Commission where the scheme crossed that river, with triangulation stations of the international boundary, and with a number of bench marks of various
organizations.
The statistics of the reconnoissance are:

Length of scheme along its axis in miles Area of scheme in square miles Number of stations in the main scheme Number of subsidiary stations Number of base lines selected Date of beginning field work Date of ending field work Total length of season, months Rate of progress per month, miles Average number of stations selected per month:
Primary
Subsidiary
GENERAL INSTRUCTIONS FOR RECONNOISSANCE.

720 17 000
74 23
2
May 2, 1911
Aug. 10, 1911 3. 3 218
22 7

1. Character offigures. The chain of triangulation between base nets shall be made up of completed quadrilaterals and of central-point figures, with all stations occupied. It must not be allowed to degenerate even for a single figure to simple triangles. There must be two ways of computing the lengths through each figure. On the other hand there must be no overlapping of figures and no excess of observed lines beyond those necessary to secure a double determina-
tion of every length, except that in a four-sided central-point figure one of the diagonals of the figure may be observed.

R= 2. Strength of figures. In the chain of triangulation between base nets the value of the quantity

( 75)

2[82l+8jJ}b+82b] for any one figure must not in the selected best chain (call it .R,) exceed 25, nor in the second best

R (call it 2) exceed 80, in units of the sixth place of logarithms. These are extreme limits never to be exceeded. Keep

the

quantities

R t

and

R2 down

to

the

limits

15

and

50

for

the

best

and

second

best chains,

respectively,

whenever

the

estimated total cost does not exceed that for a chain barely within the extreme limits by more than 25 per cent. The

R values of may be readily obtained by the use of the following "Table for determining relative strength of figures in

triangulation."

^ In the above formula the two terms

and

+9 I[81t.+8i.dB

2
B]

depend

entirely upon

the figures chosen and

are independent of the accuracy with which the angles are measured. The product of these two terms is therefore a measure of the strength of the figures with respect to length, in so far as the strength depends upon the selection of stations and of lines to be observed over.

In

the

following

table

the

values

tabulated

are

+d +8 2
2[d jL

AdB

2
B ].

The unit is one in the sixth place of loga-

rithms. The two arguments of the table are the distance angles in degrees, the smaller distance angle being given at

PRIMABY TKIANGULATION.

the top of the table. The distance angles are the angles in each triangle opposite the known side and the side required.

A B A <J and SB are the logarithmic differences corresponding to one second for the distance angles and of a triangle.

W D 4
The square of the probable error of the logarithm of a side of a triangle is 5-

C

+d +d i
j\ 2[d jL

JkdB

2
B],

in

D which d is the probable error of an observed direction.

is the number of directions observed in a figure and C is

the number of conditions to be satisfied in the figure. The summation indicated by 2 is to be taken for the triangles

DC used in computing the value of the side in question from the side supposed to be absolutely known.

The strength table is to be used in connection with the values of g to decide during the progress of the

reconnoissance which of the two or more possible figures is the strongest and to determine whether a sufficiently strong scheme has been obtained to make it inadvisable to spend more time in reconnoissance.

8

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

3. Lengths of lines. No line of the primary triangulation outside of the base nets should be less than 6 kilo-

meters long. There is little if any advantage, in so far as accuracy is concerned, in making the lines much longer

than this. Therefore endeavor, in laying out the triangulation scheme, to use the economic length of line; that is,

endeavor to use in each region lines of such lengths as to make the total cost of reconnoissance, building, and triangu-

lation a minimum per mile of progress, subject to the limitations stated in these instructions.

4. Frequency of bases. If the character of the country is such that a base site can be found near any desired

IH location

between base lines should be made about 130.
X

This will be found to correspond to a chain of from 15 to

35 triangles, according to the strength of the figures secured. With strong figures but few base lines will be needed

and a corresponding saving will be made on this part of the work. If topographic conditions make it difficult to secure

a base site at the desired location, Jfl, may be allowed to approach but not exceed 200. There will be danger when

this is done that an intervening base may be necessary, for if in any case the discrepancy between adjacent bases is

found to exceed 1 part in 25 000 an intervening base must be measured.

5. Base sites and base nets. In selecting base sites keep in mind that a base can be measured with the required

degree of accuracy on any site where the grade on any 50-meter tape length does not exceed 10 per cent, and that nar-

row valleys or ravines less than 50 meters wide in the direction of the base are not obstacles to measurement. The

length of each base is to be not less than 4 kilometers. In each base net great care should be taken to secure as good

geometrical conditions as possible. There should be no hesitancy in placing the base on rough ground, provided the

roughness is not greater than that indicated above, if by doing so the geometrical conditions in the base net are im-

proved. Each base net should not be longer than two ordinary figures of the main chain between bases. The base

net may also be strengthened by observing over as many lines between stations of the net as can be made intervisible

without excessive cost for building or cutting. Caution is necessary in thus strengthening a base net by observing

extra lines to avoid making the figure so complicated as to be excessively difficult and costly to adjust.

COST OF RECONNOISSANCE.

The total cost of the field work, including Mr. Bilby's salary and traveling expenses to the field, was SI, 995. As most of the equipment of the party had been in use in previous seasons, new articles cost the party only about $75. The cost of this reconnoissance per mile of progress
was $2.77, and is the lowest with which the writer is familiar. On page 168 of Appendix 4, Report for 1911, and page 10 of Special Publication No. 11 may be found statements of cost
of previous reconnoissances.
As a proof of the accuracy of this reconnoissance, involving the selection of 97 stations (main and subsidiary schemes) in a triangulation 720 miles (1160 kilometers) in length, in only two places was it necessary to alter the proposed scheme, one at the extreme southern end and the other in the vicinity of Cheyenne.
An occasional obstructed line is to be expected, for the officer carrying on the reconnois-
sance is supposed to adopt such methods and make such selections of stations as to make the total cost, including reconnoissance, erecting signals, and observing, a minimum. It is obvious
that the total would be greater if on the reconnoissance the officer spent enough time testing each fine to insure against every obstruction than if he took only the time necessary to make it reasonably sure that only an occasional line must be abandoned or an occasional station introduced into the scheme by the observing party. Besides, it is frequently the case that the party building the signals can test any doubtful lines, and thus avoid delays to the observing
party.
The reconnoissance party obtained the geographic locations of the stations by any means available, such as estimated distance and compass bearing to a railroad station, topographic maps, General Land Office maps, bearings on mountain peaks whose positions were known, etc. Only such accuracy is required in the geographic positions of reconnoissance stations as to enable the light keeper and observer to signal each other and to permit the computation of the strength of the figures. As the work progressed the chief of party made sketches showing the approximate location of the stations and the lines to be observed.
Descriptions of the stations were written which enabled the building and observing parties and the light keepers to find the stations selected. They also gave information as to the nearest water for drinking and cooking and for stock, nearest post office, railroad station, and place where supplies might be purchased; also as to the best approach to the station, if it were in a rough or rugged country.

PRIMARY TRIANGULATION.

9

MEASUREMENT OF BASES ON THE ONE HUNDRED AND FOURTH MERIDIAN.

General statement. According to the strength of the separate figures of the scheme of

triangulation on the one hundred and fourth meridian only two new base lines were necessary besides the known length, Pikes Peak-Divide, a line of the transcontinental triangulation.

These two bases were located by the reconnoissance party at Ambrose, N. Dak., near the Cana-

dian boundary, and at Provo, in the southwestern corner of South Dakota, and were measured

by the observing parties with invar tapes in 1912.

After the triangulation had been completed and a preliminary computation had been

made, it was found that the length discrepancy between the Provo and the Ambrose bases was

only 1 part in 83 000. However, the discrepancy between the line Pikes Peak-Divide and

A the Provo base was found to be 1 part in 13 500.

revised computation of the Provo base

made no change in the length given by the first computation, and a close inspection of the

computation of the old El Paso base and of the triangulation from that base to the line Pikes

Peak-Divide showed that no error in computation had been made there. After considering

all the facts the conclusion reached was that the discrepancy in length was probably due in

part to some systematic or constant error in the measurement of the El Paso base with the

base

bars

in

'
1878,

and

also

to

accumulated

errors

in

the

triangulation

between

the

Provo

base

and the line Pikes Peak-Divide.

It was therefore decided to remeasure the El Paso base with the invar tapes, and this
was done by Assistant C. V. Hodgson in the summer of 1913. A computation on the field
showed a change of 1 part in 59 000 in the old length of the El Paso base, but this change still left a discrepancy in length between the El Paso and Provo bases of 1 part in 24 000. This showed a rather large accumulation of error in the triangulation, and it was decided to
introduce an additional base in the scheme in the vicinity of Cheyenne, Wyo. This base also was measured with the invar tapes, by Assistant Hodgson, in 1913. The discrepancies in lengths are now:
Between the El Paso base (new length) and Cheyenne base, 1 part in 31 000. Between the Cheyenne base and Provo base, 1 part in 40 000. Between the Provo base and Ambrose base, 1 part in 109 000. Methods employed. The following instructions for the measurement of the Ambrose and Provo bases were issued to Assistants E. H. Pagenhart and C. V. Hodgson, the chiefs of the two observing parties engaged on the triangulation on the one hundred and fourth meridian

in 1912:

The two bases shown by the reconnoissance scheme, one at Ambrose and one at Provo, will be measured by the

observing parties during the progress of the triangulation.

Very little increase in the average accuracy of the lengths of the triangle sides in the triangulation connected

with a base will result from increasing the accuracy of the base measurement beyond that represented by a probable

error of 1 part in 500 000 in the length of the base. The following limits of accuracy are selected with a view of

attaining a probable error but little, if any, greater than 1 part in 500 000. You will strive to keep as far within these limits as is possible by the use of good judgment and skill, but you will restrict the time and money expended upon

each operation substantially to that required to keep barely within them.
Four invar tapes are to be standardized at the Bureau of Standards, both before and after the measurement of
the bases. Each base is to be measured with three of these invar tapes used in daylight or at night. A base shall be

measured in sections approximately 1 kilometer in length, except that one shorter section may be used. Each section

of a base shall be measured with at least two different invar tapes. Different pairs of invar tapes shall be used on

different sections, so that the three tapes used on the base shall thereby be thoroughly intercompared. Two, and only

two, measurements of each section shall be made, unless the discrepancy between these two measurements exceeds 20

VK K millimeters

(in which is the length of the section in kilometers), in which case additional measurements must

be made until two are obtained which agree within this limit. The fourth invar tape standardized is to be retained

for use in case of serious damage to any of the three tapes with which the measurements would otherwise be made.

Such precautions should be taken to secure accurate horizontal and vertical alignment of the tapes and the

determination of the tension applied to the tapes as is necessary to insure that the errors arising from these sources

on a base shall each be less than 1 part in 1 000 000.

1 For an account of the measurement of the El Paso base, see pp. 101-107 of the Transcontinental Triangulation, Special Publication No. 4,

A o/the V. S. Coast and Geodetic Survey.

description of the bars used in the measurements will be found in Appendix 17, Report for 1880, pp.

341-345.

10

U. 8. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

On the Stanton base, in Texas, the wind blowing against the tapes which had only three supports caused some trouble. The wind effect was made negligible on the Deming base measurements by using five tape supports. In the measurements of the Ambrose and Provo bases either three or five supports may be used, but in no case should the effect of wind on the length of a base be more than 1 part in 1 000 000. The wind when at an appreciable angle
with the direction of the base tends to draw the ends of the tape closer together, and thus introduces a systematic error which makes the measured length of the base too long.

The remeasurement of the El Paso base and the measurement of the Cheyenne base in 1913 were made under the same instructions as the bases at Ambrose and Provo.

Standardization of tapes. The tapes were standardized at the Bureau of Standards, at

Washington, D. C, both before and after the measurement of the Ambrose and Provo bases,

and again after the remeasurement of the El Paso base and the measurement of the Cheyenne

base.

The

length

of

the

50-meter

comparator

was

measured

with

iced

bar

B 17

just

before

and

after the comparison of the tapes with the comparator. In the determinations at the Bureau

of Standards the tapes were used in practically the same manner as in the field. They were

supported at the ends and at the middle point with all three supports in a straight line. Two

thermometers were attached to each tape about 1 meter from the graduation mark at each end,

and the fixed tension of 15 kilograms was applied. The tapes were suspended under the end

microscopes of the comparator, using the cut-off cylinders for the end supports. For a full

description of the standardization of base tapes, see pages 115-119 of Appendix 4, Report for

1907.

The same set of tapes has been used for all the primary bases measured since the season of 1906. These tapes have been standardized six times and the results are shown in tables on

pages 25 and 26.

AMBROSE BASE.

This base was located by the reconnoissance party in 1911, to the northwest of the town of Ambrose, in northwestern North Dakota. Its connection with the scheme of triangulation is shown on illustration 12 at the end of this volume. Ambrose northeast base is identical
with triangulation station School of the International Boundary Survey. The land is level and comparatively smooth, and at the time of the base measurement all of
it was covered with short prairie grass except some sections which had been under cultivation. Organization of party. The Ambrose base was prepared for measurement by Signalman
J. S. Bilby, who was assisted by some members of the triangulation observing party of Assistant E. H. Pagenhart. The setting of stakes began on May 11 and was finished on the 15th, the actual measurements with the tapes was done on three days between May 16 and 20, and on May 25 the field computation of the results was completed. Nine persons were engaged for all or part time upon the preparation, leveling, and tape measures. The party lived in tents while engaged on the measurement of this base.
Division of the base. The base was divided into three main portions, the first extending from Northeast base to the end of the third kilometer, the second from the beginning of the fourth kilometer to the end of the seventh kilometer, and the third from the beginning of the eighth kilometer to Southwest base. The total length of the base is 10 479 meters. Each of the three main divisions was measured at least twice in opposite directions with different tapes, and a different pair was used on each division in order to obtain an intercomparison of the three tapes used in the measurements. Each of the main portions was in turn divided into kilometer
sections.
The following table shows the divisions of the base with the tapes used on each and the
approximate length of the divisions.

Division.

' Special Publication No. 19.

NO.1.

PRIMARY TRIANGULATION.

11

The descriptions of the location and markings of the base ends are given on page 124. Apparatus used. As stated above, the same invar tapes have been used for measuring the primary bases since the compaign of 1906, when six primary bases were measured with both steel and invar tapes. After those measurements it was decided to discard the steel and do all primary measuring with the invar tapes. This decision has been justified by the results
obtained.
These invar tapes are 50 meters in length and are similar to those described on pages 111113 of Appendix 4 of the Report for 1907. The stretcher and other minor parts of the base apparatus were of the same types as those described on pages 149 and 154 of Appendix 4 of the Report for 1910 and are shown in illustrations 4 and 5 of that publication. The reel used for the invar tape is shown in illustration No. 1 of this publication.
Setting stakes and measuring. The method of setting the stakes on which the tape is supported while making the measurements and the method of carrying on those measurements are rather fully described in the three publications of this Survey giving the results of base
measurements in recent years. They are Appendix 1 of the Report for 1901, Appendix 4 of the Report for 1907, and Appendix 4 of the Report for 1910. It is not necessary to go into
the details of the methods here. Any one or all of those publications may be obtained free of
cost by application to the Superintendent of the United States Coast and Geodetic Survey.
On all of the bases measured on the one hundred and fourth meridian only three supports for a tape were used, as the wind on many days was found to be fight and to have a negligible effect. When the wind was strong no measurements were attempted.
Equations of tapes. -The equations of the tapes, furnished by the Bureau of Standards and resulting from the standardization in March, 1912, are:

r5U)=50ro+( 9.573mm0.029mm)+(0.0178TOTO0.0007mm)X(<-26.8 C);

Til7 =50m+( 9.96OmTO0.022TOm)+(0.O160mm0.0O07mm)X(<-26.9 C);

rM1 =50m+(10.124mTO0.021mm)+(0.0205mm0.0008mm)X(-26.8C);

r 6ffl

=50m+(10.988mTO0.017mm)+(0.0614mm0.0011mm)X(-26.8

C).

The equations of the same tapes, furnished by the Bureau of Standards and resulting from
the restandardization in January, 1913, are:

r61,=50ro+( 9.556mm0.016mm) at 23.3 C;

TM7 =50m+( 9.953rowi0.016mm) at 23.3 C;

r 621

=50ro+(10.077mTO0.016mm)

at

23.3

C;

2,623 =50m+(10.793mm0.016OTm) at 23.3 C.

The determination of the coefficient of expansion of each of these tapes was made by the Bureau of Standards in January, 1909. Tape No. 522 was carried to the field, but was not
used in the measurements.
The equations resulting from the January, 1913, standardization, reduced to the tempera-
tures of the March, 1912, standardization, are:

r616 =50TO+( 9.618mm0.016mm) at 26.8 C;

r617 =50TO+(10.01lTOTO0.0167nm) at 26.9 C;

r 521

=5Oro+(10.149mm0.016mm)

at

26.8

C;

7,622 =50m+(11.008mOT0.016mm) at 26.8 C.

The adopted equations of the tapes used in the final computations of the Ambrose base are:

!T616=50to+( 9.582mm0.012mm)+(0.0178mm0,0007mTO)X(-26.8 C);

T517 =50m+( 9.970mTO0.014mm)+(0.0160mm0.0007m.m)X(<-26.9 C);

rM1

o
=50m+(10.129mm0.007m7n)+(0.0205m?n0.0008m7n)X(<-26.8

C).

These values are based upon the assumptions that the difference between the lengths as given by the two standardizations are actual differences in the lengths (that is, that the standardizations wore made without error), and also that this change had taken place gradually and at a uniform rate from March, 1912, to January, 1913, the dates of the two standardizations.

12

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

In order to compare the lengths of the tapes, the results of the two standardizations are given in the following table:
Mar., 1912, r61(,=50m+( 9.573mm0.029mm) at 26.8 C; t>=+0.023mm; Jan., 1913, Tilt=50m+( 9.618mm0.016mm) at 26.8 C; v=-0.022mm.
Mean= 9.596mm
Mar., 1912, Tj,r =50m+( 9.960mm0.022mm) at 26.9 C; v=+0.026mm; Jan., 1913, Z'8 ,7 =50m+(10.011mm0.016mm) at 26.9 C; v= -0.025mm.
Mean= 9.986mm
Mar., 1912, 7'M1 =50m+(10.124mm0.021mm) at 26.8 C; t>=+0.012mm; Jan., 1913, 2'M1 =50m+(10.149mm0.016mm) at 26.8 C; v= -0.013mm.
Mean= 10.136mm
Mar., 1912, 2'622 =50m+(10.988mm0.017mm) at 26.8 C; u=-f-0.010mm; Jan., 1913, 7,5:a =50m-f-(11.008mm0.016mm) at 26.8 C; r=-0.010mm.
Mean= 10.998mm
Five of these residuals are smaller than the probable errors of the standardizations, and in no case do they exceed these probable errors by an appreciable amount. Therefore it is reasonable to suppose that between the standardizations the tapes underwent no permanent change in length and that the differences were due to errors in the standardization itself.
This shows that a straight mean of the results of the January, 1912, and March, 1913, standardizations could have been used in making the computations of the two bases without introducing any error as great as the probable error of the standardization of a tape, which is on an
average less than 1 part in 1 000 000. Reduction to sea level. The elevation of Ambrose Northeast base, as given by a con-
nection with the spirit leveling along the international boundary, is 623.521 meters. The mean elevation of each section of the base was obtained from the leveling which was run for
the purpose of getting the inclination corrections necessary to reduce the measures to the
horizontal.
The formula used in reducing the base to sea level is

C--sJ+s5J-fl f etc.,

in which C is the reduction to sea level for a section of length S and mean elevation h, and r is
the radius of the earth's curvature for the section in question. The reduction to sea level for each section of the base is given in the following table in the column headed "Reduction to

sea. level."
Results of the measurement. in the following table:

The results of the measurement of the Ambrose base are given
The Ambrose base line.

PRIMARY TEIANGULATION.

13

The Ambrose base line Continued.

14

V. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Division of the base. As in the case of the Ambrose base (see p. 10) this base was divided into three parts, each of which was measured twice in opposite directions with different tapes. Tho measurements were so planned that it was possible to obtain an intercomparison between each two tapes used.
The following table shows the divisions of the base, with the tapes used on each and the
approximate length of the divisions:

Division.

PEIMABY TKIANGULATION.

15

The Provo base line Continued.

Section.

Date and hour.

Di-

rec-

tion Tape Weather and

of No.

wind.

meas-

ure.

Temperature (cen-
tigrade).

Correction to

length

Mean for tem-

correct-

perature.

ed.

Set-up or set-
back.

Grade
correction.

Tape
correc-
tion.

Reduction to
sea level.

Reduced
lengths of sections.

Adopted lengths
of
sections.

Oct., 1912.

V.80-100

7, 2:20 p.m. J, 7:45 a. m.

VI, 100-120.. .

3, 12:25 p.m. .3, 11:00 a.m.

WI

VII, 120-140...

'3, 1:00 p.m. 3, 10:30 a. m.

F.
w

VIII, 140-160. .

3, 1:30 p.m. 3, 9:50 a.m.

E
W

IX, 160-180....

'3, 2:00 p.m. 3, 9:10 a.m.

E

X, 180-200

;, 2:30 p.m.
63, 8:20 a.m.

w

XI, 200-220....

3, 3:15 p.m. ,8,11:30 a.m.

XII, 220-240...

/3, 3:50 p.m. \S, 11:00a. m.

E

XIII, 240-260..

f8, 8:20 a.m. [8, 10:35 a. m.

XIV, 260-280..

f8, 8:50 a.m. [8,10:15 a.m.

XV.280-E.B.

f8, 9:20a.m. 18, 10:00 a. m.

Cy, M NW
521 C, LSE...

517 C, LW.... 51i; C, L V....

51 C.LW.... 516 C, LW....
517 C, L W.... 516 C, L W....
517 C, L W.... Sid C, L W....
517 C, L W.... 516 C, LW....

521 C,0 517 C,MW...

521 C.O
M 517 C, W...

521 517

C, C,

LNW..
MNW.

521 517

C, C,

LNW..
MNW.

521 C, LNW.. 517 C, LNW..

m + 15.6 -0.0040 0.0408 -0. 2234 +0. 1921 -0. 1769 999. 8286
+ 6.3 -0.0084 0.0371 -0.2234 +0.2028 -0. 1769 999.8312

m

mm TflTfl

999.8299 (+1.3 1.69 1-1.1 1.69

24.3 -0.0008 20.8 -0.0021

0.0099 -0.1170+0.1999 -0. 1706 999.8956 0.0000 -0.1170+0.1921 -0. 1766 999.8964

- 24.0 -0.0009 0.0138 -0.0936 +0.1999 -0. 1758 999.9158
19.5 -0.0026 0.0000 -0.0936 +0. 1921 -0. 1758 999.9201

999.8960 f+0.4 \-0.4
999.9180 (+2.2 t-2.1

0.16 0.16
4.84 4.41

24.9 -0.0006 17.4 -0.0034

0.0106 -0.1048 +0.1999 -0. 1770 999.9069 0.0000 -0. 1048 +0. 1921 -0. 1770 999. 9069

+ 24.3 -0.0008 0.0384 -0.3527 +0.1999 -0. 1754 999. 7094 + 14.9 -0.0042 0.0522 -0.3527 +0. 1921 -0. 1754 999. 7120

24.4 -0.0008 + 0.0303 -0.5497 +0.1999 -0.1745 999.5052 + 12.9 -0.0050 0.0418 -0.5497 +0.1921 -0.1745 999.5047

+ 23.6 -0.0013 0.0450 -0. 1158 +0.2028 -0. 1742 999. 9565 + 18.0 -0.0028 0.0461 -0. 1158 + 0.1999 -0. 1742 999. 9532

+ 22.4 -0.0018 0.0273 -0.2201 +0.2028 -0. 174' 99U. s:5 + 17.7 -0.0029 0.0255 -0. 2201 +0. 1999 -0. 1747 999.8277

999.9069 ( 0.0 \ 0.0
999. 7107 (+1.3 \-1.3
(-0.2 999.5050
t+0.3
(-1.6 999.9549
t+1.7
(-2.9 999.8306
\+2.9

0.00 0.00
1.69 1.69
0.04 0.09
2.56 2.89
8.41 8.41

9.7 -0.0070 16.8 -0.0032

0.0000 -0. 2744 +0.2028 -0. 1746 999. 7468

(-2.1 4.41

999. 7447

0.0051 -0. 2744 +0. 1999 -0. 1746 999. 7426

\+2.1 4.41

+ 10.8 -0.0066
16.2 -0.0034

o.ooon -0.0589 +0.2028 -0. 1752 999.9621 999.9629 (+0.8 0.64

0.0013 -0.0589 +0. 1999 -0. 1752 999.9637

\-0.8 0.64

+ 11.8 -0.0034 + 15.0 -0.0021

0.2109 -0.0164 +0.1116 -0.0966 550. 2061

1-1.2 550. 2049

1.44

0.20S8 -0.0164 +0. 1100 -0.0966 550.2037

t+1.2 1.44

The length of the Provo base is 14 559.2511 0.0046 meters. The logarithm of this length is 4.1631390 1.
This probable error of the length corresponds to one part in 3 165 000.
The computation of the probable error was made in a manner similar to that described on pages 160-161 of Appendix 4 of the report for 1910.
Cost of the Provo base. The cost of preparing this base and making the measurements was about $525. This includes all salaries, but there was nothing charged for traveling expenses
or outfit.
As the base is 14.5 kilometers in length, the field work cost at the rate of about $36 per kilometer. If to the above amount is added one-half the cost of the two standardizations of
the four tapes (the cost is $50 to anyone not connected with the Government for the fundamental standardization of a base tape by the Bureau of Standards), and also about $40 for the cost of making the revised or office computation, the total cost will be $765, a rate of about $53 per kilometer, or $85 per mile. This low cost was due in part to the absence of traveling expenses and any unproductive period before or after the preparation and the measurement of the base.
EL PASO BASE, DISCUSSION OF OLD MEASUREMENT.
This base was located in 1878 by former Assistant O. H. Tittmann (now superintendent) on the eastern slope of the Rocky Mountains, in El Paso County, Colo., about 30 miles (48 kilometers) east-northeast of Pikes Peak. The middle point of the base is in approximate latitude 38 58' and longitude 104 31'. The length is about 114, kilometers.
The base was measured by the party of Mr. Tittmann between August 7 and September 4, 1879, once forward and once backward, with the 6-meter contact-slide steel rods Nos. 3 and 4. The methods employed in the measurement of this base and the results obtained are given on pages 101-107 of Special Publication No. 4, The Transcontinental Triangulation.

16

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Length of the contact-slide rods Nos. 8 and 4- It is stated in the above-mentioned publica-

tion that these rods were compared at the survey office with the standard iron 6-meter bar

No. 1 just before and just after the measurements in the field. The length of bar No. 1 was

obtained from comparisons with six steel meter bars especially constructed for the purpose.

The coefficient of expansion of bar No. 1 was determined by extensive observations made in

1860. An account of these observations is given in Appendix 26 of the report for 1862.

The observations in 1877 for the length of the 6-meter standard (No. 1) consisted in the

first place of intercomparisons of the six steel meter bars (Nos. 1, 12, 13, 19, 28, 35) and of bar

No. 19 with the committee meter; and, secondly, of comparisons of length of the six 1-meter

bars (joined together) with the 6-meter bar (No. 1). In these comparisons several thermometers

were used and their readings were corrected for index error and defects in graduation. The

average temperature during the comparisons was about 7 length of 6-meter bar No. 1 was 5.9999547 25 at C.

C. The resulting value of the

The value derived from a comparison in 1860 was 5.9999407 8 at C.

An additional value for the length of 6-meter bar No. 1 was obtained from comparisons

made in 1882 at the survey office with a 5-meter standard to which was joined a single meter

bar, both of known length. This value was 5.9999461 46 at

C. For the final value of

6-meter bar No. 1, the weighted mean of the three values of 1860, 1877, and 1882, with their

respective weights

,

1 ,

and

$,

were

taken.

The resulting length of the standard was 5.999949

3

at C.

A comparison in May, 1879, of the 6-meter contact-slide rods Nos. 3 and 4 with standard

No. 1 gave the following results:
Length of No. 3 = 6.0010765 at 17.28 C. Length of No. 4 = 6.001142 4 at 17.28 C.
A second comparison, made in November, 1879, gave the following lengths:
Length of No. 3 = 6.000514 4 at 7.74 C. Length of No. 4 = 6.000476 4 at 7.74 C.

Before using the El Paso base length in the computation and adjustment of the trans-

continental triangulation it was decided to redetermine the coefficients of expansion of these

rods. This was done in 1897, and the resulting coefficients were:
For 6-meter bar No. 3 = 0.00001149.

For 6-meter bar No. 4 = 0.00001141.

The lengths of the bars at the mean temperature of the two standardizations and at C are:
No. 3 at 12.51 C = 6.000795 m. or at C = 5.999933 m. No. 4 at 12.51 C = 6.000809 m. or at C = 5.999953 m.

These are the final lengths used in the computations of the El Paso base. Since the question of the degree of accuracy of this base measurement is an important one, it is believed to be advisable to reproduce here the table on pages 104-106 of Special Pub-
lication No. 4, which gives a summary of the forward and backward measurements of the base.

Section measures of the El Paso base.

Section marks.

Mean Mean

tempera- temperature F. ture F.

No. of

corrected. for-

corrected, back-

(ayerage) bars.

ward.

ward.

Corrected
distance, forward.

Corrected
distance, backward.

Mean.

Difference from mean.

A East base to A East base to

(day). . . (night).

Do

A toB (day) B to A(day)

AtoB(night)
B toC(day)

CtoB(day) B toC(nlght)

CtoD(day)

DtoC(day) C toD (night)

57.41 57.38 59.79 60.76
51.11 66.45
49.29 68.35

68.37 70.09 66.'96

TO 240. 01450
.01309 .01174 198. 02356
19S. 02257 222.03368
222. 02872 201. 02329
201. 021S2

198.02533 222.03385 204.02571

TO 240.01311 198.02382 222.03208 204.02361

TOTO 1.39 0.02 1.37 0.26 1.51 1.25 1.60 1.76 3.36 0.32 2.10 1.79

PRIMARY TRIANGULATION.
Section measures of the El Paso base Continued.

Section marks.
D toE
E toF FtoG
GtoH Htol
I to J
JtoK KtoL LRMittdoogeRNitdogMe NtoO OtoP PtoQ QtoR R toS
S to Signal
Signal to T TtoU
UtoV VtoW WtoX XtoY YtoZ
Zto Gulch Gulch to Range. Range to Dot... Dot to Spring... Spring to Road.. Road toa
a to /J to r rto.) a to t
toC C ton
to e
i]
9tO I. <to*
to*
itO/l fltOll
to? to.
tOjr JT tO p p to <r a to t t to y
j to West base... Do
West base to u... Do

Mean
temperature F. corrected
for-
ward.

Mean
temperature F.
corrected backward.

No. of
(average) bars.

Corrected
distance, forward.

Corrected
distance, backward,

Mean.

Difference from mean.

64.18 54.22 63.01 71.12 80.45 88.96 82.34 63.08 74.47 60.10 64.99 71.00 62.44 58.20 69.26 78.36 65.71 76.98 84.91 94.15 67.34 66.91 75.15 82.47 87.16 61.91 71.60 79.23 89.39 72.89 87.74 67.33 81.18 88.18 87.47 68.53 76.06 83.31 60.29 66.83 74.57 65.18 67.83 75.54 68.68 80.51 85.41 85.84 80.77 60.95 61.62

75.61 66.71 72.44 77.59 76.84 68.72 61.63 73.68 83.44 74.74 82.80 85.27 81.02 76.99 82.50 84.43 86.37 86.34 88.65 82.22 77.59 87.06 84.87 81.43 77.20 69.70 60.43 88.42 82.30 85.97 89.22 80.81 84.83 87.22 86.59 83.41 82.01 78.00 73.60 66.87 56.61 91.09 87.96 79.20 69.70 61.15 53.60 48.28 78.41
74.92 85.08

TO 276.03080 198. 00429 210. 01696 192. 02778 222. 04679 234.06044 180. 02254 203. 98348 215. 97432 203.98388 174. 02009 192. 00614 204.00622 203. 97690 222. 02792 204.03384 239.99341 204.02239 204.04262 204.04997 204.03096 204.02970 204.01104 204.04171 186. 05494 264.00565 204.03409 144.00645 198. 01723 294. 00815 192.02830 222.00464 192. 03881 210. 02544 203.99345 203.99583 210. 02995 210. 03734 203.98739 209.97726 246. 03364 167.94530 143. 99969 239.96706 210.00583 215. 95311 203.98544 215.97809 173.97449 258. 20793 258. 21512

m
276. 03100 198. 00368 210.02012 192. 02788 222.04399 234. 05621 180. 02129 203.98378 215.97716 203.98487 174.02008 192. 00253 204.00438 203.97706 222.02639 204.03109 239. 99571 204.02165 204.04120 204.04668 204. 03242 204.03318 204. 01162 204.04092 186.05522 264. 00899 204.03496 144.00729 198.01803 294.00508 192. 02421 222.00468 192. 03636 210. 02297 203.99205 203.99445 210. 02866 210. 03546 203.98855 209.97842 246. 03364 167. 94447 143. 99988 239.96539 210. 00477 215. 95094 203.98431 215.97683 173.97361
258. 21586 258.21127

ra 276.03090 198. 00399 210. 01854 192. 02783 222. 04539 234. 05832 ISO. (12191 203.98363 215.97574 203. 98438 174. 02009 192. 00433 204/00530 203.97698 222. 02716 204.03247 239.99456 2(11.0221)2 204.04191 204.04832 204. 03169 204.03144 204.01133 204. 04132 186.05508 264.00727 204.03452 144. 00687 198. 01763 294.00662 192. 02625 222.00466 192.03758 210.02420 203.99275 203.99514 210. 02931 210.03640 203.98797 209.97784 246. 03364 167.94488 143.99979 239. 96623 210. 00530 215. 95202 203.98488 215.97746 173. 97405
258. 21255

TOTO 0.10 0.30 1.58 0.05 1.40 2.11 0.62 0.15 1.42 0.50 0.01 1.81 0.92 0.08 0.77 1.37 1.15 0.37 0.71 1.65 0.73 1.74 0.29 0.40 0.14 1.72 0.43 0.42 0.40 1.53 2.04 0.02 1.23 1.23 0.70 0.69 0.64 0.94 0.58 0.58 0.00 0.41 0.10 0.83 0.53 1.09 0.56 0.63 0.44 4.62 2.57 3.31 1.27

17

The length of the base as measured with rods is 11 292.8231 meters. The reduction to
sea level is 3.6467 meters; therefore the length of the base reduced to sea level is 11 289.1764 0.0150 meters. Since the length, as brought through the triangulation from the Provo base to
the El Paso base, differed from the above value by one part in 13 500, it was decided to remeasure the El Paso base, and, if necessary, to insert an additional base in the one hundred and fourth
meridian triangulation.
The length of the El Paso base reduced to sea level, as measured in 1913 with three invar tapes, is 11 288.9852 meters. (See p. 22.) There appeared to be no uncertainty whatever in the recovery of the ends of the base, nor was there any uncertainty in the recovery of the marks of the triangulation stations Pikes Peak, Divide, and Bison, the stations in or near the El Paso base net, from which the one hundred and fourth meridian triangulation started. Consequently, the difference between the new and old measures of the El Paso base must be due
to systematic or constant errors in one or both measures.
A careful study of the results of various standardizations of the same set of invar tapes (see
table on p. 25) makes it seem reasonably certain that there is no constant error in the mean length of any group of three tapes as great as one part in 500 000. The iced bar is used at the Bureau of Standards in determining the length of the 50-meter comparator, and from time to time the iced bar has been compared directly with the prototype meter held at that bureau.
48310 14 2

18

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Moreover, the measurements on the field with invar tapes give a very small probable error for the result. There seems to be nothing which could cause a large systematic or constant error in the field measurements. The possibility of a blunder in reading setups and setbacks or in obtaining the grade corrections is almost entirely eliminated by making independent measurements in opposite directions and by leveling in both directions over the tape supports to deter-
mine the differences in elevation. Any error which is likely to occur in reading the temperatures
of the tapes will have only a very slight effect, owing to the extremely small coefficient of expansion of the metal of which the tapes are made. Therefore it seems probable that the error is in the early measurement of the El Paso base with the bars.
That the error in this measurement is not due to the effect of accidental errors alone is
indicated by the small differences of the individual measures from the mean of two or more measures of a section, as shown in the last column of the above table.
The error in the length of the base, by the bar measurement, is probably due to the standardization of the bars or to differences between the true temperature of the bars and that read from the thermometers during the field measurements.
Errors of standardization. The bars used in the field were compared directly with standard bar No. 1. That bar in turn was compared with six especially constructed meter bars and with a 5-meter and a 1-meter bar, all of which had been compared with the committee meter. The length of the latter standard was obtained from comparisons with the international prototype meter. Each one of the bars mentioned above, except the prototype meter, was an end measure.
It is believed that the general experience has been that it is impossible to obtain as great accuracy
in comparisons with an end-measure standard as with a line-measure one. No doubt there was
an error of appreciable size in the lengths of bars 3 and 4 due to this fact. Again there were doubtless appreciable errors in the values of the lengths of bars 3 and 4 due to errors in the observed temperatures during the various comparisons. The metal was steel and the temperatures of the various bars were obtained by reading thermometers placed near them.
Temperature errors in the field measurements. Assistant C. A. Schott, on page 106, of
Special Publication No. 4, made the following statements:
The forward and backward measures of the subdivisions were frequently made with greatly different average temperatures, yet when we compare their respective sums we find 11 292.8331 ' meters and 11 292.8157 ' meters, showing
the small difference of 17.4 millimeters.
The matter as to whether the thermometers indicate the true temperature of the rods has been inquired into, and it seemed as if the rods were lagging somewhat behind the thermometer indications, but there are so many exceptions to this that no satisfactory result (numerical value) could be deduced.
A comparison between the day and the night measures of the first four sections, as given
in the above table, shows that the latter always gave shorter lengths. The average difference between the two is about one part in 75 000. This difference could have been caused by an average temperature 1.2 C. lower than the average recorded temperature. It is probable that the thermometers did not record the temperature of the bar with a high degree of accuracy, even at night, consequently the systematic error due to erroneous observed temperatures in
the El Paso base measurements may be somewhat greater or less than one part in 75 000.
Other sources of error. Errors in the alignment of the bars would affect the results in a systematic manner, making the length too groat, but as the alignment was carefully made the total effect could only be very small in amount. The errors made in observing the slope of the bars might be systematic on account of a possible index error in the sector attached to the outsido of the rods, but the effect would be of the opposite sign in the second running which was
made in the opposite direction. The settling of the bar supports down the grade could not have caused any appreciable error; first, because the slope upward from east to west was only about 16 meters per kilometer on an average; and, second, because any effect of settling while running up a slope would be counteracted by tho effect while running down. The effect of the errors made in bringing the rear end of one bar in contact with the forward end of the other is no doubt very small as the errors in making the contact are accidental in character. The errors
1 Not reduced to sea level.

PRIMARY TRIANGULATION.

1$

made in transferring the ends of a bar to the ground mark at the end of a section, or possibly at other points, were very small and should have been accidental in character.
There is a possibility of movements in the upper portion of the earth's crust between the dates of the first and second measurements which might change the distances between any two given points. However, this could probably not happen to any appreciable extent, such as one part ia 60 000, on a line of triangulation without serious earthquake shocks, none of which have been noted in recent years in the vicinity of the El Paso base, or the stations Pikes Peak, Bison, and Divide.
After this discussion of the various possible sources of error in the old measurement of the El Paso base, the question at once presents itself: To what degree are other primary bases measured with bars unreliable ? This question is a very difficult one to answer.
There was only one other primary base line measured with 6-meter bars Nos. 3 and 4 (those used on the El Paso base) and there are very few bases which were measured with single rod bars. Most of the bar measurements of primary bases were with various kinds of compensating bars. In a number of cases these were used in connection with steel tapes with very accordant results. The bar and tape measurements of the Holton base agreed within one part in about 340 000, as given in Appendix 8 of the Report for 1892. Also in the measurement of the nine bases on the ninety-eighth meridian with steel tapes and the duplex base apparatus, as given in Appendix 3 of the Report for 1901, the measures agreed on an average within one part in about 140 000.
In the writer's opinion, it may safely be assumed that there are very few primary bases in
the United States with actual errors in their lengths as great as one part in 59 000, the difference
between the bar and invar tape measures of the El Paso base. It is believed that by far the greater number of primary bases measured by bars have a much smaller actual error. The
uncertainty of the length of a line in a section of primary triangulation between bases, due
entirely to inaccuracies in the angle measures, is that represented by a probable error of about one part in 80 000. Therefore, if the actual error in the length of a base is comparable in size with the probable error of a line of the triangulation due to angle errors, then there is no great decrease in the accuracy of the lengths of the triangulation due to the error in the length of
the bases, it being assumed, of course, that the actual errors of the bases would vary in sign.
BASE MEASUREMENTS IN 1913.

EL PASO BASE.
On July 7, 1913, Signalman J. S. Bilby began the preparation of the El Paso base for
remeasurement in compliance with instructions from the superintendent, directing him to do all the work on the base except the actual tape measurements and to cooperate with Assistant C. V. Hodgson in that operation. Mr. Hodgson in the meantime was engaged in organizing and outfitting a latitude party for work on the one hundred and fourth meridian.
Mr. Bilby completed the stake-setting and leveling over the base on July 22, 1913, and the
tape measurements were made on four days, between July 16 and 20, inclusive. The results of the measurements were obtained and telegraphed to the office on July 23. As the result did not give a satisfactory agreement with the length as brought down from the Provo base through the triangulation, Messrs. Hodgson and Bilby were directed to locate and measure a base in the vicinity of Cheyenne, Wyoming, and to connect it with the main scheme of triangulation.
Methods used. The instructions issued to Messrs. Hodgson and Bilby were similar to those regarding the Ambrose and Provo bases (see p. 9), and the methods employed in making the measurements were the same as those used in all measurements of primary bases in recent
years. (See p. 11.)
Standardization of tapes. The tapes had been standardized in January, 1913,' by the Bureau of Standards, in connection with the Ambrose and Provo bases, and it was decided that no additional determination of the lengths need be made before sending them to the field again in July of the same year. (See also p. 10, under heading "Standardization of tapes.")
A restandardization, for the purpose of checking the lengths of the tapes as used, was made at

20

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

the Bureau of Standards in October, 1913. The results of these standardizations are given under the heading "Equations of tapes," below.
Size of party. During the preparation of the base, Mr. Bilby had in his party five temporary hands. For the measurement the party consisted of Messrs. Hodgson and Bilby, the recorder of the astronomic party, and the five hands mentioned above, eight persons in all.
The party lived in a camp pitched close to the base line, in order to make a minimum amount of traveling in going to and from the work.
Division of the bases. There were, as usual, three main divisions in the El Paso base, the approximate length of each being shown in the table which follows. Each division was measured at least twice in opposite directions with different tapes, and a different pair was used on each
division in order to obtain an intercomparison of the tapes.

Division.

PBIMAEY TRIANGULATION.

21

The lengths of the tapes as given by the January, 1913, standardization had been used in computing the lengths of the El Paso and Cheyenne bases, and those lengths had been used in the adjustments of the triangulation on the one hundred and fourth meridian before the October, 1913, values of the tapes became available. The mean length of the three tapes used in the measurement of the El Paso and Cheyenne bases as given by the January standardization differed only 0.005 millimeter, or 1 part in 10 000 000, from the mean length as given by the standardization in October, 1913. So it was decided that the results by the first standardization were satisfactory, and the second values were considered only as checks. (See p. 25 for a tabular statement of the values of the tapes resulting from the standardizations for the years 1909 to 1913, inclusive.) If the mean of the values by the two standardizations had been used, the probable error of the base would have been changed slightly, but the length of the base would not have differed by as much as 1 milhmeter.
Reduction to sea level. The elevation of the top of the monument at El Paso west base, as determined by spirit leveling, is 2167 meters. The average elevation of each of the sections of the base was obtained from spirit levels run in both ways over the tape supports to get the grade corrections. The corrections to reduce the various sections to sea level are shown in
the table which follows. It is certain that the above elevation is correct within 1 meter, and
therefore the reduction to sea level is not subject to any appreciable error. Corrections to spring oalances. In the table of the results of measurement is a column
headed "Correction for erroneous tension," in which is given a correction to the length of each section of the base due to index errors of the spring balances used. Inadvertently, the observer did not have his attention called to the fact that the index errors of the balances sent to the
field had not been corrected. He used one balance as a standard when the index read exactly 15 kilograms. It was learned later, when there were sent to the Cheyenne base additional
balances which had no index error, that the standard balance at the El Paso base had an index error of 338 grams. This made the actual pull on this balance, while it was being used as a
standard, only 14.66 kilograms instead of 15. After the effect of this difference is applied the resulting length is free of error from this source.
Results of remeasurement. The results of the remeasurement of the El Paso base are given
in the following table:
The El Paso base line.

Section. Date and hour.

22

U. 8. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The El Paso base line Continued.

Station. Date and hour.

July, 1913.

Vm,140-160 17, ,18,

7:45 a.m. 8:55 a.m.

m IX, 160-180

17, 8:45 a.
,17, 2:40 p.m.

X, 180-200..

17, 9:25 a.m. 17, 2:10 p.m.

XI, 200-220.

17,10:20 a.m. 17,11:35 a.m.

XII.220-W. 17, 11:15 a.m.

B.

17,11:25 a.m.

Temperature (cen-

1

Upade).

Weather and

5

wind.

38

i

^a I

a

S a

e

1

s

-

P Cy, L SW.. Cy.O
LW P Cy, L SW..
Cy,
PCy.LSW.. Cy,"MS
C, LSW
C,LSE
C,0 C,0

mm
21.8 -0.0006 +0.0486 -0. 1815 +0. 2015 -0.0012 -0.3261 17.7 -0.0019 +0.0664 -0. 1815 +0. 1911 -0.0105 -0. 3261

m
999.7407 999. 7375

m mm
-1.6 2.56
+ 1.6 2.56

23.1 -0.0001 +0.0975 -0.2237 +0. 1991 -0.0013 -0.32S8 25. N +0.0010 +0.0973 -0.223: +0.2015 -0.0012 -0.3288

999. 7427 999.7444 1+1.7 2.89

999. 7461

\-1.7 2.89

24.0 +0.0002 2.8474-0.3426 +0. 1991 -0.0013 -0. 3307 25.1 +0.0007 -2.8471-0.3426 +0. 2015 -0.0012 -0.3307
25.5 +0.0007 +0.0323 -0.3459 +0. 1991 -0.0013 -0.3351 27. ti +0.0018 +0.0315 -0.3459 +0. 2015 -0.0012 -0.3351

996.6773 996.6790 (+1.7

MM 996.6806

\-1.8 (+1.4

5512 '

999.5526 J999.

1.4

2.89 2.56
1.96 1.96

26.4 +0.0003 +4.8315 -0.3566 +0.059 -0.0003 -0.1030 304.4316

(-0.3 0.09

26.7 +0.0004 +4.8300 -0.3566 +0.0605 -0.0003 -0.1030 304.4310 \304. 4313 \+0.3 0.09

The length of the El Paso base is 11 288.9852 0.0031 meters. The logarithm of this length is 4.0526549 1. This probable error of the length corresponds to one part in 3 642 000. The probable error was computed in a manner similar to that described on pages 160-161 of Appendix No. 4 of the Report for 1910.
CHEYENNE BASE.
When it was found that the new length of the El Paso base did not agree closely with the
computed length as carried through the triangulation from the Provo base, it was decided to introduce a new base in the one hundred and fourth meridian triangulation. (See p. 9.) After
making a reconnaissance, Mr. Bilby located this base in the vicinity of Cheyenne, Wyo. He
also selected several triangulation stations at which horizontal directions were later observed for the purpose of connecting the base with the main scheme of triangulation. See illustrations at the end of this volume.
Organization of party. The preparation of the base for measurement was made by Mr. Bilby with the assistance of five temporary hands employed in the vicinity of the work. The
preparation and leveling over the base occupied the time between July 28 and August 6, 1913.
Upon the completion of the above work, Mr. Hodgson, who had been engaged upon latitude observations since the completion of the measurements of the El Paso base, moved to the
Cheyenne base and carried on the actual tape measurements with the cooperation of Mr. Bilby. The measuring party consisted of Messrs. Hodgson and Bilby and six hands. The actual tape
measurements were made on two days only, August 8 and 10.
Divisions of the base. Like the other bases on the one hundred and fourth meridian, this one had three main divisions, each of which was measured twice in opposite directions with different tapes. Each division was measured with a different pah of tapes in order that an intercomparison of the three tapes used might be made.
The following table shows the divisions of the base, the tapes used, and the approximate
length of each division:
Division.

PRIMABY TEIANGULATION.

23

The descriptions of the locations and permanent monuments at the base ends are shown

on page 117. Apparatus used. The same tapes were used on the Cheyenne base that had been used on
the Ambrose, Provo, and El Paso bases. (See p. 11.) The other articles of apparatus were similar in character to those used on those three bases.

Methods employed. -The base was measured in the same manner as the others on this arc.
Since the wind was not found to be troublesome, only three supports were used for each tape length, one at each end and one at the center point. (See p. 11)
Standardization and equations of tapes. On page 20, under the same heading, are given the
equations of the tapes used on the Cheyenne base as furnished by the Bureau of Standards. As on the El Paso base, the equations of the tapes resulting from the standardization in January, 1913, were used in the final computations of the base. The results of the second standardization were not available when the computation and adjustment of the one hundred and fourth

meridian triangulation was begun. After the results of the second standardization were received it was found that the average difference between the two standardizations was only 1 part in 10 000 000 which was negligible.
Reduction to sea level. The elevation above sea level of Cheyenne west base as determined

by trigonometric leveling is 2074.20 meters. The average elevation of the various sections of

the base was determined by a line of levels run over the base in opposite directions for the purpose of obtaining the grade corrections. The correction to sea level for each section is shown in the following table. Since the uncertainty in the adopted elevation of West base is less than one meter, the corrections shown in the table for reducing the measured lengths to

sea level are free from any appreciable error from this source.

Corrections to spring balances. Like the table of results of the remeasurement of the El Paso base, the table for the Cheyenne base also contains a column of corrections for erroneous

tension. The discussion on page 21 states that there were sent to the Cheyenne base spring balances which had no index error. These did not arrive, however, until after the measure-

ment had been completed. Therefore, corrections similar to those explained for the El Paso base, must be applied to the results for the Cheyenne base.
Results of measurement. The results of the measurement of the Cheyenne base are shown

in the following table:

The Cheyenne base line.

Section. Date and hour.

24

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The length of the Cheyenne hase is 6650.4367 0.0028 meters.

The logarithm of this length is 3.8228501 2. The probable error of the length corresponds to 1 part in 2 367 000. The computation of the probable error was made in a manner similar to that described on

pages 160-161 of Appendix 4 of the Keport for 1910.

The length of the El Paso base, as computed through the triangulation from this measured length of the Cheyenne base, is now shorter than the measured length of the El Paso base by

1 part in 30 800. Since the adjustment of the triangulation between these bases gives small

corrections to directions, the accidental errors therein are not sufficient to account for this

discrepancy in length. The difference, therefore, must be due to some systematic errors in

the triangulation.

One of the causes of the discrepancy between these bases may be the elevation of the

surface of the geoid above that of the ellipsoid, although the effect of this is not large enough

to cause the total difference stated above.

An attempt to show the geoid contours in the United States was made on illustration

No. 17 of the United States Coast and Geodetic Survey publication entitled "The Figure of the Earth and Isostasy from Measurements in the United States," but the area within which these

contours were drawn is very limited in extent. In the vicinity of the El Paso base the geoid contour is marked 32 meters. It is impossible, of course, to tell what will be the number for

the geoid contour at the Cheyenne base which is in southeastern Wyoming, but as the geoid contours seem to conform somewhat to the topographic contours, it may be expected that the

number at the Cheyenne base will be between 24 and 30 meters. These contours of the geoid should not be considered as giving anything more than relative elevations above the ellipsoid, for the initial point used in constructing the geoid contours was given a value of 10 meters, in

order that negative values might be avoided.

If the difference between the geoid elevation at the Cheyenne and El Paso bases is 8 meters,

a relative error of 1 part in about 800 000 would result. If the reduction to sea level at Cheyenne

were considered correct then the reduction at El Paso would be in error by 0.014 meter. This error would make the El Paso base as measured too long. This agrees in sign with what is
shown by the compaiison of that length with the one brought through the triangulation from

the Cheyenne base. However, there must be some other cause for the difference of 0.367

meter between those two bases,.

The average elevation of the geoid above the spheroid along the transcontinental triangulation, as indicated by the illustration in The Figure of the Earth and Isostasy from Measure-

ments in the United States, is about 12 meters (after subtracting 10 meters, the assumed

elevation of the starting point). Therefore, the average error in the measured lengths of the

base lines along that arc caused by the elevation of the geoid surface is 1 part in about 500 000.

Although this error is constant in its effect, it is practically impossible to apply a correction for

it, owing to the fact that available data showing relative geoid elevations are very limited, and

that no data whatever as to the absolute elevation of the geoid above or below the surface of

the ellipsoid are available.

Cost of the El Paso and Cheyenne bases. The total cost of the measurement of these two

bases was $980. In addition to the cost of labor, materials, etc., this included the salary of Mr. Bilby from the time he reached Colorado until he left for work on reconnoissance, one-half

of his traveling expenses and those of Mr. Hodgson from Washington to Littleton, Colo., and

the salary of Mr. Hodgson while not on his latitude work. The cost per base was $490 and the

cost per kilometer was $55, both bases being considered. The office computation of the two

bases took the equivalent of 22 days of one computer, with a cost of $105. The Bureau of

Standards makes a charge of $50 for a fundamental standardization of a base tape; therefore

to get the total cost of the bases to the Government the cost of two standardizations of four

tapes,

$400,

should

be

added

to

the

field

expenses

and

the

cost

of

1
computation.

' The cost of one of these standardizations was charged to the Provo and Ambrose bases but Is Included here also to make the total cost comparable with that of the other bases.

PEIMARY TEIANGULATION.

25

The total cost of the bases was $980 + $105 + $400 = $1485; this is $742 for each base, and
at the rate of $83 per kilometer.
While the measurements were being made at the Cheyenne base, the party also observed
horizontal directions at the base ends and at the two stations Waddill and Whitaker for the
purpose of connecting the base with the main scheme of triangulation. The work on the base was only slightly interrupted by these operations. The stands used at Waddill and at Whitaker in 1912 were still in place, so it was only necessary to place stands at the base ends, which required very little lumber. As nearly as the writer could determine, the cost of the additional work of connecting the base with the main triangulation scheme was only about $130. The observing was done at night on signal lamps.
Summary of tape values. The following table shows for each of the four tapes the length as determined by six different standardizations, the probable error of each determination, the mean of the results from the six standardizations, and the residuals. The values given are for the lengths of the tapes when resting upon three points of support and subjected to a fixed tension of 15 kilograms. In order to make the values comparable, they have all been reduced
to the same temperature, namely, 21.2 C.

Values of tapes with three supports at temperature of 21.2 C.

Date of standardization

26

U. S. COAST AND GEODETIC SUBVEY SPECIAL PUBLICATION NO. 19.

Each of the tapes was longer at the time of the last standardization than at the first one
the average increase being 0.143 millimeter, or 1 part in 350 000. These changes are within
the possible effect of the accidental and constant errors of standardization, except in the case
T of i2l . That tape shows a continuous increase from January, 1909, to October, 1913, but the maximum change in the length of this tape between any two consecutive standardizations is only 0.131 millimeter (March, 1910, to March, 1912), or 1 part in 380 000. The maximum T change between two consecutive standardizations for S1B is 0.088 millimeter, or 1 part in T T 570 000; for S11 it is 0.131 millimeter, or 1 part in 380 000 (the same as for 521); and for r522 it is only 0.051 millimeter, or 1 part in 980 000.
The following table is similar to the preceding one, except that the values given are for
the lengths of the tapes when resting upon five points of support. The common temperature
to which these values are reduced is 26.8 C.

Values of tapes with Jive supports at temperature of 26.8 C.

Date of standardiza-
tion.

PRIMARY TKIANGULATION.

27

The members of each party were cautioned to use every care in handling the tapes, but even so it seems remarkable that none of the tapes have been injured.
Rapidity of base measurements. The following table shows the speed attained in the measurements of the four bases. The times given are the hours of actual work, including the time spent in changing tapes and in placing the copper strips on the end stakes, but not long delays
such as the stops for luncheon :

Ambrose base.

28

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

night, the stake supports would he preferable. Either method will enable the party to secure results far more accurate than are really required for the highest grado of triangulation.

CONCLUSIONS FROM RASE MEASUREMENTS.

Some of the conclusions which may be drawn from the measurements of the four base lines
discussed in this publication are:
(a) The plan adopted on the Texas-California arc of having the observing party on triangulation measure the bases as they are reached, is an efficient one, and should be continued. This method insures that the lengths of the bases may be known in time for use in an adjustment of the arc of triangulation as soon as the last field work of the triangulation has been done.
(b) Tapes of the invar metal make an entirely satisfactory apparatus for base measure-
ments.
(c) There is no evidence that a different length than 50 meters should be used for the base

tape.
(df) The 50-meter invar tape is affected by wind of even moderate strength, when supported at only three points. But ordinarily, during the progress of the various operations at a base, sufficiently long periods of favorable wind conditions may be found for making the measurements. All four of the bases on the one hundred and fourth meridian had only three supports for each tape length, one at each end and one in the center. No serious trouble with the wind
was encountered. An efficient remedy for the wind effect, if troublesome, is to use five supports
for each tape length, as on the Deming base in 1910. (See pp. 154-155 of Appendix 4, Report
for 1910.)
(e) Owing to the small time and cost needed to measure a base, it is believed that the
R ummation of t (see p. 8) between bases should be between 90 and 140, instead of between
130 and 200. With the higher values there is the possibility of having to introduce other bases after the completion of the triangulation and the measurement of the bases provided for by
the reconnaissance.
(f) While the index error in the spring balance did not introduce an error into the El Paso and Cheyenne base lengths, at the same time it was a cause of annoyance. The index of the balance should be rigidly fastened to its stem to prevent a change in the index error if the
balance were roughly handled. (o) After the use of the same tapes on six bases in four different seasons between 1909 and
1913, inclusive, the lengths of one tape show a maximum range of only 0.297 millimeters, or 1 part in 170 000, while the average maximum variation of all the tapes is only 0.193 millimeters, or 1 part in 260 000. If the actual uncertainty in the length of each tape should be as much
as the total range in values as shown in the table on page 25, even then the uncertainty of a base measured with three or more tapes would be less than the uncertainty in the length of any one tape. Such accuracy is far greater than that of the triangulation, and hence the invar metal must be considered as a most satisfactory material from which to make a base measuring

apparatus.

RUILDING SIGNALS AND MARKING STATIONS.

The erection of the signals or instrument stands and the marking of stations were done by a party under the direction of Signalman J. S. Bilby. He arrived on the working ground
April 12, 1912. Actual field operations of the building party began on April 24 and ended August 28, 1912, a total time of four months and five days.
The building party consisted of Mr. Bilby and two men, with occasional temporary employees who assisted in cutting lines or erecting signals. One of the regular men began work
at Cheyenne, Wyo., worked southward to the end of the scheme and then northward from
Cheyenne to meet the other man who had started at the Canadian border and worked south-
ward. Mr. Bilby was with the one or the other of these men, depending upon where his assistance and guidance were most needed.

Special Publication No. 19.

NO. 2.

TWELVE-INCH THEODOLITE.

PRIMARY TRIANGULATION.

29

The building party erected stands or signals for mounting the theodolite at 102 stations, prepared the base lines at Ambrose and Provo, and gave some assistance to the observing parties in the measurement of the bases. The stations were also marked in a permanent manner by the building party. The character of the marks is described in notes 1 to 8 on page 115, and the metal tablet placed in the concrete or cemented to solid rock is shown in illustration No. 4.
Signals. The type of signal is that shown by illustrations and described in Appendix 4, Keport of the United States Coast and Geodetic Survey for 1903. In that publication are also given detailed directions for its erection. The signal is a double structure consisting of an inner tower, called the tripod, on which the instrument rests, and the outer tower, called the scaffold, near the top of which there is a platform for supporting the observer. The two structures do not
touch each other at any point and consequently the observer may move about on the platform
without disturbing the level or azimuth of the theodolite. The heliotrope and lamp are sometimes posted on the tripod and at other times on the scaffold.
The signals shown in the illustrations in Appendix 4 of the Report for 1903 were designed for use by a double observing party, and the upper platform enabled the light keeper to post his heliotrope or lamp centrally over the station even when one of the observers was at his
station. When there is only one observing party the scaffold does not extend above the tripod,
as the top platform is not needed.
It has been found that it is more economical to build the tripod to only a moderate height, say less than 70 feet, and then extend the scaffold to a sufficient height to make clear the line from its top to the tripod head at a second station and likewise to extend the scaffold at the second station to such a height that the line between its top and the tripod head at the first
station will also be clear, rather than to attempt to build the double structures to such heights that the line between the tripod heads at the two stations will be clear of obstructions.
Illustration No. 10 of Appendix 4, Report for 1903, shows a signal which has the tripod about 66 feet high and the light stand at the top of the superstructure on the scaffold 137
feet above the ground.
The one hundred and fourth meridian arc is rather remarkable for the low average elevation of the instrument above the ground. The tables on pages 43 to 47 give the elevation of the telescope of the theodolite above the station mark. There were only eight stations at
which the height of the instrument was greater than that necessary to bring the telescope to the eye of the observer as he stood upon the ground. The height of the simple stand for mounting the theodolite was about 3J feet. The average height of the tripods of the eight signals was 28.15 feet. Inasmuch as the country traversed was at most points distant from lumber yards, the reconnaissance party made such selections of stations as to make the amount of building a minimum.
On the Texas-California arc of primary triangulation (reported in Special Publication No.
11, United States Coast and Geodetic Survey) the plan previously employed of always having the telescope of the theodolite at least 10 feet above the ground except on sharp peaks, was abandoned. Where the line was clear of obstructions only stands for the instruments were used even though the country was flat for some distance in all directions from the station.
The accuracy of the Texas-California triangulation was better, on an average, than that of the other great arcs in the United States. The writer, who observed part of one season on
the Texas-California arc, noticed that the lights and heliotropes observed from a station where the theodolite was only a few feet from the ground were more unsteady than when the lines were high, and especially when high near the station occupied by the observer.
The plan used on the Texas-California arc was adopted on the one hundred and fourth meridian arc of primary triangulation, and the instrument was never mounted at a greater height than was barely necessary to clear the line. The accuracy of the work on the one hundred and fourth meridian is discussed later in this report.
Cost of building signals and marking the stations. The total cost of the work of the building party was about $4200. This includes the salaries and traveling expenses for the chief and all the members of the party, also the cost of lumber and cement delivered to the stations,

30

V. S. COAST AND GEODETIC SUBVEY SPECIAL PUBLICATION NO. 19.

and various small expenditures. This is at the rate of $5.83 per mile of progress, a remarkably low amount.
The use of instrument stands instead of signals, even of low height, decreased greatly t he expenses of preparing the stations for the observing parties. The lumber necessary for signals would have been expensive and hauling it to the stations would also have been costly.
INSTRUMENTS USED ON TRIANGULATION.
Theodolites. The type of instrument used for the horizontal measures is described in
detail in Appendix 8 of the Report for 1894. It is believed that the portion of that description shown below will be of interest and value to the reader. These theodolites have been
used on all of the primary triangulation done by the United States Coast and Geodetic Survey since they were made in the early nineties. One of them is shown in illustration No. 2.
The base is of cast iron, into the socket of which is fitted another cast-iron socket, to which is rigidly attached the brass circle and into which is fitted the center which carries the alidade. Under the circle is a device for firmly clamping this socket to the base in any position of the circle. The center is 22.2 centimeters (8 inches) long, its two bearing surfaces being cones of different angles. It is made of the best quality of tool steel, and the cones are made glass hard. No pains were spared in the construction of these centers and sockets, and it is believed they are the most perfect ever made for theodolites, and are probably the first theodolite centers with glass-hard bearing surfaces.
In the alidade the cover of the circle, the supports for the micrometer microscopes, the wye supports, axis, and setting circle of telescope are made of aluminum. The bearing surfaces of the wyes are of brass, and the pivots of telescope axis are of bell metal. The draw tube of telescope, micrometer microscopes, clamps, and other small parts
are of brass.
The use of aluminum in the construction of these instruments was not with the special purpose of reducing the total weight of the instrument, but to reduce the weight supported upon the centers. The cast-iron bases of these instruments, in proportion to the whole mass of the instruments, are much heavier than is usual in other theodolites of the same size. These heavy bases and long centers give great stability to the instruments. The weight of the whole alidade is 7.5 kilograms (17 pounds), whereas in other instruments of the same size that have been used in the Survey the weight of similar parts is 18 kilograms (40 pounds). The centers of the old instruments are of various forms, and the friction is so great that it has to be relieved by some device at lower end of centers. No such device is necessary with the new instruments. The total weight of one of the new instruments is 18.5 kilograms (41 pounds).
The telescope objective was made by J. Brashear, and is 6.1 centimeters (2.4 inches) aperture, and 73.7 centimeters (29 inches) focus. The telescope has an ocular micrometer, with three Ramsden eyepieces, giving powers of 30, 45, and 60. Several levels, all made by A. Pesseler, of Germany, are attached to the alidade for convenience. The
stride level has divisions of 2 millimeters, with arc value of 4 seconds.
The graduation of the circle is on coin silver and is 30.5 centimeters (12 inches) in diameter. It is divided to 5 minutes and reads to seconds by three equidistant micrometer microscopes. Each degree of the graduation is numbered. The degrees and nearest 5 minutes are read by a low power index microscope 50 degrees to the right of micrometer microscope A. Attached to the cover of the circle is a small camel's-hair brush which sweeps over the
'
graduation.
The circles were graduated on the United States Coast and Geodetic Survey engine. This graduating engine
was originally made by Troughton & Simms, of London, and bears the date of 1841. In the hands of the Survey it
has received various improvements, the chief of which are a new tracing apparatus and new support for the same. The engine is driven by a small turbine wheel upon which a constant water pressure is maintained. To graduate a circle to 5 minutes takes about 3 hours and 35 minutes. The graduations are made at a temperature of 36.66 C. (98 F.), that temperature being most easily maintained at any season of the year and least affected by the occasional presence of the operator. For the last nine years this engine has been manipulated exclusively by the present chief instrument maker of the Survey and in his hands has produced some very fine graduations, as the results with the two new theodolites, Nos. 145 and 146, show.
Vertical collimator. In centering a signal over the mark of a previously established station, when placing a mark under a new signal, and for centering the theodolite over the station mark, there was used a vertical collimator which is shown in illustration No. 3a. In order that this
instrument may be used there must be an opening in the center of the cap block of the tripod
head of the signal. Into the vertical socket of the base of the instrument fits a telescope carrying a fixed level and having adjustable cross wires in its reticule. The axis of the level is at right angles to the line of sight of the telescope. The base rests on three leveling screws.
The adjustments of the instrument are extremely simple. After Having focusscd the eyepiece on the cross wires, the cross of the wires is adjusted to make it remain on a point as the telescope is revolved about its axis. Then the level is adjusted to make the bubble remain in

Special Publication No. 19.

NO. 3a.

VERTICAL COLLIMATOR (TWO VIEWS).

PRIMABY. TKIANGULATIOW.

31

the center as the telescope is revolved. With the instrument in perfect adjustment and the bubble brought to the center in two positions at right angles, the line through the cross of the
wires will be vertical. In actual use it is not essential that the instrument be in perfect adjustment, for if the bubble is brought to the center in each of four positions of the telescope, about
90 degrees between each two positions, four points may be determined and the mean position
of them will be in the vertical line through the center of the telescope. After the instrument has been placed directly over some mark the telescope is withdrawn
and there is inserted a plunger, the lower end of which is a point. The center of the instrument
may be marked by the intersection of two strings at right angles drawn across the tripod head with their intersection at the point of the plunger ; or small nails may be used to mark two lines
approximately at right angles whose intersection is at the point of the plunger. These are only
two of various methods which may be used to indicate on the tripod head the center of the
vertical collimator.
When only a stand is used for mounting the theodolite, heliotrope, and lamp, the centering
is done by means of a plummet. Heliotropes and lamps. The observations for the horizontal directions in the main scheme
were made entirely on heliotropes and acetylene signal lamps. The heliotrope is of the box type and is shown in illustration No. 3b. The diameter of the fixed mirror is 2f inches (70 millimeters). The lamp is shown in illustration No. 3c. It is an ordinary automobile acetylene headlight fitted with a base which may be easily set up centrally over a triangulation station. One charge of calcium carbide will give a satisfactory light for about four hours.

LIGHT KEEPERS.

The plan of having the same men throughout all or a large part of a season and the method

of directing them by heliographing with the Morse alphabet were first used on triangulation in

the United States on the ninety-eighth meridian in 1902. (See pp. 826-S29 of Appendix 4 of

the Report for 1903.) Previous to that time it had been the custom to employ some one near

A a triangulation station to show the heliotrope and to attend to the signal lamp.

simple

code of signals was sometimes used to indicate to the man that the work had been completed,

but no systematic and elaborate method of signaling had been used, and serious delays were

inevitable, as an officer would have to visit and post men at the new stations before the obser-

vations could proceed. The method of signaling by means of the Morse alphabet was used

in guiding and directing a heliotroper by Prof. J. F. Hayford when he was the astronomer on

the United States-Mexican Boundary Commission, and it was he who proposed its use in the

1902 work.

There are a number of causes which have contributed to the rapid progress made by the
observing parties of the United States Coast and Geodetic Survey engaged on primary triangulation in recent years, but one of the most important is the trained corps of light keepers and the ease with which their movements can be directed and controlled by the observer with

the aid of the signaling.
Six regular heliotropers (or light keepers) were used by each observing party on the one hundred and fourth meridian triangulation. Sometimes, in order to avoid delays, an additional light keeper was engaged for work at a single station, and in a few cases the driver of the observing party showed the heliotrope and lamp at a station. It was only occasionally that one of the stations to be observed on did not have a light keeper when the observer was ready to begin work.
Each light keeper's outfit consisted of a tent, bedding, a small number of cooking utensils,

binoculars, signal lamp, heliotrope, prismatic compass, sketch of the triangulation, a few tools,
and such other small articles of camp equipage as were deemed necessary. At some of the
stations the light keepers were able to get their meals with a farmer or ranchman, but nearly
always they prepared their own food. They made their moves between stations in farm

wagons hired especially for the trip.

82

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The light keepers posted their own lights and heliotropes during the entire season. At all stations occupied by the observer lines were accurately drawn on the light stand to each signal

observed upon, and a light keeper following had simply to use these lines. The stations ahead

of the observer had no lines laid out; consequently the light keepers had to use their ingenuity

in finding the direction to the observer. This, however, did not prove very difficult, as each
man was given a sketch of the reconnaissance, and by placing the sketch on the light stand

and orienting it approximately by the magnetic meridian line as gotten by his compass he was
enabled to locate at least one of the stations. He would then orient the sketch accurately

over this direction and lightly mark on the stand the directions to all of the stations as given
by the sketch. He would then begin showing to the observer. If he did not get lights from

him in reply, he would swing his heliotrope or lamp through a small angle to each side of the

approximate direction. - (The term "light" will be used hereafter to indicate either the heliotrope or lamp.) As soon as the observer saw a light from one of the stations ahead he showed

a steady light to enable the light keeper to get a correct line. Most of the forward lines were

found at night, as the lamps would show over a wider angle than the heliotropes and were not

affected by clouds.
A light keeper was usually able to find some object in the line to a station, such as a lone

or high tree or a rock, by which he could post his heliotrope and also the lamp if put up before

dark. This method was preferable to simply using the lines drawn on the light stand.
A man to be a good light keeper must have education enough to keep his accounts, but,

what is more essential, he should have a practical turn of mind which will enable him to over-

come difficulties

and

get

his

lights

posted

in

spite

of

floods,

breakdowns,

etc. ;

of course it goes

without saying that he must be conscientious and faithful. Unless a man shows the above

qualities, it is not advisable to keep him in the party a longer time than is required to get

another man.

SIGNAL CODE AND INSTRUCTIONS TO LIGHT KEEPERS.

In order to facilitate the work, written directions were given the light keepers, which included the Continental Morse alphabet, the code signals, and such other information as the light keepers might need in conducting their work. The signal code and instructions, as issued to the light keepers for the one hundred and fourth meridian triangulation, are as follows :
Continental Morse alphabet.

H
Z O
D

PRIMARY TBIANGULATION.

33

An observer calls a light keeper by showing a steady light to him until answered. A light keeper calls the observer by sending his own letter until answered.

Answer a call by a series of slow dots (not more than seven), then watch for the signal by aid of the binoculars.

Repeat every few minutes until answered by observer.

Darken light before beginning message for a period of about 15 seconds.

All messages are to be repeated by the receiver, except in case of messages from light keeper to observer. Here

the observer will answer by sending slow dots. Never repeat a word unless you are sure it is right. This is a decided

annoyance to the observer and a source of a great deal of trouble. If an observer knows that a message has not been

received, he is at least in a position to know what to do to remedy matters.

Code signals.

A series of

quick.dots means,

" I

have

made a mistake

and

will begin again."

An A means, "Wait a while." A G, followed by the name of a station, means, " Get person at that station by calling him, and tell him where

observer is."

An N: "Your light is too faint." An R: "Repeat message; I could not get it." A series of slow dots: " I understand your message." An M: "Moderate your light; it is too strong."

Signals to be used by the observer lohen communicating with a light keeper. 5 T, followed by name of station and

date,

means:

"
Stop showing light to

this station;

show

to the station indicated on date

named, and look for observer's

call."
S T, with no name of station, means: "Stop showing light to this station, and show light to the station to which
observer goes, which is indicated in the written schedule of observer's moves, a copy of which has been furnished to you. If no date is given, show to new station at next observing period."
H T D: " Have finished on you for this afternoon (or night)."
D G, followed by name of station and date, means: "Done where you are; go to the station named, show light,
and look for observer's call on date given."
D G, with no name, means: " Done where you are; go to the next station mentioned in your written schedule of
moves, and show light to the observer at his old or new station, according to the schedule. If no date is given, begin
showing light at first observing period after station is reached."
If the observer sends an "A" after 10.00 p. m., it means that the light keeper is to stay on the tower and keep a sharp lookout until called again. Should this be followed by an "Z, " it signifies that the light keeper is to recharge
the lamp and leave the station for the night. FINI: "Have finished on you; obey written instructions." "Money," "Mail," etc., followed by name of place, means: "The article is at the place named."
Signals to be used by light keepers to observer. "Money," "Carbide," etc., means: "I am in need of same."
Other necessary messages will be spelled out in full. Keep a sharp lookout for signals for 10 minutes after each recharging of lamp and for 10 minutes after each hour and half hour.

TV's may be sent any time if your light is poor. Signals to be used by a light keeper to another light keeper. 0, followed by the name of a station, means: " Observer is at that station; show to him at once."
General co-asiderations. Before starting out alone be sure that some one of the party has taught you how to use the signal lamp and how to test and adjust a heliotrope and to put on the cut-off rings on the heliotrope and lamp.
Test your heliotrope and lamp so that the light goes to the observer, for the line through the sights may point to
the observer but the light may not be centered on him.
Every day, if necessary, see that your lamp drops water fast enough to give a strong light.
Keep your heliotrope and lamp in good condition. When the air is clear, a poor light possibly may be seen,
but if it is hazy only a clean lamp and reflector will give good results. The carbide chamber should be cleaned as
soon as possible after getting through using the lamp, as the metal is corroded if carbide is allowed to stand in it. At every opportunity get the correct standard time and keep your watch within a few minutes of it.
The first thing to do when reaching a station is to try to locate all of the stations to which you will show. By doing this at the first opportunity, and not waiting for the exact moment that you expect your light to be used on a
line, you will avoid causing delays to the observing party. Where smoke, clouds, and fog are encountered, the value of getting your pointings on the clear days is evident.
After finding a station you should hold the direction to it by lines marked on the stand or by any other means practicable. When you are on a wooded peak and there has been a delay in seeing the observer's light, watch carefully for him, for the light might be obstructed close to your station and you might be able to see the call from the top of a tree or from some other point on the mountain. In other words, do not be absolutely sure that the line is open unless you have seen a light from the other station, and unless you are sure keep trying to get the observer's call by watching

very closely.
When the observer's light is once seen, set your telescope on it and fasten or mark it so that you will know you have the direction of the line even if the weather should become cloudy or smoky. Then point your heliotrope,
using thin wedges if necessary to get the proper elevation, and mark the place on the stand where each wedge belongs

48310 14 3

34

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

and also mark the wedge to show how far it is to be pushed under the heliotrope; also mark along the side of the helio-
trope box for the direction. Then you can replace your heliotrope exactly after it has been disturbed. The lamp may be set and pointed by the lines made for the heliotrope. When in trouble about the direction of the lines, always

keep watching for calls from stations other than the observer's, for the observer may be sending a message to you

through one of the other light keepers.

Your work on the tower begins at 1 p. m. From then until 4.30, unless instructed otherwise by the observer,

you should show your heliotrope all the time if there is sun enough to make a shadow. If your heliotrope is pointed

with care, a faint sun is just as good to show the observer as a bright sun on comparatively short lines; also, if you get

only a faint sun every 10 minutes or so, which lasts for a short time, it may be used by the observer. It is not for you

to decide whether you think it worth while, or whether the observer can use it or not. An effort will be made to send

THD you

as often as practicable.

At night go on the tower each hour and each half hour and look for signals from the observer, remaining 10

minutes each time. Begin doing this as soon as you have finished your evening meal. At 11 p. m. begin sending slow dots (about 20 at a time) and remain on the lookout for signals for 15 minutes
(until 11.15). If no signals are received, see that the light is burning well (recharging if desirable) and then you can

leave the tower for the night.

Keep a lookout for the observer's call from his next station, as he may have moved without notifying you. The lamp should be set up and lighted a half hour before sundown. Be careful to sight your lamp and heliotrope accurately; if in doubt, send your initial, then the observer will

show you a light. Be extremely careful not to have lanterns or other extra lights about the tower. They are often mistaken for the

signal lights by the observer. Frequently they can be seen at the foot of the tower as well as on the top. When your line is 10 miles long, or less, watch for an M, meaning that your light is too strong and should be

reduced by means of the concentric rings provided, or by paper rings cut out true. Keep your tents, mess outfits, instruments, and other articles of equipment clean and in order.

It should be remembered that the towers are built with the least material required for safety; that the signal notices apply to light keepers as well as to other people, and therefore you should in no way weaken the scaffold by

removing any of its parts.
An extra effort should be made to move between stations as rapidly as possible to prevent holding back the

observing party longer than is necessary.
So much depends upon the efficiency and faithfulness of the light keeper that an indifferent one must be disposed

of as soon as convenient.

Light keepers' accounts. Each light keeper was given in writing detailed directions for making out his accounts, for shipping by freight or express, and he was also given copies of the various kinds of bills, receipted, of which he might have need in his accounting.
In addition to the sketches showing the scheme of triangulation as located by the reconnoissance party, the light keepers were given descriptions of the stations which enabled them to move from one station to another. They were given lists of the triangulation stations in the order in which they would be occupied by the observer and each light keeper was also given a statement of his own moves and for each of his stations the line or lines over which b.e was to show a light. This information was tabulated in the following form:

Schedule of moves for observer and light keepers.

Observer.

PRIMARY TRIANGULATION.

35

OBSERVATIONS FOR HORIZONTAL DIRECTIONS.
Two observing parties, under Assistants E. H. Pagenhart and C. V. Hodgson, completed
all of the observations for horizontal directions in one season, extending from the spring to the autumn of 1912. The actual days on which observations for horizontal directions were made are shown in the tables on pages 38 and 39.
Each party was organized practically in the same manner as the observing party of the season of 1908-9 on the Texas-California arc of primary triangulation except that each had a second officer. Assistant C. M. Cade was with Mr. Hodgson during the whole season and for a part of the time conducted a second observing party under his direction. Assistant T. L. Warner was in the party of Mr. Pagenhart from the beginning of the season until September 28, 1912. Besides the chief of party and his assistant, there were in each observing party a teamster and a recorder. They lived in tents and carried a small mess outfit, cooking their food over an open
fire.
Each party had a freight wagon and a light spring wagon, each drawn by two horses or mules, for transporting the instruments and camp equipage from station to station.
A number of the stations occupied by Mr. Hodgson were on mountain peaks to which the
instruments and observing tent were carried by pack animals. This was the case also for several of the stations occupied by Mr. Pagenhart.

GENERAL INSTRUCTIONS TO OBSERVERS ON PRIMARY TRIANGULATION.

There are given below the general instructions to chiefs of the observing parties on primary triangulation, under which practically all of the primary triangulation in the United States has been done in recent years. They were approved by the Superintendent of the United States Coast and Geodetic Survey in 1905, upon the recommendation of Prof. John F. Hayford, at that time inspector of geodetic work in the survey. The general instructions were first printed on pages 170-174 of Appendix 4 of the report for 1911. The observers on the one hundred and fourth meridian triangulation worked under these instructions.
1. Instruments. In general , direction instruments of the highest grade should be used in triangulation of this class.
Repeating theodolites are to be used only when the station to be. occupied is in such a position as to be difficult of occupation with a direction instrument or when there is doubt of the instrument support being of such a character as to insure that the movement of the observer about the instrument does not disturb it in azimuth. Such stations usually occur on lighthouses and buildings.
2. Number of observations Main scheme Direction instrument. In making the measurements of horizontal directions measure each direction in the primary scheme 16 times, a direct and reverse reading being considered one measurement, and 16 positions of the circle are to be used, corresponding approximately to the following readings upon
the initial signal:
Num-
ber.

36

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

adjacent base, is about 1 part in 88 000, and that the actual discrepancy between bases is always less than 1 part in 25 000.

5. Rejections Direction observations. The limit for rejection of observations upon directions in the main scheme

shall be 5 seconds from the mean. No observation agreeing with the mean within this limit is to be rejected unless

the rejection is made at the time of taking the observation and for some other reason than simply that the residual is

A large.

new observation is to be substituted for the rejected one before leaving the station, if possible without much

delay.
6. Number of observations Supplementary stations Direction instrument. In observing upon supplementary stations and in observing from supplementary stations upon stations in the main scheme, four measures of the character
outlined above shall be made of each direction, using the circle in the first four positions stated in that paragraph. A
supplementary station is one which is not in the main scheme, but which is observed upon or from which observations are taken for the purpose of connecting with stations which can not be effectively reached from the stations in the main scheme and with which a connection is required by specific instructions.
7. Number of observations Intersection stations Direction instrument. An intersection station is a station of
which the position is determined by intersections from stations of the main scheme or supplementary stations and which is not occupied. One such measure as is outlined on page 35 shall be made of each direction to each inter-
section station. A second such measure shall be made if it can be secured under conditions nearly as favorable to accuracy as were the conditions when the first measure was made and without much delay to observations in the main
scheme. Each series of observations on intersection stations is to contain some one, and only one, of the main scheme or supplementary stations. It is important to have at least three lines to each intersection station in order to secure
a check, but a possible intersection station should not be neglected simply because only two lines to it can be secured. 8. Observing Supplementary and intersection stations. Observations upon and from supplementary stations
and observations upon intersection stations may be taken under any atmospheric conditions whenever the object to be pointed upon is visible and no delay is likely to be made to secure good seeing before observing.
9. Land section corners and other survey marks. Whenever it is feasible to do so without incurring undue' expense and delay, the section corners established by the United States Land Survey, and survey marks of any kind found upon the ground, shall be connected with the triangulation either by direct measurement of a distance and direction from a station or by using them as intersection stations.
10. Value of intersection stations. In selecting intersection stations it should be kept in mind that the geographic value of a piece of triangulation depends upon the number of points determined, the size of the area over which they are distributed, and the permanence with which they are marked. The geographic value of the triangulation is lost for a given area when points can not be recovered within that area. The chance of permanency is increased by increasing the number of points as well as by thorough marking. These considerations should lead to the determination as intersection stations of many artificial objects of a permanent character, such as lighthouses, church spires, cupolas, towers, and large chimneys; should lead occasionally to the determination of specially marked stations established
for this particular purpose; and should frequently lead to the permanent marking upon the ground of topographic or hydrographic stations and their determination as intersection stations. The practice of permanently marking such hydrographic points as are in commanding positions on promontories, for example and which are so situated that the station is not likely to disappear if permanently marked (on firm ground not likely to be washed away or on rocks), and determining their positions as intersection stations will frequently obviate the necessity which would otherwise exist for new triangulation when a later hydrographic survey is made. It is especially desirable to increase the area effectively covered for geographic purposes by selecting intersection stations which are outside the area covered by
the main scheme.

11. Vertical measures in main scheme. At each station in the main scheme vertical measures are to be made

over all lines in the main scheme radiating from it. These vertical measures should be made on as many days as
possible during the occupation of the station, but in no case should the occupation of the station be prolonged in order to secure such measures. Three measures, each with the telescope in both the direct and the reversed positions, on
each day, are all that are required. These measures may be made at any time between 11.00 a. m. and 4.30 p. m., except that in no case should primary vertical measures bo made within one hour of sunset. It is desirable, however,
with a view of avoiding errors due to diurnal variation of refraction, to have a fixed habit of observing the verticals in the main scheme at a certain hour, as, for example, between 2 and 3 p. m. If tho vertical measures at a station are made by the micrometric method, double zenith distance measures shall be made on at least two of the lines radiating

from that station.

12. Vertical measures Supplementary and intersection stations. In addition to the vertical measures required in the main scheme, vertical measures must be made at each station, whether in the main scheme or supplementary,
over every line of which the horizontal direction is measured. Three measures each with the telescope in both the direct and reverse positions are all that ate required on all lines to or from supplementary or intersection stations, except when the observations upon such stations are made for the purpose of connecting with bench marks of which the elevations are fixed by precise leveling or tidal observations. In the latter case observations should bo made on
as many days as possible during the occupation of the station, but in no case should tho occupation of a station be prolonged in order to obtain measures. Also, in the latter case, the vertical observations are to be made in both directions over every line more than 5 kilometers long, even though horizontal measures may be necessary in but one

direction over the line.

PEIMAEY TEIANGULATION.

37

13. Marking of stations. Every station, whether it is in the main scheme or is a supplementary or intersection

station, which is not in itself a permanent mark, as are lighthouses, church spires, cupolas, towers, large chimneys,

sharp

peaks,

etc. ,

shall

be

marked

in

a

permanent

manner.

At least one reference mark of a permanent character

shall be established not less than 10 meters from each station of the main scheme and accurately referred to it by a

distance and direction. Such reference marks shall preferably be established on fence or property lines, and always

in a localitv chosen to avoid disturbance by cultivation, erosion, or building. It is desirable to establish such refer-

ence marks at all marked stations. At all stations where digging is feasible both underground and surface marks

which are not in contact with each other shall be established. Wood is not to be used in permanent marks.

14. Descriptions of stations. Descriptions shall be furnished of all marked stations. For each station which is

in itself a mark, as are lighthouses, church spires, cupolas, towers, large chimneys, sharp peaks, etc., either a descrip-

tion must be furnished, or the records, lists of directions, and lists of positions must be made to show clearly in con-

nection with each point by special words or phrases if necessary the exact point of the structure or object to which

the horizontal and vertical measures refer. Every land section corner connected with the triangulation must be

fully described. The purpose of the description is to enable one who is unfamiliar with the locality to find the exact

point determined as the station and to know positively that he has found it. Nothing.should be put into the descrip-
tion that does not serve this purpose. A sketch accompanying the description should not be used as a substitute for

words. All essential facts which can be stated in words should be so stated, even though they are also shown in the

sketch.

15. Abstracts and duplicates. The field abstracts of horizontal directions and vertical measures are to be kept

up and checked as the work progresses, and all notes as to eccentricities of signals or instrument, of height of point

observed above ground, etc., which are necessary to enable the computation to be made, are to be incorporated in

the abstracts. As soon as each volume of the original record has been fully abstracted and the abstracts checked, it

A is to be sent to the Office, the corresponding abstracts being retained by the observer.

duplicate of the description

of stations is to be made. If the original descriptions of stations aie written in the record books, a copy of these descrip-
tions compiled in a separate book may be considered the duplicate and should then be marked as such. A duplicate
of the miscellaneous notes mentioned above may also be made if considered desirable. No other duplicates of the

original records are to be made. Pencil originals should not be inked over.

16. Number of observations Main scheme Repeating theodolite. If a repeating theodolite is used for observa-

tions in the main scheme, corresponding to those indicated in paragraph 2, make the observations in sets of six repeti-

tions each. For each angle measured follow each set of six repetitions upon an angle with the telescope in

the direct position immediately by a similar set of six on the explement of the angle with the telescope in the

reversed position. It is not necessary to reverse the telescope during any set of six. Make the total number of sets

of six repetitions on each angle ten five directly on the angle and five on its explement. Measure only the single

angles between adjacent lines of the primary scheme and the angle necessary to close the horizon. With this scheme

of observing no local adjustment is necessary, except to distribute the horizon closure uniformly among the angles

measured. The limit of rejection corresponding to that stated in paragraph 5 shall be for a set of six repetitions 4"

from the mean.

17. Number of observations Supplementary stations Repeating theodolite. If the observations at a supplementary station or upon a supplementary station, corresponding to those indicated in paragraph 6, are made with a repeater,

our sets of six repetitions each should be made, two directly upon each angle with the telescope in the direct position
and two upon its explement with the telescope in the reversed position. No measures introducing station conditions other than closure of horizon are to be made upon or at supplementary stations.

18. Number of observations on intersection stations Repeating theodolite. If the observations upon intersection stations, corresponding to those indicated in paragraph 7, are made with a repeater, two seta of three repetitions each should be made, one directly upon an angle with the telescope in the direct position and one upon its explement with the telescope in the reversed position . Fix the direction to each intersection station by measuring the angle between it and some line in the main scheme or to a supplementary station. No measurements introducing conditions are to

be made.

19. Field computations. The field computations are to be carried to hundredths of seconds in the angles, azimuths, latitudes, and longitudes, and to seven places in the logarithms. The field computation may be stopped with the completion of the lists of directions for all stations and objects, and the triangle side computation for the main scheme and supplementary stations, unless there are special reasons for carrying it further. The computation to this point should be kept up as closely as possible as the work progresses to enable the observer to know that the observations are of the required degree of accuracy. No least square adjustments are to be made in the field. All of the computation, taking of means, etc., which is done in the record books and the lists of directions should be so thoroughly checked by some person other than the one who originally did it as to make it unnecessary to examine it in the Office. The initials of the person making and checking the computations in the record books and the lists of directions should be signed to the record as the computation and checking progress.

METHODS OF OBSERVING EMPLOYED.

All the angle measures were made by the direction method, using the 12-inch (30-centimeter) theodolites which had been made in the Instrument Division of the Survey and which are described on page 30.

38

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The telescope of the theodolite has two parallel vertical wires, about 20 seconds apart, for making the pointings for horizontal angles. The results from a number of seasons' work indicate that this arrangement of the wires in the telescope is more satisfactory than either the single vertical wire or tho oblique cross. The double wire is especially effective when the image of the light or heliotrope is largo and unsteady.
The theodolites used on the one hundred and fourth meridian primary triangulation had two pairs of lines, about four minutes apart, in the micrometer microscope. This arrangement saved much time, for, when a reading backward or forward was made by placing one pair of lines on a five-minute graduation of the circle, then the other pair of lines would have to be moved through the space of only one minute to bring it in contact with a second graduation to make the forward or backward reading.
The readings upon the initial signal were so selected that the mean value of any angle is
practically free from errors due to periodic errors of graduation and is almost entirely free from the effects of the run of the micrometers. However, the micrometer microscopes were adjusted
whenever tests showed that the mean run of the three was more than one second for a five-
minute space or when any one micrometer microscope had a run greater than three seconds.
PROGRAM OF OCCUPATION OF STATIONS, ONE HUNDRED AND FOURTH MERIDIAN.
In the following tables the stations occupied during 1912 by each of the observers are arranged in the chronological order in which the observations were made. The second column indicates the days on which observations on the primary stations were taken, and the third column gives the number of dates at each station on which primary horizontal directions were
observed.
In the party of Mr. Hodgson there was a second observing party in charge of Assistant C. M. Cade, from September 4 to November 24, 1912. During part of this period the first observing party (Mr. Hodgson, observer) was engaged in revising the reconnoissance at the southern end of the scheme and in measuring the Provo base line.
Several stations were reoccupied in order to strengthen the angles of some of the triangles. The reoccupied stations are shown by a reference to a footnote in the tables below.
Mr. Pagenhart's party, working south from the Canadian boundary, suffered no interrup-
tions, as the Ambrose base was measured before observing began. He had only one observing
party under him.
Stations occupied.
Assistant E. H. Paqenhakt, Chief of Party and Observer; Season of 1912.

Station.

Days on which observations of
primary horizontal directions were made.

Total days.

Station.

Days on which observations of
primary horizontal directions were made.

Total days.

Ambrose northeast base. . Ambrose southwest base. Bowie 1
Norge Ambrose
Crosby Stady
Muddy' Howard '
Gladys

May 28, 29 May 29, 31; June 1,3.
June4,5, 17 June 10, 11 June 12
June 13, 15 June 18
June 19, 29 June 20, 21; July 1,2. June 24

Bonetraill .
Marmon . . .

June 27. June 28

Williston..

July 6, 8,9

Bull

July 10,11

Snake

July 12

Bainville.. Lanark

July 13 July 15

Buford

July 17,18,19

>

Montana...

July 20, 22, 23

Mondak . . .

July 24, 25, 27

Ferry
Cut-off.... Jackson...
Lovering. Sheep Flat Trotter... Blue

Assistant E. H. Pasenhart, Chief of Party, Assistant T. L. Warneb, Obsorver; Season of 1912.

July 30
July 31; Aug. 1. Aug. 2, 3, 5
Aug. 6,8,9 Aug. 10, 12 Aug. 13 Aug. 15 Aug. 17, 20, 21..

Cook Hump...
Sentinel. Saddle... Badland. Rainy. . . Black.... Butte....
1 This station was reoccupied.

Aug. 23,24.. Aug. 26 Aug. 29,30..
Sept. 2,3,4. Sept. 6 Sept. 9, 10... Sept. 12 Sept. 16, 17.

PKIMARY TRIANGULATION.

39

Stations occupied Continued . Assistant E. H. Pagenhakt, Chief of Party and Observer; Season of 1912.

Station.

40

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The data in regard to these connections may be found by consulting the index and illus-
trations at the end of the report, and the table of geographic positions and the descriptions which begin on pages 88 and 115, respectively.
The bench marks connected with the one hundred and fourth meridian triangulation for the purpose of controlling the elevations determined by trigonometric leveling are referred to on page 141 and 145, under the heading, "Computation, adjustment, and accuracy of the
elevations."
CONNECTIONS MADE BETWEEN THE THIRTY-NINTH PARALLEL TRIANGULATION AND STATIONS AND MONUMENTS OF OTHER SURVEYS.
The United States Geological Survey, and no doubt other organizations which have carried on surveys in Colorado, Utah, and Nevada, have connected their work with the stations of the thirty-ninth parallel triangulation. At the time the triangulation of the Coast and Geodetic Survey was done in those States, the other organizations of the Government had not carried on very extensive operations in them. Several connections were made, however, between the stations of the thirty-ninth parallel triangulation, at the time they were established, and stations of the United States Geological Survey and the General Land Office. Monuments of the Colorado-Utah and the Utah-Nevada boundaries were also connected with the triangulation. The geographic positions of the stations of other organizations and of the state boundary monuments are given in the table beginning on page 88. The index of stations and the sketches
should also be consulted.
The bench marks connected with the thirty-ninth parallel triangulation for the purpose of controlling the elevations determined by trigonometric leveling are referred to on page 145, under the heading "Computation, adjustment, and accuracy of the elevations."
STATEMENT OF COSTS.
The following table gives a statement of the cost of the triangulation along the one hundred and fourth meridian for each of the two observing parties, and also the cost of the entire work. For comparison and for use in estimating the cost of future work, there are given simdar data for the primary triangulation on the ninety-eighth meridian, done later than 1901, and on the
Texas-California arc.

Name of observer or arc.

PRIMARY TRIANGULATION.

41

The total expenses include the cost of preparing and marking the stations and all salaries,
but not the cost of the reconnoissance.
The cost per mile of progress, which the writer believes is the fairest unit for comparison, is practically the same for the two parties $41 for Mr. Pagenhart and $39 for Mr. Hodgson. In Mr. Pagenhart's party there was only one observer, while in that of Mr. Hodgson's there was one observer for about half the season and two observers for the other half.
The cost per mile of progress is only about 60 per cent of that of the ninety-eighth meridian triangulation after 1901, but it is 25 per cent greater than the cost per mile of the TexasCalifornia arc. The cost of the building on the one hundred and fourth meridian triangulation was much less than that on the ninety-eighth meridian triangulation and only slightly less than the building on the Texas-California arc. The weather conditions on the one hundred and fourth meridian were not so favorable on an average as those ,on the Texas-California arc. Considering the fact that no one of the observers on the one hundred and fourth meridian triangulation had ever done primary triangulation previously, it must be concluded that the work was done in a remarkably rapid and efficient manner. The completion of a continuous arc of primary triangulation 720 miles (1159 kilometers) in length during one summer is an exceptional and noteworthy performance.
There were 8 subsidiary stations occupied by Mr. Pagenhart and 12 such stations occupied by Mr. Hodgson which have not been classed as occupied stations in the above table. At each of these stations the amount of observing was much less than at a primary station, and as a rule the additional time required in traveling for a subsidiary station was not so much as for a primary station. It would seem to be advisable, therefore, to give a weight of onehalf to the subsidiary stations and then obtain the rates of progress and the costs per stations
occupied, which are given below.

Name of observer.

42

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

and fourth meridian triangulation starts from the line Pikes Peak-Divide adjoining the El Paso

base net which had been fully adjusted as reported in Special Publication No. 4, pages 101-114.

The length discrepancies developed in the triangulation along the thirty-ninth parallel

assembled on page 614 of Special Publication No. 4 disclosed the fact that the lengths in the

El Paso base net were too long by 85 in the seventh decimal place of logarithms (one part in

51 000) when compared with the Salt Lake base and also too long by 92 in the seventh decimal

place of logarithms (one part in 47 000) when compared with the Sauna base to the oastward. This not only strengthened the decision to adopt the new measured length for the El Paso base

but also made necessary a readjustment of the triangles in and adjoining the El Paso base net

to distribute this length change without changing the standard positions along the parallel to

the east and west for any very great distance.

It was determined to readjust the triangulation of the thirty-ninth parallel from the line

Arapahoe-Monotony near the Colorado-Kansas boundary to the line Tushar-Mount Nebo of

the Nevada-California series, adjoining the Salt Lake base net. The geodetic positions already

adopted for these two lines were held fixed and by means of one adjustment the 191 conditional

or observation equations relating to the one hundred and fourth meridian were combined with

the

14

equations

of

the

El Paso

base

1
net,

the

28

observation

equations

of

the

Rocky

Mountain

2
series,

27

of

the

observation

equations of the Kansas-Colorado

3
series,

2

azimuth

equations,

1

latitude equation and 1 longitude equation. The last-mentioned two and one of the azimuth

equations were necessary to hold fixed the standard positions at the east and west ends of this

section of the thirty-ninth parallel. The extra azimuth equation was necessitated by the intro-

duction of the Laplace azimuth as the true geodetic azimuth at station Watkins. The total

number of normal equations solved was 264.

Three Laplace azimuths were computed and adopted at stations Watkins astronomic, Provo

astronomic, and Mondak. The introduction of these into the adjustment made two other

azimuth equations necessary.

The fixed lengths in the adjustment were six, viz., the line Arapahoe-Monotony, with its

length

as

adjusted

in

the

thirt3'-ninth

4
parallel;

the El Paso base;

the fine Tushar-Mount Nebo,

with

its

length

as

ajusted

in

the

Nevada

series

of

the

thirty-ninth

5
parallel;

the Cheyenne

base;

the Provo base; and the Ambrose base.

ABSTRACT OF HORIZONTAL DIRECTIONS AND ELEVATION OF TELESCOPE ABOVE THE STATION MARK.

All observed directions in the one hundred and fourth meridian triangulation have been given equal or unit weight. Those directions were reduced to center where either the instrument or the object observed was not coincident with the center of the station mark.
The horizontal directions are all reduced to sea level. The correction expressed in seconds

is given by

e2h sin2<r cos2 <

2 p sin 1"

where = e2

s

,

h = height

of

station

sighted,

= the
,o

radius

of

curvature

in

a

plane

normal

to

the

meridian,

= the
</>

latitude,

and

nr = the

azimuth

counted

from

the

south

westward.

In the following table are also given the elevations of the telescope of the theodolite above

the station mark at each of the primary stations of the one hundred and fourth meridian and

at those primary stations of the thirty-ninth parallel where the data were available. These

elevations enable the reader to judge of the amount of building done and they permit the engi-

neer or surveyor who uses the stations to form an estimate of the probable amount of building

required to make any particular fine clear.

The abstracts of horizontal directions and the condition equations in the thirty-ninth

parallel triangulation are reprinted, but the numbers assigned to the directions were preserved.

The table of corrections to the observed directions enables the reader to compare directly with

the corresponding corrections in the original adjustment.

' See Special Publication No. 4, pp. 110-111. Ibid., pp. 560-563.

' Ibid., pp. 527-539. Ibid., p. 548.

Ibid., p. 591.

PRIMARY TRIANGULATION.

43

Station occupied and elevation of
instrument above
station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjustment.

Station occupied and elevation of instrument above station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjustment.

Arapahoe, 12.08 me-
ters.
Monotony, 12.68 me-
ters.
Cheyenne Wells..
First View, 9.62 me-
ters.
Landsman.
Kit Carson, 2.11 me-
ters.
Eureka, 1.90 meters
Aroya, 1.90 meters.
Overland, 1.75 me-
ters.
Hugo, 1.91 meters...
Adobe, 5.61 meters.
Square Blufls, 1.88 meters.
Holt, 1.83 meters.... Cramer Gulch, 6.22
meters.
Holcolm Hills.

154 First View 155 Cheyenne Wells.
Monotony; McLane Curlew
McLane Curlew Arapahoe First View Cheyenne Wells. Landsman

00 59. 98 33 03 37. 83 60 41 14. 87 106 32 46. 02 158 31 39. 74
00 00.00 27 57 07. 25 66 02 45. 24 135 50 58. 10 147 15 48. 65 163 46 19. 23

Monotony..
Arapahoe. . First View. Landsman .

00 00.08 71 09 20. 69 160 18 22.37 212 27 29. 72

Kit Carson Eureka Landsman
Cheyenne Wells.. Monotony Arapahoe

00 00.06 57 33 37. 39 99 35 36. 20 147 25 30. 46 155 42 18. 79 205 12 52. 89

Monotony Cheyenne Wells.. First View
Kit Carson
Eureka

00 00.05 15 56 56.61 95 57 59. 24 148 12 39. 99 205 13 38. 86

Aroya Overland... Eureka Landsman . First View .
Landsman . First View . Kit Carson. Aroya Overland . . .
Adobe Hugo Overland.. Eureka Kit Carson.
Azimuth mark. 195 Eureka 196 Kit Carson 197 Aroya 198 Adobe 199 Hugo
200 Overland 201 Aroya 202 Adobe 203 Square Bluffs . 204 Holt
Mark 207 Hugo 208 Overland 209 Aroya 205 Cramer Gulch. 206 Square Bluffs .
210 Holt 211 Hugo 212 Adobe 213 Cramer Gulch. 214 Big Springs 215 Holcolm Hills.

00 59793 32 24 48. 48 67 39 53. 21 108 58 51. 12 137 08 34.21
00 59.97 28 42 22. 12 81 40 04.71 137 13 18.52 186 32 02. 17
00 00.08 69 40 19. 90 115 08 24.66 167 53 52. 18 224 40 46. 23
00 00.00 104 10 37. 47 144 03 38. 94 182 06 29. 09 219 50 30. 24 277 58 13. 86
00 59.97 38 40 10. 21 86 51 30. 29 130 05 35. 37 166 31 20.55
00 00.00 4 35 07. 30 39 35 56. 52 66 43 33. 19 254 09 13.06 309 09 14. 59

216 Hugo
217 Square Bluffs. . 218 Holcolm Hills.

219 Big Springs... 220 Square Bluffs. 221 Adobe
Dry Camp
Holt 223 Square Bluffs
20 Big Springs 21 Corral Bluffs 22 El Paso east base. . 23 El Paso west base. 24 Divide
,

Big Springs..

Divide, 1.45 meters.

Pikes Peak, 1.33 meters.

El Paso east base. El Paso west base. . .

37.68 38.68 29.01 30.23 14.00

Corral Bluffs.

59788 11.06 30.08 34.96 20.43

Bison..

Plateau.

Mount Ouray.

Uncompahgre. .

59.29 13.21 27.47 05.37 35.83 58.37 36.31

Tushar..

25 Corral Blufls 26 El Paso east base. 27 Divide 28 Holcolm Hills....
224 Square Bluffs 225 Cramer Gulch
Dry Camp
Plateau Pikes Peak

00 59. 90 27 23 27.38 33 35 42.043 54 4204.94 138 58 19. 89 18803 38.51 235 37 57. 079 279 28 24. 430 344 22 41.480

Holcolm Hills....
BigSprings
E lJPaso east base.
Corral Bluffs El Paso west base Pikes Peak Bison Elbert
Hilltop
Azimuth mark, Mount Rosa.
Plateau
Mount Ouray Mount Elbert Bison Divide BigSprings
Morrison
Hilltop Elbert

000 59.89 3319 29.08 4647 59.79 831411.32 9842 24.44 12659 20.22 16829 32.54 229 0144.02 23046 25.14
00000.00
02412.57 1071136.82 145 46 20. 91 17936 26.33 281 54 23. 84 3190136.65 2114845.82 2474311.09 263 47 48.56

Azimuth mark. . . Holcolm Hills....
Big Springs Corral Bluffs El Paso west base Divide

00000.00 674834.55 14117 47.24 2295710.61 2824801.53 3405834.40

Divide Holcolm Hills El Paso east base. Corral Bluffs Bear Creek Glen Eyrie
E 1 Paso west base
Divide
E 1 Paso east base.
Holcolm Hills
BigSprings Bear Creek Glen Eyrie

00000.14 50 45 56. 49 6955 02.78 14854 53.35 2023337.97 219 44 24.05
00000.01 15 3652.53 480918.10 56 4011.19 11206 29.59 255 15 13. 89 2751841.66

Reference mark. . Pikes Peak Mount Ouray Mount Elbert Divide

00 00.000 8 05 07.647 84 58 58. 452 130 53 06. 876 33153 09.941

Pikes Peak Corral Bluffs
BigSprings
Dry Camp Mount Ouray

00 59. 714 36 49 56. 694 73 43 16.683 9812 57.315 312 14 50. 449

Reference mark . . Azimuth signal... Uncompahgre Treasury Moun-
tain.
Mount Elbert Bison Pikes Peak
Plateau

000 00.000
4 43 02. 772 73 3143.901 134 01 13. 790
169 02 58.555 217 35 12. 159 248 16 47.931 273 44 33. 126

Azimuth mark Mount Ellen Mount Waas
Tavaputs Treasury Moun-
tain.
Mount Elbert Mount Ouray

00 00 000 17 57 20. 789 34 57 59. 822 66 53 01. 218 122 33 55. 882
142 52 07. 746 175 40 48. 333

Beaver Pioche Wheeler Peak
Ibepah
MountNebo Wasatch Mount Ellen

000 00 000
27 52 18 310
%671711.920 32 39. 837 155 33 43. 20! 182 45 10. 509 238 4136.230

00.03 26.88 41.31 05.17 20.46 38.64
"25.'6i 41.04
00.11 28.50 60.56 11.21 25.00 20.33 33.38 43.54 23.81
12.52 36.74 21.86 26.20 23.58 37.08 45.85 10.38 48.40
33.93 48.24 10.28 01.48 34.41
59744 57.17 02.40 53.76
00.09 52.17 17.87 11.22 30.08
50.93
44.54 14.16
48.15 12.56 47.65 32.40
21.30 59.81 01.38 56.00
07.52 47.77
18.40 12.29 39.44 43.20 10.56 37.26

44

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Station occupied and elevation of instrument above
station mark.

Num-
ber o( direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjustment.

Station occupied and elevation of instrument above station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjust-
ment.

Mount Nebo.
Patmos Head. Wasatch. Mount Waas. . Mount Ellen.. Treasury Mountain. Tavaputs. Mount Elbert. Hilltop, 1.34 meters. Indian, 1.10 meters.
Morrison, 1.42 me-
ters. Elbert, 1.38 meters..
Brighton, 1.36 me-
ters.

Azimuth mark. 1'atmosHead.. Wasatch Tushar Wheeler Peak..
Ibepah Pilot Peak Deseret Ogden Peak
Azimuth mark.
Tavaputs Mount Waas... Mount Ellen... Wasatch Mount Nebo. . .

Azimuth mark. .. Mount Nebo Patmos Head Mount Ellen
Tushar

Azimuth mark.. Mount Ellen Patmos Head...
Tavaputs Treasury Mountain Uncompahgre..
Azimuth mark.. . Tushar Wasatch Patmos Head Mount Waas Uncompahgre
Azimuth mark. Mount Elbert.. Mount Ouray . . Uncompahgre.. Mount Waas...
Tavaputs
Azimuth mark... 21 Treasury Moun-
tain.
25 Uncompahgre Mount Waas Patmos Head

Reference mark.. 45 Bison 46 Pikes Peak 47 Mount Ouray 48 Uncompahgre 49 Treasury Moun-
tain.
17 Indian 12 Divide
13 Elbert 14 Pikes Peak
15 Morrison
16 Douglas

25 24a

BWraitghktoinns astro-

nomic.

21 nilltop 22 Douglas 23 Morrison

24 Boulder

26 Boulder

27 Brighton 27a Watkins
nomic.
Indian

astro-

Douglas

Hilltop Elbert
Pikes Peak

Hilltop Divide Pikes Peak. Morrison
Indian Morrison Boulder II orse tooth..
Dewey

41.97 16.61 40.43 45.93 49.37 12.85 29.47 13.83

Watkins astronomic, 3.23 meters.
Warren, 1.27 meters.

01.25 05.08 05.40 46.98 30.22

Dewey, 0.98 meter.

20.99 25.26 19.79 50.53

Horsetooth, 1.36
meters.

34.25 58.92 49.70 22.02 30.86
16.90 53.79 51.24 14.96 08.65

Boulder, 1.26 meters Douglas, 1.40 meters Ragged, 1.40 meters

55.70 22.77 26.93 07.08 27.78

Wadill, 1.38 meters.

24b Indian . . . 24c Morrison. 24d Boulder..

61 Twin
62 Russell 63 Wadill
59 Dewey
60 Horsetooth..

00 59.97 27 11 38.16 68 54 53.96 239 23 26.51 291 59 14.69

45 Horsetooth..
46 Twin 47 Warren
43 Brighton 44 Boulder

00 59798 41 11 10.44 61 06 10.73 283 57 46.45 312 17 14.36

50 Dewey
51 Brighton 52 Boulder
48 Twin
49 W'arren

00 59.99 52 59 00.94 93 51 37.90 260 21 54.73 293 41 48.62

Horsetooth

00 00.04
,

34 Dewey

38 25 45.65

35 Brighton

73 16 02.22

35a Watkins astro- 104 24 42.78

nomic.

36 Indian

111 31 36.80

37 Morrison

161 17 19.55

20 Indian... 18 Hilltop... 19 Morrison .
Whi taker
Wadill Greentop Notch Chugwater

00 00.09
141 16 23. 19
264 00 04.64 ~~
000
23 39
74 41
262 30
294 23

Greentop Ragged
Whi taker Warren Twin
Russell
Cheyenne west
base.
69b Cheyenne east

59 03 18.14

H. sy 19.74 15.37
59.69 37.95 53.71 27.35 14.57
00.79 10.32 09.72 45.99 15.15
59.59 01.04 38.12 55.31 48.13
00.30 45.08 01.27 43.94
36.61 19.82
59796 23.54 04.41
59782 47.98 55.11 14.31 51.82
59.61 38.30 19.78 02.35 14.23 33.51 52.65
17.90

! 32. 17 120.17
02. 77 I 48.31 ! 16.56

Greentop, 1.28 me-
ters.
Russell, 1.30 meters
Twin, 1.42 meters...
Cheyenne west base, 1.44 meters.
Cheyenne east base, 1.44 meters.
Haystack, 122 me-
ters.
Coleman, 1.31 me-
ters.
Notch, 1.42 meters.

76 Wadill....
77 Twin
78 Russell
74 Ragged . . . 75 Whitaker.

70 Greentop. . 71 Wadill....
72 Warren . . . 73 Twin

00 59. 98 91 03 54. 17 127 06 08.19 173 13 00.65

58 Horsetooth.
53 Russell 54 Greentop... 55 Wadill
56 Warren 57 Dewey

00 59.97 174 39 01. 24 177 10 29. 96 234 59 37.06 281 20 33. 34 320 49 06.91

430 Whitaker
431 Cheyenne
base. Wadill

east

00 00.04 89 53 02.02
107 42 25.25

435 Wadill

00 00.20

433 Cheyenne west 120 10 12.51

base.

434 Will taker

180 38 03. 19

101 Coleman . . . 102 Willow 103 Hobbs 104 Rawhide. . .
99 Chugwater. 100 Notch

107 Haystack . . 108 Chugwater. 109 Notch
105 Willow
106 Hobbs

Chugwater.
N Whi taker..
Ragged Coleman . . .
Haystack..

511.07 08.66 40.01 44.13 25.07
59795 53.89 09.00 00.18
00.35 01.22 29.72 37.28 33.53 06.41
00.21 02.14
24.96
00.26 12.23
03.42
00.09 07.33 03.93 16.36 05.77 07.85
59740 15.92 05.29 27.55 22.18
59751 37.01 22.03 31.02 36.72

PRIMARY TRIANGULATION.

45

Station occupied and elevation of instrument above
station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjustment.

Station occupied and elevation of
instrument above
station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjust-
ment.

Chugwater, 1.41 me-
ters.
Whitaker, 1.38 me-
ters.

Notch. Coleman
Haystack Whitaker
Ragged

00 59. 85 36 24 45. 62 71 39 42.03 219 21 18.01 256 19 55.49

80 Greentop

00 00.06

81 Ragged

19 32 24. 87

82 Notch

79 26 58.96

83 Chugwater
79 WadM

96 57 42.36 269 19 52.31

79a Cheyenne east 269 26 54. 72

base.

79b Cheyenne west 299 06 01. 98

Hobbs, 1.32 meters. .
Rawhide, 1.46 me-
ters.
Willow. 1.42 meters.
Manviue, 1.37 me-
ters.
Kirtley, 1.28 meters
Cottonwood, 1.33 meters.
Sullivan, 1.37 me-
ters.
Provo east base, 9.70 meters.
Provo astronomic, 1.35 meters.
Provo west base, 4 14 meters.
Parker, 1.33 meters.
Alkali, 1.41 meters.

110 Haystack. 111 Coleman..
112 Willow.... 113 Rawhide. .

00 00.03 53 10 21. 77 142 26 35. 12 256 16 37. 78

116 Willow.... 117 Manville..
118 Kirtley... 114 Haystack . 115 Hobbs....

00 59.89 38 OS 35.01 98 00 51.88 255 11 35. 13 316 53 58.85

119 Manville..
120 Kirtley . . . 121 Rawhide- .
122 Hobbs
123 Haystack. 124 Coleman . .

00 00.07 45 50 57. 05 107 04 41. 10 130 08 38. 74 155 25 07. 50 205 49 33. 21

126 Kirtley . . . 127 Rawhide128 Willow... 129 Alkali 125 Parker

00 00.01 78 31 22.84 113 18 06.68 277 07 28.80 321 46 21. 80

134 Rawhide. 130 Willow... 131 Manville.
132 Alkali.... 133 Parker...

00 00.11 20 45 26. 12 41 36 25. 18 113 38 26. 69 162 36 37. 49

153 Sullivan

00 00.04

154 Parker

52 03 21.60

155 Provo east base. . 88 42 55.29

156 Provo astronomic 94 16 19.06

157 Provo west base.. 108 56 44. 65

152 Alkali

311 53 38.06

172 Alkali 173 Elk 170 Parker 171 Cottonwood.

00 59798 68 27 42.52 213 03 56. 23 274 41 18.98

169 Parker

00 00.03

166 Provo west base.. 245 27 12. 79

167 Provo astronomic 251 21 54.32

168 Cottonwood

269 55 51. 79

164 Parker 165 Provoeastbase.. 162 Provo west base. 163 Cottonwood

00 00. 07 56 03 54.33 224 42 18. 72 260 11 14.61

160 Provo astronomic

00 00.04

161 Provo east base . . .

5 26 53. 74

158 Cottonwood

230 09 21.21

159 Parker

325 13 07.02

140 Cottonwood

00 00.06

141 Alkali

48 18 44.86

142 Sullivan 143 Elk

, 66 19 17. 29 77 26 37. 90

135 Provoeastbase... 306 43 40. 20

136 Provo astronomic 322 01 40.61

137 Kirtley

325 03 35. 88

138 Provo west base.. 331 57 05. 13

139 Manville

345 49 50. 78

144 Inyankara... 145 Cambria 146 Elk 147 Sullivan
148 Parker 149 Cottonwood.
150 Kirtley 151 Manville

00 00.04 17 37 42.20 64 05 41. 19 87 18 25.96 102 21 52.04 133 53 28. 96 150 08 45. 09 175 14 18.77

00.12 45.72 41.21 18.11 55.86

Elk, 1.40 meters

Alkali
Cambria Crow Parker
Sullivan

00.70 24.59 59.02 42.13 53.07 54.35

Cambria, 1.24 meters

01.43 Crow, 19.28 meters .

182 Inyankara... 183 Laird
184 Crow 185 Elk
186 Alkali
180 Cambria 181 Laird 179 Elk

Laird, 1.19 meters..

188 Cambria
189 Inyankara... 190 Sundance. ..
191 Terry 187 Crow

Inyankara, 1.42 me-
ters.

192 Sundance...
193 Terry 194 Laird 195 Cambria 196 Alkali

Terry, 1.52 meters...

199 200 .201

Laird
Inyankara... Sundance...
Wymonkota
Castle

Sundance, 1.37 me-
ters.

208 Inyankara...
202 Wymonkota
203 Castle
204 Terry 205 Laird

Castle, 1.32 meters .

210 Harding 211 Moreau 212 Reva
207 Terry 208 Sundance . . .
209 Wymonkota

Table, 1.31 meters.

233 Butte 234 Whetstone.. 235 Lodge 236 Reva 237 Harding I...

Reva, 1.27 meters.

232 Lodge 228 Castle 229 Moreau
230 Harding 231 Table

Harding, 1.38 me-
ters.
Moreau, 1.30 meters.

218 Table 219 Lodge 220 Reva 221 Moreau 222 Castle
223 Wymonkota
227 Reva
224 Castle
225 Wymonkota
226 Harding

Wymonkota, 1.44
meters.

213 Harding 214 Moreau
215 Castle
216 Terry 217 Sundance...

Lodge, 1.28 meters..

238 Reva
239 Harding 240 Table 241 Butte 242 Whetstone..

Whetstone, 1.05 me-
ters.

248 Lodge 249 Table 250 Butte 251 Black
252 Rainy

00 00.04 87 45 17. 78 116 49 38.08 247 24 02.20 271 40 27.31
00 59790 72 54 00. 28 120 20 22. 73 195 31 11.22 241 17 58.26
00 00. 01 81 10 47. 84 284 15 07. 14
00 00.00 51 41 47.47 91 10 54. 64 187 07 35. 74 308 37 11. 74
00 59794 87 51 00.08 105 57 00. 82 161 21 15.42 205 01 33. 54
00 00. 12 26 28 14.73 62 38 02. 19 118 54 04. 12 155 05 17. 13
00 59794" 221 18 22. 86 248 10 28.02 304 00 44.73 325 26 05.38
00 59.93 11 24 39.43 56 41 33.52 241 59 15.90 273 41 55.01 310 18 33.07
00 00.05 24 55 31. 84 64 48 04.49 104 14 39. 12 165 58 52. 50
00 00.03 177 38 48.71 217 22 55. 84 227 14 20.30 296 30 26. 21

00.45 17.79 38.31 01.68 27.17
00.26 59. 69 22.90 11.15 58.38
59783 48.25 06.91
00.54 47.75 54.82 35.13 11.35
59796 00.68 00.39 15.03 33.75
00.61 14.44 02.02 04.11 17.12
59790 22.99 27.81 44.86 05.36
ooToo 39.28 33.35 16.12 54.70 33.43
59772 31.60 04.53 39.75 52.41
00.70 48.83 55.82 19.95 25.80

00 00.03 32 26 17. 99 48 59 48. 17 85 01 09.45 122 42 50.92 184 34 52.02

00.01
18.11. 48.24 09.20 51.13 51.88

00 00.06 94 59 04. 10 162 04 59.95 225 52 43.78

00.05 04.05 59.84 43.96

00 00.04 16 38 34.51 68 26 38. 10 143 56 17.40 184 58 01.48

00.11 34.79 37.84 17.10 01.71

00 00.04 30 40 51.22 77 03 52.92 129 20 40. 16 173 26 34. 75

59716 51.73 52.65 40.61 34.94

00 00.02 43 44 48.93 74 24 24. 44 104 44 11.74 156 09 28. 72

59772 49.30 24.68 11.84 28.30

46

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Station occupied and elevation of instrument above
station mark.

Num-
ber of direction.

Object observed.

Observed direction .reduced to
si>;\ level.

Final seconds
after
figure adjust-
ment.

Station occupied and elevation of
instrument above
station mark.

Num-
ber of direction.

Object observed.

Olwrad
(liriM'tion
reduced to sea level.

Final
MMOda
after
figure
adjustment.

Butte, 1.19 meters. .

243 Black
244 Rainy 245 Whetstone.
248 Lodge 247 Table

Black, 1.15 meters.

257 Butte
253 Sentinel 254 Badland . . .
255 Rainy 256 Whetstone.

Rainy, 1.08 meters..

258 Whetstone. 259 Butte 260 Black 261 Sentinel 262 Badland... 263 Saddle

Badland, 1.22 me-
ters.

264 Rainy 265 Black...
266 Sentinel. 267 Saddle..

Sentinel, 1.20 me-
ters.

274 Cook
275 Hump . . .
276 Saddle... 277 Badland.
278 Rainy 279 Black....
273 Blue

Saddle, 1.28 meters. .
Hump, 1.22 meters.

272 Cook 268 Rainy 269 Badland . 270 Sentinel.. 271 Hump...
282 Cook 283 Saddle.. 280 Sentinel.. 281 Blue

Cook, 1.21 meters..

Hump...
Sentinel..
Blue
Trotter... Flat Saddle...

Blue, 1.29 meters.. Flat, 1.33 meters.. Trotter, 1.26 meters

292 Flat 293 Trotter... 294 Cook
295 Hump
296 Sentinel.. 290 Lovering.
291 Sheep
300 Cook
301 Trotter...
302 Blue 303 Lovering. 304 Sheep
299 Cook 297 Blue 298 Flat

Lovering, 1.23 me-
ters.

305 Jackson. 306 Buford.. 307 308 Flat.. 309 Blue.

Sheep, 1.17 meters..

310 311 312 313 313a 314

Flat Blue
Lovering. Jackson.. Montana . Buford. . .

Jackson, 1.30 me-
ters.

330 Lovering 323 Snake 325 Lanark
324 Bainville 326 Cutoff
327 Montana 328 Buford
329 Sheep

00 59.98 52 25 12.90 98 56 10.07 160 25 54.94 223 21 05.67
000 59798
162 54 13. 57 206 49 32. 60 263 20 52.96 309 15 57.14
00 59.98 51 44 02.26 82 39 44. 04 135 50 82.53 146 15 40. 61 176 00 05. 90
00 59.95 59 52 45. 90 161 44 44. 10 239 21 03.45
00 00.02 3 38 41.07 61 19 00. 66 102 47 22. 58 110 37 51.39 137 00 08. 21 316 08 09.11
00 59797 227 58 11.52 257 34 54.46 318 30 15.01 329 06 21.73
00 00.02 73 24 55. 15 185 08 30.31 308 28 04. 85
00 00. 02 1 29 48. 36 97 01 11.35 139 34 02. 53 150 43 32. 73 284 18 30.03
00 59.97 102 54 07. 79 208 09 05. 79
00 00. 01 31 45 16.96 96 55 04.02 124 33 05. 20 159 10 11.87
00 00.02 20 50 43.31 89 01 49. 76 116 21 25.84 143 16 34.09 149 46 28.06
00 00.01 192 48 26.90 194 56 01.34
1% 07 40.19
' 232 13 53.60 235 36 26. 65 237 32 30.81 304 14 39. 43

Buford, 1.24 meters.

317 Jackson... 318 Muntima.. 319 Bainville.. 320 Snake 321 Bull 322 Williston.
315 Sheep 316 Lovering. .

Cutoff, 0.98 meter...

348 Jackson... 349 Lanark 350 Montana.. 351 Mondak...
352 Ferry

362 Montana..
Mondak, 1.25meters. { 360 Ferry 361 Cutoff

Ferry, 0.28 meter....

363 Cutofl
364 Montana.. 365 Mondak. . .

Montana, 1.18 me-
ters.
Bainville, 1.30 me-
ters.

357 Jackson... 358 Cutoff 359 Lanark 353 Buford... 354 Sheep 355 Mondak... 356 Ferry
342 Snake
343 Buford... 344 Jackson..

Lanark, 1.09 meters.

347 Jackson . . 345 Montana . . 346 Cutoff

Bull, 1.32 meters

368 Will iston. 369 Buford....
366 Gladys.... 367 Bonetraill 370 Snake

Snake, 1.25 meters.

331 Bull 332 Williston. 333 Buford.... 334 Bainville., 335 Jackson...

Wflliston, ters.

341 Marmon.. 336 Buford.... 337 Snake 338 Bull
339 Gladys.... 340 Bonetraill.

Bonetraill, 1.27 me-
ters.
Gladys, 1.40 meters.

374 Marmon..
371 Williston. 372 Bull 373 Gladys....
375 Howard... 376 Muddy... 377 Marmon.. 378 Bonetraill 379 Williston. 380 Bull

Marmon, 1.28 meters

381 Williston. 382 Bonetraill
383 Gladys... 384 Howard..
385 Muddy...

Muddy, 1.42 meters

386 Marmon..
387 Gladys. . . 388 Howard..
389 Stady.... 390 Crosby...

Howard, 9.27 meters

391 Norge 392 Stady.... 393 Crosby... 394 Muddy... 395 Marmon..
396 Gladys. . .

00 00.03 8 20 03.62 76 25 16. 46 87 36 54.68 110 53 52.67 154 10 39.52 280 07 05.91 334 12 44. 71
00 00.07 100 20 36.34 188 41 28.57 208 37 31.54 231 02 19.22
00 59799 223 14 56.04 274 20 C7. 65
00 59798 86 11 44.09 106 30 01.43
00 00.03 5 18 56.35 61 10 17.19 190 16 08.24 275 33 17.26 290 54 53. 26 313 51 32.05
00 00.01 135 12 00. 52 197 21 53.35
00 00.02 281 50 43. 73 317 38 29. 23
000 59797
59 45 10.05 287 55 21.16 305 24 33. 83 116 48 35.36
00 00.04 41 09 48.35 99 39 37. 74 133 16 01.06 147 18 39.80
00 00.03 186 31 01.72 241 27 31.02 263 29 08. 16 304 26 15. 67 311 29 24.32
00 00. 01 85 29 01.71 162 53 21.03 231 51 54.47
00 00. 01 30 47 24. 37 74 25 24. 06 116 10 34. 78 142 44 33. 99 209 42 46. 29
00 00.03 46 00 24. 56 56 07 07. 62 106 24 04. 09 150 14 28. 56
000 00.00
42 14 39.76 77 24 40.43 153 08 10.50 179 45 31.34
00 00.01 32 50 36.22 33 25 50.64 73 30 37.30 132 15 32.90 187 33 13.58

00.04 03.44 17.08 54.78 52.71 39.05 05.73 44.81
59.62 36.12 28.55 31.97 19.47
00.40 56.16 07.13
59777 44.36 01.36
59792 56.29 17.85 08.28 17.48 52.91 31.69
00.45 59.99 53.43
00.47 43.10 29.41
00.41 09.81 20.79 34.06 35.32
00.19 48.49 37.65 00.71 39.97
59798 02.23 30.65 08.11 15.56 24. 4 J
00.29 02.04 20.21 54.66
59.94 24.20 24.19 34.67 33.34 47.17
00.15 23.79 07.89 04.28 28.73
59.64 40.24 40.57 10.03 31.53
00.02 36.49 50.55 37. 13 32.91 13.53

PRIMARY TRIANGTJLATION.

47

Station occupied and elevation of
instrument above
station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjustment.

Station occupied and elevation of instrument above station mark.

Num-
ber of direction.

Object observed.

Observed direction reduced to sea level.

Final seconds
after
figure adjust-
ment.

399 Norge

Stady, 1.37 meters..

400 Crosoy
397 Muddy

'.

Howard

00 59. 97 81 25 15. 10 195 58 20. 42 259 36 51. 57

Crosby, 9.25 meters.

403 Stady

00 00.03

404 Norge

63 16 36. 70

405 Bowie

100 48 59. 14

406 Ambrose south- 117 35 01.79

west base.

407 Ambrose

168 04 59. 73

401 Muddy 402 Howard

321 12 26.24 358 46 49. 88

Norge ,6.35 meters .

418 Stady 419 Howard 415 Bowie 416 Ambrose south-
west base.
417 Crosby

00 59797 46 46 16. 05 241 13 49. 88 284 52 32. 85
324 41 52. 95

59.60 15.40 20.74 51.32

Ambrose, 1.35 me-
ters.

59.71 36.48 59.43 02.34

Bowie, 1.27 meters.

59.65 26.22 49.67

School, 1.15 meters.

00.20 16.27 49.39 33.48
52.37

Ambrose southwest
base, 9.25 meters.

Ambrose southwest base.
410 Bowie 411 School 408 Crosby
420 School 421 Ambrose 422 Ambrose south
west base.

56 35. 24 74 02 54. 17 267 48 51. 92
00 00.00 27 36 38. 57 28 25 26. 13

414 Bowie 412 Ambrose 413 Ambrose south-
west base.

00 00.00 280 42 56. 81 332 59 22. 94

425 School 426 Ambrose
427 Crosby 428 Norge 429 Bowie

00 00.02 53 40 38. 69 90 59 32. 76 176 51 47.79 235 26 00. 16

35.31 54.04 51.67
59.64 38.84 26.05
58.96 56.50 24.29
59.71 38.33 32.57 48.22 00.57

CONDITION EQUATIONS.
ONE HUNDRED AND FOURTH MERIDIAN.
No.
1. 0=+1.82-(2)+(4)-(5)+(7)-(12)+(14)
2. 0= -0.81 -(6)+(7)+(8) -(11) -(12)+(13)
3. 0=+0.70-(3)+(4)-(5)+(6)-(8)+(9) 4. 0=+2.87-(10)+(ll)-(13)+(15)-(30)+(31) 5. 0=-0.33-(l)+(3)-(9)+(10)-(31)+(32) 6. 0=+0.38-(15)+(17)-(21)+(23)-(28)+(30) 7. 0=-0.85-(19)+(20)-(22)+(23)-(28)+(29) 8. 0=+0.61-(16)+(17)+(18)-(20)-(21)+(22) 9. 0=-0.62-(23)+(24)-(26)+(28)-(36)+(37)
10. 0= -0.05 -(23) +(25) -(27)+(28) -(38) +(39) 11.0= -0.96 -(26) +(27) - (35) +(37) - (39) +(40)
12. 0=-1.80-(41)+(42)-(43)+(45)-(50)+(51) 13. 0=+0.19-(33)+(34)-(44)+(45)-(50)+(52) 14. 0= 0.99-(34)+(35)-(40)+(42)-(43)+(44) 15. 0=+1.03-(45)+(46)-(48)+(50)-(57)+(58)
16. 0= +2.70 -(46) +(47) - (56) +(57) - (59) +(61)
17. 0=+1.04-(48)+(49)-(56)+(58)-(60)+(61) 18. 0=-O.33-(55)+(56)-(61)+(63)-(64)+(65)
19. 0= -0.02 - (53) +(55) -(65) +(66) -(71) +(73)
20. 0=+1.00-(53)+(56)-(61)+(62)-(72)+(73) 21. 0=-2.20-(54)+(55)-(65)+(67)-(76)+(77)
22. 0= -0.12 -(66)+(67) -(70)+(71) -(76)+(78)
23. 0=-r0.55-(67)+(68)-(74)+(76)-(87)+(88) 24. 0=+1.36-(68)+(69)-(79)+(81)-(86)+(87) 25. 0=-0.34-(74)+(75)-(80)+(81)-(86)+(88) 26. 0=-0.62-(81)+(83)-(85)+(86)-(89)+(90) 27. 0=-0.07-(82)+(83)-(89)+(91)-(96)+(97)
28. 0= -0.41 -(84) +(85) - (90) +(91) -(96) +(98)
29. 0=+0.52-(91)+(92)-(94)+(96)-(108)+(109) 30. 0=+0.62-(92)+(93)-(99)+(101)-(107)+(108) 31. 0=-0.79-(94)+(95)-(100)+(101)-(107)+(l(W) 32. 0=+1.00-(101)+(102)-(105)+(107)-(123)+(124) 33. 0=-0.52-(102)+(104)-(114)+(116)-(121)+(123) 34. 0=+2.06-(101)+(103)-(106)+(107)-(110)+(111) 35. 0=-0.74-(105)+(106)-(lll)+(112)-(122)+(124) 36. 0=+1.10-(112)+(113)-(115)+(116)-(121)+(122) 37. 0=-0.25-(116)+(117)-(119)+(121)-(127)+(128) 38. 0=+L24-(117)+(118)-(126)+(127)+(131)-(134) 39. 0=+0.05-(116)+(118)-(120)+(121)+(130)-(134)

48

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

No.
40. 0=-2.;:5+(126)-(]29)-(131)+(132)-(150)+(151) 41. 0=-0.39-(125)+(126)-(131)+(133)-(137)+(139) 42. 0=+0.86-(132)+(133)-(137)+(141)-(148)+(15:>) 43. 0=+0.39-(140)+(141)-(148)+(149)-(152)+(154) 44. 0=+2.42-(138)+(140)-(154)+(157)-(158)+(159) 45. 0=+0.44-(155)+(157)-(15S)+(16])-(166)+(168) 46. 0=+0.13-(135)+(140)-(154)+(155)-(168)+(169) 47. 0=+0.92-(136)+(140)-(154)+(156)-(163)+(164) 48. 0=+0.01-(135)+(136)-(164)+(165)-(167)+(169)
49. = -0.41-(160)+(161)+(162)-(165)-(166)+(167)
50. 0=-].31-(140)+(142)-(153)+(154)-(170)+(171) 51. 0=+2.15-(147)+(149)-(152)+(153)-(171)+(172) 52. 0=-2.28-(141)+(143)-(146)+(148)-(174)+(176) 53. 0=-1.33-(142)+(143)+(170)-(173)-(174)+(175) 54. 0=+96.5+7.31(2)-13.75(3)+6.44(4)-0.45(5)-68.67(6)+69.12(7)-92.35(12)-94.80(13)+2.45(14) 55. 0=-9.4+2.91(l)-10.22(2)+7.31(3)-1.38(9)-3.02(10)+4.40(ll)+6.21(30)-7.68(31)+i.47(32) 56. 0=+15.8+1.73(15)-5.91(16)+4.18(17)+9.93(21)-10.84(22)+0.91(23)+6.70(28)-24.6(29)+17. 98(30) 57. 0=+4.7+4.04(23)-6.46(24)+2.42(25)+1.90(26)-1.42(27)-0.48(28)-0.40(38)-2.90(39)+3.30(40) 58. 0=+5.1+0.63(33)-3.03(34)+2.40(35)+3.39(43)-3.91(44)+0.52(45)+1.59(50)-4.02(51)+2.43(52) 59. 0=-2.3+1.16(45)-5.81(46)+4.65(47)+3.20(48)-4.12(49)+0.92(50)+2.14(56)-2.56(57)+0.42(58) 60. 0=-6.9-1.20(53)+3.21(55)-2.01(56)-4.10(61)+6.46(62)-2.36(63)-0.99(64)+3.73(65)-2.74(66)-2.89(71)
+4.92(72) -2.03(73) 61. 0=-31.0-46.55(53)+47.75(54)-1.20(55)-2.74(65)+7.85(66)-5.11(67)-0.91(76)+28.28(77)-27.37(78) 62. 0=+12.0+7.57(67)-8.81(68)+1.24(69)-0.02(79)-5.91(80)+5.93(81)+0.58(86)-1.70(87)+l. 12(88) 63. 0=-0.2+0.47(81)-6.67(82)+6.20(83)+3.38(84)-4.33(85)+0.95(86)+3.10(96)-5.25(97)+2.15(98) 64. 0=+1.6-2.15(91)+2.85(92)-0.70(93)-3.48(99)+6.56(100)-3.08(101)+0.83(107)+3.34(108)-4.17(109) 65. 0=+0.2+9.67(102)-17.77(103)+8.10(104)+1.13(]14)-3.38(115)+2.25(116)+4.94(121)-9.40(122)+4.46(123). 66. 0=+23.5-0.16(101)-9.67(102)+9.83(103)+7.83(105)-11.14(106)+3.31(107)+3.92(122)-4.46(123)+0.54(124) 67. 0=-5.5+2.98(116)-2.68(117)-0.30(118)-0.91(126)-3.03(127)+3.94(128)-11.09(130)+5.53(131)+5.56(134) 68. 0=-14.3-2.67(125)+2.41(126)+0.26(129)+5.30(137)-5.55(139)+0.25(141)+1.91(148)-6.41(150)+4.50(151) 69. 0=+19.6+4.47(135)-8.42(138)+3.95(140)+2.83(154)-8.54(155)+5.71(157)-0.19(158)-2.30(159)+2.49(161)
+4.62(166) -4.62(168) 70. 0=+53.5+21.65(155)-29.69(156)+8.04(157)-1.76(158)-20.31(160)+22.07(161)+20.34(166)-26.61(167)+6.27(168) 71. 0=+40.2+7.70(135)-19.73(136)+12.03(138)+3.03(159)-25.10(160)+22.07(161)+20.34(166)-19.63(167)-0.71(169) 72. O=+7.2+0.92(140)-6.48(141)+5.56(142)+5.84(147)-7.83(148)+1.99(149)+1.89(152)-3.53(153)+1.64(154) 73. 0=+15.4-6.48(141)+17.19(142)-10.71(143)-4.91(146)+12.74(147)-7.83(148)-4.67(174)+4.73(175)-0.06(176) 74. 0=+18.0-0.05(2)+0.05(3)-0.41(8)+0.41(9)+1.88(10)-1.88(12)+0.24(11)-0.24(14)+1.77(16)-1.77(18)
+4.06(25)-4.06(26)+1.82(27)-2.78(54)-1.82(67)-2.91(l)+2.91(2)+2.78(4)+0.52(5)-0.52(7)+2.34(12)
-2.34(14)-0.47(17)+0.43(21)-0.43(23)-2.42(24)+2.42(25)+0.48(26)-0.48(28)+1.47(30)-1.47(32)-0.63(33)
+0.63(35)+1.78(36)-1.78(37)-0.40(38)+0.40(40)-1.71(41)+1.71(42)+0.52(43)-1.68(45)+1.16(47)-3.20(48)
+3.20(49)+2.43(51)-2.43(52)-1.32(54)+1.32(55)+0.42(56)-0.42(58)+1.61(59)-1.61(60)-0.81(61)+0.81(63)
+0.99(64)-0.99(65)-3.68(75)+4.79(76)-l.ll(77)-0.02(79)+0.02(80)-3.70(79a)+3.70(79b)-2.30(69a)
+2.30(69)+1.19(433)-1.19(434)-0.67(430)+0.67(432) 75. 0=+0.32-(145)+(146)-(176)+(177)-(185)+(186) 76. 0*=-0.03-(177)+(178)-(179)+(180)-(184)+(185) 77. 0=-2.28-(180)+(181)-(183)+(184)-(187)+(188) 78. 0=-0.63-(144)+(145)+(182)-(186)-(195)+(196) 79. 0=+2.70-(189)+(191)-(193)+(194)-(197)+(198) 80. 0=+0.57-(189)+(190)-(192)+(194)-(205)+(206) 81. 0=-0.53-(192)+(193)-(198)+(199)-(204)+(206) 82. 0=+1.17-(182)+(183)-(188)+(189)-(194)+(195) 83. 0=+0.03-(199)+(201)-(203)+(204)-(207)+(208) 84. 0=-0.69-(199)+(200)-(202)+(204)-(216)+(21-) 85. 0=-0.82-(202)+(203)-(208)+(209)-(215)+(217) 86. 0=+0.97-(209)+(210)-(213)+(215)-(222)+(223) 87. 0=+l.ll-(209)+(211)-(214)+(215)-(224)+(225) 88. 0=-0.47-(210)+(211)-(221)+(222)-(224)+(226) 89. 0=+0.57-(210)+(212)-(220)+(222)-(228)+(230) 90. 0=+0.84-(220)+(221)-(226)+(227)-(229)+(230) 91. 0=+0.69-(218)+(220)-(230)+(231)-(236)+(237) 92. 0=-2.36-(219)+(220)-(230)+(232)-(238)+(239)

PEIMABY TBIANGULATION.

49

No.
93. 0= -2.28 - (231) +(232) - (235) +(236) - (238) +(240)

50

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

No. 154. 0=+3.60-0.60(192)-6.44(193)4-7.04(194)+3.14(197)-4.23(198)+1.09(199)+5.37(204)-8.43(205)+3.06(206) 155. 0=-3.00+1.41(199)-4.29(200)+2.88(201)+3.89(202)-4.16(203)+0.27(204)+0.84(207)-2.83(208)+1.99(209) 156. 0=+5.40+1.16(209)-10.43(210)+9.27(211)+7.04(213)-8.70(214)+1.66(215)+3.07(221)-2.72(222)-0.35(223) 157. 0=-0.90+10.43(210)-12.51(211)+2.08(212)+2.90(220)-5.62(221)+2.72(222)+2.53(228)-14.65(229)
+12.12(230) 158. 0=+8.50+3.31(218)-10.39(219)+7.08(220)+0.80(230)-1.85(231)+1.05(232)+2.56(235)-3.69(236)+1.13(237)
+3.55(238) -5.56(239) +2.01(240) 159. 0=+2.60+3.54(233)-4.53(234)+0.99(235)+1.63(240)-3.80(241)+2.17(242)+0.59(248)-3.55(249)+2.96(250) 160. 0=-3.00+1.95(243)-1.62(244)-0.33(245)+3.60(250)-5.28(251)+1.68(252)+0.27(258)-3.51(259)+3.24(260) 161. 0=-1.5-2.19(253)+3.58(254)-1.39(255)-1.58(260)+13.04(261)-11.46(262)-1.22(264)+0.78(265)+0.44(266)
-15.29(277)+19.54(278) -4.25(279) 162. O=+6.20+11.46(261)-15.15(262)+3.69(263)+3.70(268)-4.87(269)+1.17(270)+2.38(276)-17.67(277)
+15.29(278) 163. 0=-7.10+11.25(270)-14.77(271)+3.52(272)+33.05(274)-34.38(275)+1.33(276)+0.54(284)-81.13(285)
+80.59(286) 164. 0=-25.70-1.93(273)+33.05(274)-31.12(275)-80.85(285)+80.59(286)+0.26(287)-3.44(294)+16.49(295)
-13.05(296) 165. 0=-4.30+2.29(287)-12.96(288)+10.67(289)+4.50(292)-7.56(293)+3.06(294)+6.89(300)-8.68(301)+1.79(302) 166. 0=-1.50+0.99(290)-7.73(291)+6.74(292)+4.02(307)-7.07(308)+3.03(309)+5.49(310)-5.53(311)+0.04(312) 167. 0=+7.80+3.66(305)-3.40(306)-0.26(307)+4.07(312)-7.26(313)+3.19(314)+0.38(315)-4.36(316)+3.98(317)
168. 0= +58.4+4.15(313) -22.63(313a) +18.48(314) +0.07(315) - 14.36(317) +14.29(318) +61.52(327) -62.34(328)
+0.82(329) 169. 0=+4.45-(136)+(143)-(162)+(164)-(174)+(178)-(179)+(181)-(187)+(191)-(197)+(201)-(207)+(212)
. -(228)+(232)-(238)+(242)+(252)-(258)+(263)-(268)+(272)-(284)+(289)-(300)+(304)-(310)+(313a) -(354)+(355)
170. 0=+21.7+0.51(317)-11.15(319)+10.64(320)+36.29(323)-38.68(324)+2.39(328)+3.17(333)-11.59(334) +8.42(335)
171. 0=-1.20+4.89(320)-7.13(321)+2.24(322)+2.77(331)-2.41(332)-0.36(333)+0.49(336)-5.20(337)+4.71(338) 172. 0=+19.10+2.76(325)-38.45(326)+35.69(327)+2.92(345)-5.23(346)+2.31(347)+22.63(357)-24.06(358)+1.43(359) 173. 0=-1.50+1.89(338)-17.01(339)+15.12(340)+6.68(366)-8.18(367)+1.50(368)+4.34(378)-4.21(379)-0.13(380)
174. 0= -8.90+17 .01(339)-18.87(340)+1.86(341)+2.36(377)-6.57(378)+4.21(379)+2.03(381)-13.84(382)
+11.81(383) 175. 0=+5.20+5.80(350)-10.91(351)+5.11(352)+4.38(355)-4.97(356)+0.59(358)-0.62(363)-5.69(364)+6.31(365) 176. 0=+0.7+2.94(375)-3.53(376)+0.59(377)+1.75(383)-3.94(384)+2.19(385)+0.47(386)-2.99(387)+2.52(388) 177. 0=-66.50+0.54(388)-4.73(389)+4.19(390)+202.98(392)-205.43(393)+2.45(394)+2.62(401)-98.91(402)
+96.29(403) 178. 0=+0.40+0.54(388)-4.73(389)+4.19(390)+3.26(391)-5.71(392)+2.45(394)+2.62(401)-3.68(403)+1.06(404)
+2.97(417)-4.95(418)+1.98(419) 179. 0=+6.90+1.51(404)-6.99(405)+5.48(406)+2.21(415)-4.74(416)+2.53(417)+5.73(422)-6.19(423)+0.46(424) 180. 0=+22.50-6.99(405)+8.73(406)-1.74(407)+0.08(408)+127.83(409)-127.91(410)-148.32(421)+154.51(422)
-6.19(423) 181. 0=-14.8-6.99(405)+8.73(406)-1.74(407)+0.08(408)+0.52(4O9)-0.60(411)-1.63(412)+5.76(413)-4.13(414)
-3.89(420)+10.08(422)-6.19(423) 182. 0=-1.40+4.47(135)-4.47(138)-3.78(141)+3.78(143)-2.00(145)+2.00(146)+3.43(148)-3.43(149)+0.38(152)
+0.99(154)-1.37(157)+0.19(158)-0.19(159)+0.96(166)-0.96(169)-0.88(174)+0.88(176)-3.79(177)+3.79(178) +0.54(179)-0.87(180)+0.33(181)-0.65(182)+0.65(183)+2.05(185)-2.05(186)+1.68(187)-1.68(188)+2.14(189) -2.14(191)-0.08(192)+0.08(193)+1.45(194)-1.45(195)+4.23(197)-4.23(198)-2.88(200)+2.88(201)-0.27(202)
+1.69(204) - 1.42(206) +0.84(207) -0.84(209) - 1 .38(210) +1 .38(212) -0.83(213)+0.83(215) +2.42(216) -2.42(217)
-1.83(218)+1.83(220)+1.12(222)-1.12(223)+1.79(228)-1.79(230)-1.05(231)+1.05(232)-0.99(233)+0.99(235) +1.13(236)-!. 13(237)+0.48(238)-0.48(240)-2.17(241)+2.17(242)-1.62(243)+1.62(244)+1.08(246)-1.08(247) +0.59(248)-0.89(250)+0.30(252)-2.19(253)+2.19(254)-0.25(255)+0.25(257)+1.66(258)-1.66(259)-1.05(260) +1.05(262)+1.22(264)-1.22(265)-0.46(266)+0.46(267)+1.17(269)-3.55(270)+2.38(272)-2.19(273)+2.19(274) +3.10(277)-3.10(279)+0.48(284)-0.48(286)-1.55(287)+1.55(289)-0.99(290)+0.99(292)+2.46(294)-2.36(296) +0.91(300)-0.91(302)-1.06(303)+106(304)+0.26(305)-0.26(307)+3.05(308)-3.05(309)+0.04(310)-0.04(312) -3.19(313)+3.19(314)+0.38(315)-0.38(317)-0.91(320)+0.91(322)-2.13(323)+2.13(328)+1.43(329)-1.43(330) -2.41(331)+2.41(332)+1.92(333)-1.92(335)+1.48(336)-1.48(337)-1.44(339)+1.44(341)-0.68(366)-0.38(368) +1.06(370)-0.59(375)+0.59(377)+0.89(379)-0.89(380)+1.41(381)-1.41(383)-2.19(384)+2.19(385)+0.47(386)
+ -0.01(388)-0.46(390)-3.19(391)+3.19(393)+1.46(395)-1.46(396)+2.74(401)-2.74(402)-1.74(406) 1.74(407)
-0.08(4O8)-0.52(409)+0.60(411)+1.63(412)-1.63(413)-2.53(416)+2.82(417)-0.29(419)+0.]5(427)-0.15(428) 183. 0=+2.49-(24c)+(24d)-(26)+(27a)-(35a)+(37) 184. 0=-2.25-(23)+(24a)-(27a)+(28)-(24b)+(24c)
+ 185. 0= -39.0+0.44(23)-!. 72(24) 1.28(24a)-0.07(26)-ll.OO(27a)+11.07 (28)+15.49(35a)-16.86(36)+1.37(37)

PRIMARY TRIASTGULATION.

51

No.
186. 0=+4.81-(24a)+(25)-(38)+(42)-(43)+(47)-(59)+(63)-(64)+(69)-(79)+(83)-(89)+(93)-(99)+(104) -(114)+(118)+(133)-(134)+(136)-(137)+(162)-(164)
259. 0=+1.50-(69a)+(69b)-(431)+(432)+(433)-(435) 260. 0=-0.28-(79a)+(79b)-(430)+(431)-(433)+(434) 261. 0=4.2.53-(79)+(79b)-(69a)+(69)-(430)+(432)
262.
0=+11.530-0.023(69a)+2.356(69b)-2.333(69)-10.279(79)+10.316(79a)-0.037(79b)+0.065(431)-0.065(432) 257. 0=+5.36+(l)-(5)+(8)-(15)+(17)-(19)+(23)-(29)+(33)-(39)+(43)-(50)+(4)-(5)+(7)-(]2)+(17)-(21)
+(24a) 258. 0=+13.4-2.02(68)-0.28(69)-0.47(81)+0.47(83)-3.38(84)+3.38(85)+4.81(86)-4.81(87)+2.80(89)-2.80(90)
-2.98(92)+2.98(93)+0.82(94)+1.33(96)-2.15(98)+0.96(99)-0.96(101)-4.16(102)+4.16(104)-1.93(106) +1.93(107)+3.34(104)-3.34(109)-0.56(114)+0.56(116)-1.22(117)+1.22(118)+0.65(119)-0.65(121)
+1.74(123)-1.74(124)+0.26(126)+3.03(127)-3.03(128)-0.26(129)-2.37(131)-1.83(132)+1.83(133)
+2.37(134)-4.47(135)+0.25(137)+4.47(138)-0.25(141)-3.43(148)+3.43(149)+4.50(150)-4.50(151)
-0.38(152)-0.99(154)+1.37(157)-0.19(158)+0.19(159)-0.96(166)+0.96(169),-1.19(433)+1.19(434) +0.67(430) -0.67(432)+3.70(79a)-3.70(79b)+2.30(69a)

187. 0=+0.68+(l)-(4)-(5)+(6)

ROCKY MOUNTAIN SERIES.

188. 0=-0.22-(l)+(2)+(5)-(8)-(14)+(15)

189. 0=+0.27-(3)+(4)-(6)+(7)-(12)+(13)

190. 0=-1.08-(7)+(8)-(ll)+(12)-(15)+(16)

191. 0=-0.13-(10)+(ll)-(16)+(17)-(19)+(20)

192. 0=-1.27-(9)-!-(10)-(20)+(21)-(26)+(27)

193. 0=4-0.i9-(21)+(22)-(24)+(26)-(37)+(38)

194. 0=-0.23-(22)+(23)-(29)+(31)-(36)+(37) 195. 0=+0.61-(24)+(25)-(30)+(31)-(36)+(38)

196. 0=+0.47-(17)+(18)+(19)-(23)-(28)+(29)

197. 0=+0.61-(31)+(33)-(35)+(36)-(39)+(40)

198. 0=+l-37-(31)+(32)-(34)+(36)-(48)+(49)

199. 0=+1.13-(32)+(33)-(39)+(41)-(47)+(48)

200. 0=-1.00-(41)+(42)-(45)+(47)-(58)+(59)

201. 0=-1.44-(41)+(43)-(46)+(47)-(50)+(51)

202. 0=+0.39-(45)+(46)-(51)+(52)-(57)+(59)
203. 0=+0.76-(43)+(44)+(50)-(55)-(60) + (61)
204. 0=-0.18+(4)-(5)-(52)-(56)+(57)+(65)

205. 0=+2.31-(54)+(55)-(61)+(63)-(66)+(67)

206. 0=-1.09-(4)+(5)-(16)+(27)+(54)-(67)

236. 0=-0.79+5.52(l)-1.42(2)-1.43(3)+4.00(4)-1.72(ll)+4.30(12)-2.58(13)-1.79(14)4-4.11(15)-2.32(16) 237. 0=-0.64-1.72(9)+3.05(10)-1.33(ll)-1.45(16)+7.56(17)-6.11(18)-1.78(25)+2.21(26)-0.43(27)-6.88(28)

+10.26(29) -3.38(30)

238. 0=-0.18+1.04(21)-4.09(22)+3.05(23)+3.15(24)-3.48(25)+0.33(26)+0.09(27)-1.44(30)+1.35(31)

239. 0=+2.44+4.11(31)-5.69(32)+1.58(33)+1.19(39)-4.20(40)+3.00(41)-0.10(47)-2.42(48)+2.52(49)

240. 0=+7.68+1.86(41)-5.41(42)+3.55(43)+4.71(45)-4.87(46)+0.16(47)+0.67(50)-3.14(51)+2.47(52)

241. 0=-4.36-2.24(5)-0.14(16)+1.82(27)+3.55(42)-7.97(43)+4.42(44)+2.88(56)-3.37(57)+0.49(58)+1.91(60)

-2.53(61)+0.62(63)+2.38(65)+0.99(66)-2.80(67)

242. 0=+6.35+2.78(4)-0.14(5)+0.24(ll)-0.24(14)+1.91(16)-1.77(18)+1.09(25)-5.17(54)+2.39(55)+0.62(61)

-3.90(62)+3.28( 63) -1.09(66)

254. 0=+5.76-1.42(l)+1.42(2)-2.56(4)-0.91(5)+0.91(6)-0.11(7)+0.11(8)-1.72(9)+1.72(10)+l.'72(ll)-l:72(12)

+1.79(14)-1.79(15)-1.45(16)+1.45(17)+0.90(19)-0.90(20)-3.05(22)+3.05(23)-0.34(24)+0.77(26)-0.43(27)
+ +0.09(29)-1.67(31) 1.58(33)-1.63(34)+1.63(35)+2.97(37)-2.97(38)+1.19(39)-1.19(40)-3.55(42)+3.55(43)

-0.16(45)+0.06(47)+0.10(49)+0.67(50)-0.67(52)+2.78(54)-2.88(56)+2.88(57)+2.04(58) -2.04(59) -2.38(65)

+1.82(67)-2.78(4)+2.38(5)-0.81(3)+0.81(5)+0.41(8)-0.41(9)-1.88(10)-0.24(ll)+1.88(12)+0.24(14)
+ -2.85(17)+2.85(18)-3.17(25) 1. 35(27)

EL PASO BASE NET.

207. 0=-0.17-(4)+(5)-(6)+(8)-(17)+(19) 208. 0=-0.76-(3)+(4)-(8)+(9)-(10)+(12) 209. 0=+0.41-(3)+(5)-(ll)+(12)-(17)+(18) 210. 0=+1.33+(l)-(4)-(7)+(8)-(22)+(23) 211. 0=+0.38+(l)-(5)-(15)+(17)-(22)+(24)
212. 0=+0.07-(l)+(3)-(12)+(13)-(21) + (22)
213. 0=+1.24-(2)+(3)-(12)+(14)-(25)+(26)

52

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

No.

214. 0=-2.12+(2)-(5)-(16)+(17)-(26)+(27)

215.

2.6O-(l)+(2)-(;s0)+(22)-(26)+(28)

243. 0=+7.79-1.60(3)+2.91(4)-1.31(5)-5.65(10)+7.54(ll)-1.89(12)-1.65(17)+7.61(18)-5.96(19)

244. 0=+21.22-6.06(7)+6.47(8)-0.41(9)-1.89(10)+15.95(12)-14.06(13)-12.80(21)+20.22(22)-7.42(23)
245. 0= - 10.97 -0.77(6)+6.06(7)-5.29(8) -1.98(15)+3.63(17) -1.65(19) -5.41(22)4-7.42(23) -2.01(24)

246. 0=-15.94-3.30(ll)+4.33(12)-1.03(14)-8.79(16)+11.64(17)-2.85(18)-4.06(25)+23.43(26)-19.37(27)

247. 0=+1.59-3.30(ll)+4.33(12)-1.03(14)-1.98(15)+4.83(17)-2.85(18)-0.40(20)+2.41(22)-2.01(24)-4.06(25)

+8.14(26) -4.08(28)

COLORADO 8ERIB8.

216. 0=+1.44+(20)-(28)-(214)+(215)-(223)+(224) 217. 0=+0.10-(213)+(214)-(219)+(220)-(224)+(225) 218. 0=-3.17-(205)+(206)-(212)+(213)-(220)+(221) 219. 0=-1.59+(210)-(215)-(217)+(218)-(222)+(223) 220. 0=-2.85-(203)+(2O4)-(210)+(211)-(216)+(217)
221. 0=+3.92-(202) + (203)-(206)+(207)-(211)+(212)
222. 0=-0.20-(198)+(199)-(200)+(202)-(207)+(208) 223. 0=+0.28-(190)+(192)-(197)+(198)-(208)+(209) 224. 0=-2.21-(191)+(192)-(197)+(199)-(200)+(201) 225. 0=+1.00-(188)+(189)-(192)+(193)-(195)+(197) 226. 0=+1.59-(181)+(182)-(187)+(189)-(195)+(196) 227. 0=-1.03-(180)+(182)-(187)+(188)-(193)+(194) 228. 6=-1.18-(169)+(170)-(182)+(184)-(186)+(187) 229. 0=-0.33-(178)+(179)-(182)+(183)-(185)+(187) 230. 0=-0.42-(170)+(171)-(177)+(179)-(185)+(186) 231. 0=-2.85-(163)+(164)+(165)-(168)-(175)+(176) 232. 0=+1.57-(162)+(164)-(171)+(173)-(175)+(177J 233. 0=+0.13-(154)+(155)-(166)+(167)-(172)+(174) 234. 0=-1.61-(154)+(162)-(173)+(174) 235. 0=-0.86-(155)+(163)-(165)+(166) 248. 0=-13.3-1.34(20)-0.21(28)-2.24(202)+5.09(203)-2.85(204)-1.48(205)+2.93(206)-1.45(207)-0.98(216)
+0.08(217)+0.90(218)-0.57(219)+1.95(220)-1.38(221)-3.76(222)+5.10(223)+2.03(224)-1.82(225) 249. 0=+4.9+2.94(197)-2.72(198)-0.22(199)+2.64(200)-4.53(201)+1.89(202)+l.ll(207)-4.11(208)+3.00(209) 250. 0=+3.7+2.45(180)-3.32(181)+0.87(182)+1.44(187)-3.25(188)+1.81(189)+0.45(195)-2.69(196)+2.24(197) 251. 0=+5.5+0.35(169)+2.33(170)-2.68(171)-2.40(182)+6.33(183)-3.93(184)-3.54(185)+3.85(186)-0.31(187) 252. 0=+1.4-3.23(154)+7.25(155)+7.42(163)-7.10(164)-1.90(171)4-3.22(172)-1.32(174)-7.37(175)+7.74(176)
-0.37(177) 253. 0=-16.0-3.23(154)+7.25(155)+10.43(162)-10.11(163)-13.15(172)+14.47(173)-1.32(174) 255. 0=-ll.l+0.81(3)-0.81(5)-0.41(8)+0.41(9)+1.88(10)-1.88(12)-1.45(13)+1.45(14)-1.77(16)+2.85(17)
-1.08(18)+2.11(20)-0.77(21)+3.17(25)-3.17(27)+1.18(154)+3.97(162) -3.97(164) -0.35(169)+0.35(171)
-1.80(173)+1.80(174)+0.22(175)-0.22(177)+1.36(178)-1.36(179)+0.87(180)-0.87(182)-3.93(183)+3.93(184)
-0.31(185)+0.31(187)+1.81(188)-1.81(189)+0.78(190)-0.78(171)-1.38(193)+1.38(194)-0.45(195)
+0.23(197)+0.22(199)-2.64(200)+2.64(201)+2.24(202)-2.24(203)+1.48(205)-1.48(206)-l.ll(207)
+1.11(209)-0.32(211)+0.32(212)+2.66(214)-2.66(215)+0.57(219)-1.96(220)+1.39(221)-1.34(223) -1.82(224)4-1.82(225) 256. 0=-3.34+(l)-(5)+(8)-(15)+(17)-(19)+(23)-(29)+(33)-(39)+(43)-(50)+(54)-(67)+(225)-(219)+(221) -(205)+(209)-(190)+(194)-(180)+(184)-(169)+(174)-(154)

PBIMABY TKIANGULATION.

53

ACCURACY AS INDICATED BY CORRECTIONS TO OBSERVED DIRECTIONS.
The corrections to observed directions resulting from the figure adjustments indicated by
the preceding observation equations are as follows:

Table of corrections to observed directions. ROCKY MOUNTAIN SERIES.

Number

54

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Table of corrections to observed directions Continued. ONE HUNDRED AND FOURTH MERIDIAN.

Number

PRIMARY TRIANGULATION.

55

Table of corrections to observed directions Continued. ONE HUNDRED AND FOURTH MERIDIAN Continued.

Number

56

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

The probable error of an observed direction resulting from the figure adjustment for the
entire one hundred and fourth meridian is 0".38. When considered as divided into throe
sections by the base lines, the probable error of an observed direction for each section is as
follows :
Divide-Pikes Peak to Cheyenne base 0".41.' Cheyenne base to Provo base 0".39. Provo base to Ambroso base 0".36.
ACCURACY AS INDICATED BY CORRECTIONS TO ANGLES AND CLOSURES OF TRIANGLES.
The correction to each angle is the algebraic sum of the corrections to two directions. In order to make it possible to study the corrections to the separate angles, they are shown in the following table for every triangle in the primary scheme. There are shown the corrections to
the angles resulting from the figure adjustment, the errors of closure of the triangles, the corrected spherical angles, and the spherical excess for each triangle. The plus sign prefixed to
the error of closure of a trianglo indicates that the sum of the angles is less than 180 plus the spherical excess. The spherical excess is a convenient indication of the size of the triangle,
since it is proportional to the area.
Table of triangles.
ROCKY MOUNTAIN SERIES.

Station.

Correction to
angles from
figure adjustment.

Wasatch. Tushar Mount Nebo. .
Mount Ellen. . Tushar.... Wasatch.
Patmos Head. Wasatch Mount Nebo..
Patmos Head. Mount Ellen.. Wasatch.
Mount Waas.. Mount Ellen. . Patmos Head.
Tavaputs Mount Waas.. Patmos Head.
Uncompahgre Mount Ellen. . Mount Waas. .
Uncom Mount
Tavaputs
Treasury Mountain UMnocuonmtpWaahagrse
Treasury Mountain Uncompahgre Tavaputs
Treasury Mountain Mount Waas Tavaputs
Mount Ouray Uncompahgre Treasury Mountain

Station.
Coral Blulls Divide Big Springs
El Paso west base. Divide Coral Bluffs
El Paso east base . Big Springs Coral Bluffs
El Paso east base. Coral Bluffs El Paso west base
El Paso east base. Coral Bluffs Divide
El Paso east base. El Paso west base Divide
El Paso east base. Divide Big Springs
Holcolm Hills..... Big Springs Coral Bluffs.......
Square Bluffs. Big Springs. . . Holcolm Hills.
Cramer Gulch. Big Springs... Square Bluffs.
Holt Square Bluffs. Holcolm Hills.
Hugo
Square Bluffs. Holt
Adobe Cramer Gulch. Square Bluffs.
Adobe Square Bluffs. Hugo
Overland Adobe Hugo
Aroya Adobe Hugo
Aroya Adobe Overland
Aroya Hugo Overland
Eureka Aroya Overland
Kit Carson Aroya Overland
Kit Carson Aroya Eureka

PRIMARY TRIANGTJLATION.
Table of triangles Continued. EL PASO BASE NET.

Correc-
tion to angles Error of
from closure of
figure triangle. adjustment.

Corrected spherical
angles.

Spherical excess.

Station.

+0.85 +0.48 -0.86
+1.11 +0.67 -0.44
-1.33 -0.63 +0.72
+0.28 -0.31 +0.79
+0.34 +0.13 -0.88
+0.06 +0.32 -0.21
+0.99
+ 1.36
-0.23
+0.87 +0.10 +0.46

+0.47

96 29 37.91 49 54 42. 72 33 35 41. 28

+1.34

:148 54 54. 32 15 28 13. 79 15 36 52.08
[

88 39 22. 04 27 23 26. 85 63 57 12. 21

+0.76

52 50 51.20 48 09 17.78 78 59 51.36

1111 01 24.13
{ 32 32 25. 70 I 36 26 10. 65

+0.17

I 58 10 32. 93 69 55 02. 96 51 54 24. 44
[

+2.12

160 19 13. 83 13 28 32. 07 6 12 14.43

+1.43

69 51 37.90 54 42 05. 14 55 26 18. 86

Holcolm Hills
Big Springs El Paso east base .

0.19

Holcolm Hills
Big Springs Divide

1.10

Holcolm Hills Coral Bluffs El Paso east base.

0.34

Holcolm Hills Coral Bluffs El Paso west base

Holcolm Hills Coral Bluffs Divide

Holcolm Hills El Paso east base. El Paso west base.

0.33

Holcolm Hills El Paso east base. Divide

Holcolm Hills El Paso west base. Divide

COLORADO SERIES.

-0.50 +0.34 -1.28
+0.40 -0.44 -0.06
-0.14 +0.07 +1.66
+0.29
+ 1.64
+0.92
+ 1.90
+0.30 +0.97.
-1.61 -2.11 -0.20
+0.15 +0.17 -0.12
-1.40 +0.17 -1.06
-0.35 0.00
+0.07
+ 1.05
+0.94 +0.22
-0.60 -0.11 -0.29
+ 1.03
+0.41 +0.18
+0.39 +0.52 +0.12

38 21 33. 21 84 16 15. 29 57 22 14. 26

74 58 26. 45 49 05 18. 18 55 56 17. 81

(113 09 57.85
+ 1.59 { 37 35 49. 93
I 29 14 13. 92

+2.85

|37 68

25 24

45. 47 60. 37

65 09 16. 38

+3.17

55 00 03. 43 56 38 46. 93 68 21 11.82

55 25 51. 10 81 20 06.86 43 14 04. 88

+0.20

58 07 43. 77 35 00 49. 39 86 51 30.20

69 40 18.42 62 08 26. 06 48 11 19.02

5 08 24. 23 27 07 36. 67
fi37 44 01.22

+2.21

45 28 05. 81 38 40 11.18 95 51 44. 99

49 18 43.05 52 45 27.41 77 55 51.33

+ 1.62

32 24 49. 58 109 32 21.98 38 02 50.33

+ 1.03

67 39 53. 67 56 46 54. 57 55 33 13.93

2.76
1.70 2.22

Kit Carson Overland Eureka
Landsman Kit Carson Eureka
First View
KU Carson
Eureka
First View Kit Carson Landsman
First View Eureka Landsman

Cheyenne Wells. 2.84 First View
Landsman

Monotony First View Cheyenne Wells.
Monotony 3.50 First View
Landsman

Monotony 2.12 Cheyenne Wells.
Landsman

Arapahoe First View Cheyenne Wells
Arapahoe First View Monotony
Arapahoe Cheyenne Wells. Monotony

2.17

57

Correc-
tion to angles Error of from closureof
figure triangle. adjustment.

Corrected spherical
angles.

Spherical excess.

+0.25 +0.73 +1.62
-0.06 +0.96
-a 80
-0.62 +0.26 +0.29
-0.32 -6.05 -0.27
-0.93 +0.39 -0.32
+0.30 -0.57 -1.06
-0.30 -0.63 +0.55
-0.61 +1.38 +0.35

+2.60

79 12 08. 36 27 18 38.29 73 29 14.31

[125 34 08. 84 +0.10 21 06 23.86
1
I 33 19 28. 39

-0.07

I 20 30. 46 I 30 53. 35 ! 08 36. 35

i 10 53. 00 i 40 11.13 ! 08 56. 59

| 55 42 30. 94 41 03 19. 05
I 83 14 11.11
IS 50 22. 54 146 00 32.45
1 09 05. 23

411 22 00. 49 86 49 59.52 48 47 60. 45

+1.12

30 31 37.94 50 45 57.73 98 42 24. 90

1.09 0.16
0.22 0.46 0.57

-0.64 -0.47 -0.48
+0.31 +0.13 -0.11
+0.10 +0.44 +0.64
+0.73 +0.31 +0.23
+0.63 -0.75 +0.54
-0.98 -1.16 -1.40
-1.31
+ 0.37
+0.06
-0.56 -0.79 -0.22
+0.75 +0.92
+ 1.18
-0.09 +0.62 -0.66
+0.38 +0.25 +0.98
+0.47 +0.72 -0.33

-1.59

35 15 04. 09 39 53 01. CO 104 51 56. 98

+0.33

+1.18
+ 1.27

+0.42

-3.54

-1.57 +2.85
+ 1.61
+0.86

58
Station.

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.
Table of triangles Continued. ONE HUNDRED AND FOURTH MERIDIAN.

Correc-
tion to angles Error of from closure of
figure triangle. adjustment.

Corrected spherical
angles.

Spherical

Station.

Correc-
tion to angles Error of from closure of
figure triangle. adjustment.

Corrected spherical
angles.

Elbert Divide 1'ikes Peak .
miitop. Divide. Elbert..
Hilltop Divide Pikes Peak.
Hilltop Elbert Pikes Peak.
Morrison.. Hilltop... Elbert....
Morrison Hilltop Pikes 1'eak.
Morrison Elbert Pikes Peak.
Douglas.. Hilltop... Morrison. .
Indian. . . Hilltop.. Douglas.
Indian Hilltop.. Morrison.
Indian Douglas.. Morrison.
Watkins astronomic. Indian Morrison
Watkins astronomic . Indian Boulder
Watkins astronomic . Morrison Boulder
Boulder.. Indian Morrison.
Brighton.. Indian Morrison..
Brighton.. Indian Boulder....
Brighton. Morrison. . Boulder. .
Horse tooth. Brighton Boulder
Dewey
Brighton. Boulder...
Dewey
Brighton.... Horse tooth. ,
Dewey
Boulder Horse tooth.
Warren Dewey Horsetooth. .

-0.01 -0.59 -0.10
+0.33 -0.85 +1.33
-0.84 -1.43 +0.45
-1.17 -1.31 +0.55
-0.68 -1.76 -0.43
+0.72 -0.59 -0.74
+ 1.40
-0.88 -0.19
-0.58 +0.40 -0.44
-0.22 -0.87 +0.48
-0.31 -0.47 +0.40
-0.09 +0.10 +0.84
+ 1.72
-1.19
+ 1.72
+ 1.50
-1.01 -1.35
-0.22 -1.38 -0.89
+0.46 -0.18 +0.34
+1.23 -0.78 -0.40
+0.23 -0.60 +0.76
-1.00 +0.74
+ 1.22
+0.12 +0.09 -1.21
+ 1.25
+0.12 -0.38
+ 1.27
+0.03 +0.50
+0.02 -0.83 +0.62
-0.96 -1.82 +0.09

( 59 51 04.09
h02 02 23.21
I 18 06 35. 18

1 18 22.139
|
+0.81 \ 1 44 40.274 (176 56 57.646

I 42 01 49.05 h03 47 03.49 I 34 11 13.20

( 40 43 26. 91
-1.93 H23 11 58.27
I 16 04 38.02

-2.87

15 19 44. 86 129 47 58.48 34 52 19.36

-0.61

55 01 14.51 89 04 31.57 35 54 24.53

+0.33

39 41 29.65 88 19 38.91 51 58 62. 55

-0.62

122 43 40. 87 50 35 37. 78
6 40 42. 16
.

-0.61

11 58 04.27 26 45 32. 34 .141 16 23. 58

-0.38

78 31 21.96 77 21 10. 12 24 07 31.00

+0.85

66 33 17. 69 95 59 55. 55 17 26 48. 84

+2.25

90 56 20. 85 78 17 40.90 10 45 59. 62

[122 06 16.48 i 50 46 52. 24 I 7 06 52. 67
31 09 55. 63 91 57 32. 95 56 52 35. 88

+0.62

49 45 43. 21 27 30 48. 68 102 43 32. 57

+0.05

64 41 56.60 68 35 22. 08 46 42 46.96

(100 39 56.33 +0.39 { 41 04 33.42
I 38 15 35.34

+0.96

35 57 59. 73 56 00 45. 61 88 01 18. 55

-1.00

40 52 37. 08 65 51 29.28 73 15 60. 97

+0.98

28 19 29. 16 116 50 20.55 34 50 16. 19

+1.80

76 02 14. 80 50 58 51. 27 52 58 61. 45

-0.19

47 42 45. 64 38 25 44. 78 93 51 38. 53

I 52 35 47. 22 1
I 61 00 08.93 \i I 66 18 11.46 I

2.48 0.06 5.74

Twin Warren Dewey
Twin Warren
Horse tooth. .
Twin Dewey
Horsetooth. .

3.20

Wadill.. Warren. Twin...

2.70

Russell . Wadill.. Warren.

10.61

Russell . Wadill.. Twin...

11.11

Russell
Warren Twin

0.81

Greentop. Wadill...
Russell...

0.19

Greentop. Wadill....
Twin

Greentop.
Twin
Russell...
Whitaker. Wadill.... Greentop.
Ragged... Whitaker. Wadill....

Ragged... Whitaker. Greentop..
Ragged... Wadill.... Greentop .
Cheyenne west base., Whitaker Wadill

Cheyenne east base . . Cheyenne west base. Whitaker

5.09

Chevenne east base. Whitaker Wadill

Cheyenne cast base . . Wadill
Cheyenne west base. .

7.33 5.90

Chugwater. Whitaker. . Ragged
Notch Chugwater.. Whitaker. . .

7.52 8.95 7.61

Notch Chugwater. . Ragged
Notch Whitaker. Ragged...
Coleman Chugwater.. Notch

-0.69 -1.12 -0.89
+0.19 -0.16 -1.07
+AM
-0.93 -0.98

-2.70

39 28 32.88 120 36 32.34
19 54 59.40
.

78 39 26.82 68 00 45. 12 33 19 52. 82

39 10 53.94 41 11 09.53 99 38 04. 28

+0.33 +0.03 -0.03
+ 1.09
+0.30 -0.04

+0.33

64 44 11.88 68 54 54. 02 46 20 56. 25

+1.35

36 02 15. 11 102 14 31. 16
41 43 15. 76

-0.19 -0.03 +0.24

+0.02

82 09 06. 29 37 30 19. 28 60 20 33. 03

-1. +0.07 +0.21

46 06 51. 18 27 11 38. 26 106 41 32.31

+0.70 I -0.33 i +0.12 -0.25

66 31 40.94 22 24 26. 10 91 03 53.94

+2.10 -0.36 +0.46

+2.20

62 16 09. 59 59 54 45. 38 57 49 07.56

-1.40 -0.22 -0.44
-0.12 +0.05 -1.08

4 15 31.35 2 31 28. 50 173 13 00. 23
90 40 07.63 59 34 20. 17 29 45 33. 40

+0.38
I- -1.04
-0.70

23 39 48. 16 110 12 31.52 46 07 41. 48

+0.57 -0.92 +0.69

+0.34

74 41 55. 29 19 32 23. 89 85 45 41.54

+0.19 +0.75 -0.39

+0.55

51 02 07. 13 13 26 38.69 115 31 14.94

-0.46'
-1.31 -0.76 [

-2.53

107 42 24.75 29 46 08. 36 42 31 27. 13
.

+0.51 -0.05 -0.18

+0.28

60 27 51. 19 89 53 01. 93 29 39 07.08

-0.17 -1.12 -0.02

-1.31

179 21 56. 84 07 01. 29 31 01.87

-0.34 -0.75 -1.50 -0.41 [

120 10 11.97 42 00 25.25 17 49 22.82

+0.27 +0.05 +0.30

+0.62

+0.20 +0.17 -0.30

+0.07

+0.85 -0.10 -0.34

+0.41

+0.65 +0.35 -0.04

+0.%

0.00 -0.17 -0.35

Station.
Haystack... Chugwater. . Notch
Haystack. . . Chugwater. . Coleman
Haystack... Notch Coleman
Hobbs Haystack. . . Coleman
Willow Hobbs Haystack...
Willow Hobbs Coleman
Willow Haystack... Coleman
Rawhide Haystack. . . Hobbs
Rawhide Haystack. . . Willow
Rawhide... Hobbs Willow
Manville Rawhide... Willow
Kirtley
Rawhide . . . Willow
Kirtley
Rawhide . . . Manville
Kirtley Willow Manville
Alkali Kirtley Manville
Parker Kirtley Manville
Parker Kirtley Alkali
Parker Manville Alkali
Cottonwood Alkali Parker
Sullivan Parker Cottonwood
Sullivan.... Parker Alkali
Sullivan.... Cottonwood Alkali

PRIMARY TRIANGULATION.

59

Table of triangles Continued. ONE HUNDRED AND FOURTH MERIDIAN Continued.

Correction to angles Error of
from closure of
figure triangle. adjustment.

Corrected spherical
angles.

Spherical excess.

Station.

Correction to angles Error of from closure of
figure triangle. adjustment.

Corrected spherical

Spherical excess.

-0.37 -1.09 -0.47
-0.35 -0.92 +0.65
+0.02 +0.12 +0.65
-0.07 -0.42 -1.57
+0.50 -0.39 -0.43
-0.43 -0.32
+ 1.49
-0.93 +0.01 -0.08
+ 1.16
-0.17 +0.95
+0.25 -0.60 +0.87
-0.91 -0.50 +0.37
+0.63 -0.12 -0.26
-0.48 -0.07 +0.50
-0.33 +0.05 -0.96
+0.15 -0.76 -0.33
+ 1.46
-0.19 +0.98
-0.61 +0.01 +0.99
-0.01 +0.20 -1.05
+0.60 -0.01 +0.41
-0.18 -1.16 +0.95
+0.42 +0.33 +0.56
-0.33 -0. 62 +0.50
-0.75 -0.74 -0.66

31 10 02. 08 71 39 41.09 77 10 22. 79

65 33 54. 32 35 14 55. 49 79 11 16. 52

+0.79

34 23 52. 24 34 11 05. 70 .111 25 05.89

-2.06

53 10 21. 67 94 24 03. 84 32 25 37. 22

25 16 29. 26 142 26 34. 70
12 16 56. 60

+0.74

75 40 54. 04 89 16 13. 03 15 02 54.63
.

50 24 24. 78 82 07 07. 24 47 28 31.85

+ 1.94

61 42 24. 88 14 34 12. 43 103 43 23. 20

+0.52

104 48 25. 01 26 51 09. 03 48 20 27. 27

f 43 06 00. 13
-1.10 hl3 50 02.10
I 23 03 58.01

+0.25

34 46 44. 47
I
38 08 35. 60 [107 04 40. 77

20 45 25.53
[
98 00 51. 92 61 13 44. 55
[

-1.24

41 36 24. 74
[
59 52 16. 32
78 31 21.87
[

20 50 59. 21
[
45 50 56. 22
[113 18 06.34

25 05 35. 14 72 01 61.32 82 52 32. 19

+0.39

20 46 14. 29 121 00 12. 32 38 13 39. 20
.

-0.86

83 15 08.97 48 58 11.00 47 46 52. 00

682 28 54. 68 +1.00 44 38 52. 99
I 7:2 52 27. 14

-0.39

100 09 43. 36 31 31 35. 76 48 18 45. 75
.

+ 1.31

61 37 23. 17 66 19 17.56 52 03 22. 12

146 56 03. 42 18-00 31.81 15 03 26. 58

-2.15

85 18 40. 25 48 06 21. 24 46 35 02. 34

Provo west base . . Cottonwood Parker

Provo east base. . Provo west base.. Cottonwood

Provo east base. . Provo west base. . Parker

2.73

Provo east base... Cottonwood Parker

0.56

Provo astronomic. Provo west base . . Cottonwood

1.70

Provo astronomic Provo west base . . Parker

3.87

Provo astronomic. Cottonwood Parker

Provo astronomic. Cottonwood Provo east base...

Provo astronomic. Parker Provo east base. . .

Provo astronomic. Provo east base. . . Provo west base..

Elk Parker: Sullivan

2.00

Elk Parker Alkali

Elk Sullivan Alkali

1.77

Cambria Elk Alkali

8.65

Crow Elk Cambria

Laird Crow Cambria

Inyankara 11.97 Laird
Cambria
Inyankara Cambria Alkali

Terry Laird Inyankara
Sundance Terry Laird

1.81

Sundance
Terry Inyankara

3.83

Sundance Laird Inyankara

-0.28 -0.96 -1.18

95 03 45. 53 56 53 22. 09 28 02 53. 75

+1.05 -0.59
-0 90 ;
+1.20 -0.31 +0.96

24 28 40.05 135 17 31.94 20 13 48. 46

+ 1.85

114 32 48.44 40 13 46. 41 25 13 25. 89

+0.15 -0.06 -0. 13 -0.22 [

90 04 08. 39 36 39 33. 63 53 16 19. 64

+0.84 +0.02 -0.91

35 28 56.' 73 129 50 38. 85
14 40 24. 68

+0.58 +0.30 +0.57

(135 17 41.93 +1.45 \ 34 46 53. 32
9 55 25. 09

-0.26 -0.05 -0.61

-0.92

99 48 45. 20 42 12 57.41 37 58 18. 84

-0.37
+0.01 -0.44

155 52 39.35 5 33 23. 7S
18 33 57. 03

-0.11 +0.39 -0.29

56 03 54. 15 15- 18 00. 80 108 38 05. 42

-0.47
+ 1.49
-0.61

I 0. -11

168 38 23. 92 5 54 43. 02 5 20 53. 09

+0.38
+ 1.06
-0.11

+ 1.33

24 16 25. 49 11 07 21.67 144 36 13.60

+0.93 +0.44 +0.91
+0.55 +0.44 +0.41

[112 35 58. 77 +2.28 { 29 07 53. 48
I 38 16 11. 76

+ 1.40

88 19 33. 28 68 27 42. 98 23 12 45. 18

+0.19 -0.40 -0.11

-0.32

45 46 47. 23 87 45 17.34 46 27 58. 88

+0.05 +0.22 -0.24

+0.03

75 44 52. 92 29 04 20. 62 75 10 48. 25

+0.93 +0.59 +0.76

+2.28

51 22 49. 19 81 10 48.42 47 26 23. 21

+0.04 -0.26 -0.95

-1.17

55 24 14.64 51 41 47.21 72 53 59. 43

+0.60 +0.24 -0.21

+0.63

43 40 18. 72 118 42 01.88
17 37 41.95

-0.78 -0.89 -1.03

-2.70

26 28 13. 83 135 25 47. 38
18 05 59. 71

-0.15 -0.66 -0.79

21 25 20. 50 C2 38 01.41 95 56 40. 31

-0.17 +0.12 +0.58

+0.53

55 59 15. 04 30 09 47. 58 87 50 60. 72

-0.02 -0.10 -0.45

31 33 54. 54 39 29 07. 07 105 56 60. 43

1.37
0.74 1.66 0.26 0.34 1.45 0.16 0.37 0.03
4.01
3 45
0.82
2.55
2.22 3.34

60
Station.

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBUCATION NO. 19.
Table of triangles Continued. ONE HUNDRED AND FOURTH MERIDIAN- continued.

Correc-
tion to angles Error of
from closureof
figure triangle. adjustment.

Corrected spherical
angles.

Spherical

Station.

Correction to angles Error of
from closureof
figure triangle. adjustment.

Corrected
spherical acta.

Spherical excess.

Wymonkota
Terry Sundance
Castle Terry
Sundance
Castle Terry
Wymonkota
Castle
Sundance Wymonkota
Horeau
Castle
Wymonkota
Harding Moreau Castle
Harding Moreau
Wymonkota
Harding Castle
Wymonkota
Reva
Castle
Moreau
Reva
Castle Harding
Reva Moreau Harding
Table Reva Harding
Lodge Reva Harding
Lodge Reva Table
Lodge Harding Table
Butte Lodge Table
Whetstone Lodge Table
Whetstone Lodge Butte
Whetstone Table Butte
Rainy Whetstone Butte
Black Rainy Whetstone
Black Rainy Butte

+0.53 +0.16
0.00
-0.53 +0.16 +0.34
+0.14 0.00
-0.04
+0.67 -0.34 +0.49
-0.06 -0.51 -0.54
+0.46 +0.23 -0.22
+0.11 +0.29 +0.21
-0.35 -0.29 -0.33
-0.14 -0.02 -0.04
-0.47 -0.24 +0.14
-0.33 -0.19 -0.32
-0.72 -0.06 +0.09
+ 1.39
+1.02 -0.05
+0.61
+ 1.08
+0.59
-0.78 +0.14 -0.13
+0.69 +0.72 +0.37
+0.67 +0.46 +0.28
+0.54 -0.26 -0.75
-0.13 +0.09 -0.06
-1.32 -0.66 +0.82
-1.47 -0.64 -0.52
-0.02 +0.68 -0.55

+0.6

41 01 44.61
{ 56 15 62.09 I 82 42 21. 87

-0.03

31 42 38.58 92 27 15. 10 55 50 17.05

+0.10

68 19 17.31
|
36 11 13.01
75 29 39. 26

+0.82

36 36 38. 73
[
26 52 04. 82
[116 31 23.87

67 05 55. 79 61 06 05. 85 51 48 03.05

I 37 41 41.
+0.47 U30 53 39.
I 11 24 39.

+0.61

99 33 42. 68 63 47 44. 12 16 38 34.68

-0.97

61 51 60. 75 49 41 26.57 68 26 37. 73

-0.20

39 44 06. 99 45 16 54. 07 94 59 04. 00

-0.57

49 35 31. 12 56 41 33. 35 73 43 02. 89

-0.84

9 51 24. 13 134 07 16. 09 36 01 20. 96

-0.69

61 44 12. 66 69 16 05. 85 48 59 48. 23

( 30 40 52. 57
+2.36 032 45 40.75
I 16 33 30. 13

77 03 53. 49
[
+2.28 < 63 29 34. 90
I 39 26 35. 22

( 46 22 60. 92 i 32 26 18. 10
(101 10 47. 88

+ 1.78

62 55 11.42 52 16 47. 96 64 48 04. 81

+ 1.41

43 44 49.58 96 22 42. 29 39 52 32. 93

-0.47

74 24 24. 96 44 05 54. 33 61 29 44. 12

39 35.38 55 31.88 24 55. 54

-1.16

51 44 00.96 81 45 03.62 46 30 57. 99

-2.63

45 55 02. 71 82 39 43. 42 51 25 16.46

+0.11

96 39 07. 00 30 55 42. 46 52 25 12. 37

8.57 10.73

Black Whetstone Butte
Badland.. Rainy Black

7.42

Sentinel... Badland.
Rainy
Sentinel... Badland.. Black

Sentinel...
Rainy Black

Saddle. . .
Rainy Badland..

1.48

Saddle....
Rainy
Sentinel. . .

5.05

Saddle. . . . Badland.. Sentinel. . .

5.06

Hump
Saddle. . . .
Sentinel...

7.36 1.18

Cook Saddle. . . .
Hump
Cook Saddle...
Sentinel...

6.74

Cook
Hump
Sentinel. . .

Blue 3.45 Cook
Hump

Blue Cook Sentinel...

6.90

Blue
Hump
Sentinel...

Trotter... Cook Blue

Flat Cook Trotter . . .

Flat: Cook Blue

2. M)

Flat Trotter... Blue

levering . . Flat
Blue

Sheep Flat
Blue

Sheep Flat
Lovering . .

+ 1.45
-0.14
+0.27

+1.58

50 44 04. 29 30 19 47. 16 98 56 10. 36

-0.26
+0.20 -0.43 -0.37 [

59 52 45.1)9 63 35 56. 77 56 31 19. 99

-0.10 +0.08 +0.07
-0.42 +0.34 +0.90

7 50 28.71
|
+0.05 {161 44 44.23 I 10 24 48. 15

+0.82

34 12 45.21 101 51 58. 54 43 55 19. 93

-0.32 +0.13 +0.53
-0.54 -1.17 -0.74

+0.34

26 22 16. 50 53 11 08.62 [100 26 39. 92

-2.45

29 36 42. 40 29 44 24. 12 120 38 55. 76

-0.32 -1.10 +0.63

-0.79

90 32 03. 17 40 09 12. 27 49 18 51.36

+0.22 +0.66 +0.73

+ 1.61

60 55 20. 77 77 36 20. 01 41 28 22. 65

-0.19 +0.40 -0.71

-0.50

111 43 34.97 10 36 07. 12 57 40 18. 88

-0.25 -0.70 +0.02

-0.93

75 41 29. 74 30 53 37. 54 73 24 55. 15

+0.11 -0.30 -0.29

-0.48

77 11 18.44 41 29 44.66 61 18 60.35

+0.36 +0.17 +0.42

1 29 48. 70
H +0.95 174 51 29.88 3 38 41.47

-0.02 -0.29 -0.14

31 26 55. 93 97 01 11.04 51 31 55.03

-0.85 -0.65 -0.42
-0.83 +0.31
0.00
+0.08 +0.23 +0.49

40 36 50. 00 95 31 22. 34 43 51 50. 49
I

-0.52

9 09 54. 07 123 19 34. 85
47 30 31.96
.

+0.80

102 54 07. 90 42 32 51.41 34 33 01. 88

+0.13 +0.31 +0.18

+0.62

10 59 35. 45 11 09 30.51 151 50 54. 36

-0.12 +0.54 +0.18

+0. no

66 41 13.69 53 42 21. 92 59 36 26. 68

-0.25 -0.26 -0.31
+0.40 +0.42 +0.34

aa

49 41 38. 24
[
105 14 57.74
25 03 24. 80
[

+ 1.10

34 37 07. 07 80 34 28.34 64 48 28. 26

+0.10 +0.14 -0.02
-0.26 -0.28 -0.33

+0.22

20 50 43. 39 143 54 40.46
15 14 37. 17
;

-0.87

89 01 49. 48 03 20 12. 12 27 38 00. 85

2.45 3.68 5.04 6.80 3.43 0.97 2.43 3.45 0.05
0.78 3.67

Station.
Sheep Blue Lovering
Jackson.. Sheep Lovering.
Buford . . Sheep Lovering
Buford.. Sheep Jackson..
Buford . . Lovering . Jackson..
Montana. Buford.. Sheep
Montana. Buford.. Jackson..
Montana. Sheep Jackson..
Lanark.. Montana. Jackson. .
Cutoff... Jackson.. Lanark . .
Cutoff... Lanark . . Montana.
Cutoff... Montana. Jackson..
Mondak .
Cutoff... Montana.
Ferry Cutoff... Montana.
Ferry Cutoff...
Mondak .
Ferry Montana.
Mondak .
Bainville Buford . . Jackson. .
Snake... Buford.. Bainville
Snake . . . Buford.. Jackson..
Snake . . .
Bainville. Jackson. .
Bull Buford.. Snake
Williston. Buford . . .
Snake

PRIMARY TRIANGULATION.

61

Table of triangles Continued. ONE HUNDRED AND FOURTH MERIDIAN Continued.

Correction to
angles from

Error of closure of

figure triangle.
adjustment.

Corrected spherical
angles.

Spherical excess.

Station.

Correc-
tion to angles Error of
from closure of
figure triangle. adjustment.

Corrected spherical
angles.

Spherical

-0.36 +0.36 +0.07

+0.07

68 11 06.09 49 33 51. 09 62 15 07.92

+0.59 +0.83 +0.52

+ 1.94

55 45 21. 17 27 19 36. 91 96 55 0-1. 53

+0.28 +0.14 +0.04

+0.46

54 05 39. 08 60 44 38. 44 65 09 47. 10

+0.19 -0.69 I -1.46 -0.96

79 52 54.31 33 25 01. 53 66 42 07. 66

-0.09 +0.48 -0.37

+0.02

25 47 15.23 31 45 17.43 122 27 28. 83

+0.18
0.00 -0.03 -0.21 [

85 17 09.20 88 12 57. 71
6 29 53. 76

-0.15 -0.19 +0.86

+0.52

169 43 51. 64 8 20 03. 40 1 56 05. 02

-0.33 -0.48 -0.10

84 26 42. 44 26 55 07. 77 68 38 12. 68

+1.08 +0.77 +0.21

78 09 17.37 61 10 17. 93 40 40 25.52

+0.23 +0.65 +0.27
+0.20 +0.81 +0.72

[100 20 36. 50
+ 1.15 < 37 17 52.91
[ 42 21 31.06

+ 1.73

88 20 52. 43 35 47 46. 31 55 51 21.56

-0.43 +0.05 -0.44

-0.82

171 18 31.07 5 18 56. 37 3 22 32. 61

+0.93 +0.45 +0.29

+ 1.67

85 39 53. 27 19 56 03. 42 74 24 03. 38

+0.48 +0.27 +0.30

+ 1.05

86 11 44.59 42 20 50. 92 51 27 24.60

+0.14 -0.18 -0.64

-0.68

106 30 01. 59 22 24 47. 50 51 05 10.97

-0.34 -0.01 +0.29

20 18 17.00 22 56 38. 78 136 45 04. 24

+0.61 +0. 61 +0.45

+ 1.67

02 09 53.44 76 25 17.04 41 24 51.07

-0.26 -0. 52 -0.97

33 36 23. 06 11 11 37.70 135 11 59.54

+0. 20
+0.09
+ 1.06

47 39 02. 32 87 36 54. 74 44 44 04. 97

+0.52 +0.36 +0.61

+ 1.49

14 02 39. 26 162 38 07.02
3 19 13.90

+0.20 -0.06 -0.24

57 03 25.51 23 16 57.93 99 39 37.46

-0.88 -0.57 -0.23

-1.63

54 56 28. 42 66 33 44. 27 58 29 49. 16

5.10

Williston . Buford... Bull

2.61

Williston. Snake Bull

-0.56

-0.51

1.75

-0.68 1-

76 58 05. 88 43 16 46. 34 59 45 09. 40

+0.32 -0.01 -0.48

-0.17

22 01 37. 46 41 09 48.30 116 48 34.91

4.62

Bcnetraill . Williston.. Bull

-1.15 +0.14 +0.21

77 24 18. 17 48 00 16.30 54 35 26. 35

3.50

Gladys Bonetraill .
Williston . .

1.49

Gladys Bonetraill. Bull

0.67

Gladys.... Williston. Bull

Marmon...
Williston . . Bonetraill..

-0.54 -0.14 +0.20
+0.99
+ 1.01
+0.60
+ 1.53
-0.06 +0.81
-0.89 -0.14 +0.05

| 26 33 58. 67
-0.48 U46 22 52.62
I 7 03 08. 85

+2.60

93 32 12. 50 68 58 34. 45 17 29 13.27

+2.28

66 58 13.83 40 57 07.45 72 04 39. 62

46 00 23.64 48 30 35.57 85 29 01.75

0.82 0.47 0.30

Marmon..
Williston. Gladys....
Marmon . . .
Bonetraill. . Gladys
Howard. . Marmon .
Gladys...
Muddy . . Marmon.
Gladys...
Muddy.. Marmon. Howard..

+0.15 +0.06 -0.78
+ 1.04
+0.09 -0.24
-0.04 -0.08 +0.20
+0.84 -0.10 +0.30
+0.50 -0.02 +0.18

-0.57

56 07 07. 74 55 33 44.42 68 19 09. 15

10 06 44.10
+0.89 UI 28 08 05.63
I 41 45 10.48

+0.1

55 17 40.62
|
< 50 16 56.39
I 74 25 24.25

+ 1.04

42 14 40.60 94 07 20. 84 43 37 59.99

+0.66

77 24 40. 93 43 50 24. 45 58 44 55. 78

Muddy..
Gladys... Howard..

0.11

Stady....
Muddy . .
Howard..

-0.34 -0.10 +0.14
-0.57 -0.61 -0.44

( 35 10 00. 33 t 30 47 24.26 (114 02 36.40
03 38 30. 58 75 41 29.46 40 40 00. 64

0.06

Crosby...
Muddy..
Stady....

Crosby...
Muddy.. Howard..

-0.30 +0.66 +0.02
-0.19 +0.05 -0.08

38 47 33. 49 26 39 21.50 114 33 05.34
37 34 23.45
f
h02 20 50.96
I 40 04 46. 58

1.55

Crosby... Howard..
Stady....

Norge... Crosby.. Stady...

2.03

Norge
Crosby... Howard..

-1.02

1 13 10.04 35 14.06
178 11 35.92

+ 1.58

35 18 07.83 63 16 36. 77 81 25 15.80

+0.69

82 04 23. 90 64 29 46. 81 33 25 50.53

Norge
Stady.... Howard..

+0.13

46 46 16. 07 100 23 08.28 32 50 36. 47

Bowie School Ambrose southwest base. . .

i -2.83

28 25 26.41 27 00 34.67 124 33 59. 14

Ambrose Ambrose southwest base. . Bowie

56 35.04
(

{178 14 37.76

[

48 47.21

1.62 0.67 0.82 0.14 0.22 0.90 0.96 1.31 0.21
1.43 1.16 0.99 0.68 0.33 0.99 0.02 0.40
0.82 0.22

62
Station.

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.
Table of triangles- Continued. ONE HUNDRED AND FOURTH MERIDIAN Continued.

I'orrtvtlon to
from
figure adjust-
ment.

Error of closureof
triangle.

Corrected spherical
angles.

Spherical

Station.

Correction to angles Error of from closureof
figure triangle. adjust-
ment.

Corrected spherical
angle*

Spherical

Ambrose Bowie School
Ambrose Ambrose southwest base School
Crosby Bowie Ambrose southwest base
Crosby Bowie Ambrose

-0.20
+0.63 -0.73

-0.30

73 06 18.73 27 36 39.20 79 17 02. 46
;

-0.43 -0.05 +1.66

+1.18

74 02 53.77
I
53 40 38.62 52 16 27.79
.

+0.26 +0.32 +0.60

+1.18

16 46 02.91 18 47 29.25 144 26 28.00

-0.37

67 16 00. 22

-0.03 I -0.08 1 19 36 16.46

+0.32

93 07 43.64

Crosby Ambrose southwest base. Ambrose
Norge 0.18 Bowie
Ambrose southwest base.
Norge Bowie Crosby
Norge Ambrose southwest base. Crosby

-0.63 +0.17 +0.55
+ 1.12
-0.01 -0.02
-0.09 -0.33 +0.51
-1.21 +0.62 +0.77

+0.09
+ 1.09
+0.1 +0.18

50 29 57.31 37 18 54.24 92 11 08.60
43 38 44.09 77 47 03.68 58 34 12.35
53 28 02.98 58 59 34.61 37 32 22.95
39 49 18.89 85 52 15.65 54 18 25.86

0.15 0.30 0.54

The maximum correction 2".39 to any angle is to the angle at School between Ambrose
southwest base and Bowie.
The statistics as to closures of triangles and the mean error of an angle for the sections of the one hundred and fourth meridian are given in the following table. The mean error of

an angle a

, in which IA 2 is the sum of the squares of the closing errors of the triangle

and n is the number of triangles in the season's work or in the section.

Season.

PRIMAKY TRIANGULATION.

63

The comparison of the average closing errors is given below:

Average
closing error.

Texas-California Ninety-eighth meridian
One hundred and fourth meridian
Transcontinental triangulation Eastern oblique California-Oregon

0. 90 0. 92 0. 99 1. 06
'.
1. 19 1. 22

No attempt has been made here to set forth the agreement of the separate measures of

each direction as a criterion of accuracy, since it is well known that it is of little value for that

A purpose.

close agreement of the separate measures of a given direction is of little conse-

quence, since such measures are usually subject to constant errors of considerable size, which

become evident as soon as the closures of the triangles are studied or an attempt is made to

adjust a figure.

ACCORD OF BASES.

As already stated, there are six bases which serve to fix the length in the triangulation

under discussion. Four of these bases are connected directly by the triangles adjusted. The

Salt Lake base determines the length of the line Tushar-Mount Nebo adjacent to the base net,

with little loss of accuracy. The Salina base is more remote from the line Arapahoe-Mono tony,

which was the fixed length in this adjustment, and the outstanding discrepancy is consequently

somewhat greater than would have been the case if the intervening triangles had been readjusted.

In solving the normal equations of the figure adjustment the length equation was, as usual,

assigned to the last place, so that after all the conditions relating to triangle closures and ratios

of lengths had been satisfied the discrepancy in length became known. In the following table

the discrepancies developed between bases are given in terms of the seventh place of logarithms

A and are also expressed as ratios.

plus sign before the discrepancy expressed in terms of

logaiithms means that the first base mentioned is longer as measured than as computed through

the intervening triangulation from the second base mentioned.

Arapahoe-Monotony to El Paso El Paso to Tushar-Mount Nebo (Salt Lake) El Paso to Cheyenne Cheyenne to Provo Provo to Ambrose

Discrepancy in Discrepancy

seventh place expressed as a

of logarithms.

ratio.

+ 31

+6

+ 141

+-

108 40

1:140 000 1:724 000
1:30 800 1:40 200 1:109 000

ACCORD OF AZIMUTHS.
Laplace azimuths were computed at three stations of the one hundred and fourth meridian triangulation, viz, at Watkins astronomic, Provo astronomic, and Mondak. It was reasonably certain that the Laplace azimuths computed for these stations were more accurate than the geodetic azimuth computed through the triangulation, and they were therefore introduced into the triangulation. The azimuth equations which reconciled the computed and the Laplace azimuths were placed at or near the last of the group of normal equations so that after the conditions relating to triangle closures and ratios of lengths had been satisfied, the discrepancy in azimuth became known.
Tne azimuth computed to Watkins astronomic station, through the triangulation, from the North American Datum azimuth at the edge of the Salt Lake base net, was found to be too large by 5". 05 when compared with the Laplace azimuth at Watkins. The azimuth computed to Provo astronomic station, through the triangulation, from the Watkins Laplace azimuth, was too large by 2". 37 when compared with the Laplace azimuth at Provo. The azimuth computed to Mondak, through the triangulation, from the Provo Laplace azimuth, was too small by 1".08 when compared with the Laplace azimuth at Mondak.

64

U. S. COAST AND GEODETIC SUBVEY SPECIAL PUBLICATION NO. 19.

STUDY OF ERRORS.

While the primary triangulation done by the Coast and Geodetic Survey is sufficiently accurate for geographic and geodetic purposes, at the same time it is well to search for the causes of the larger errors and to tiy to eliminate them, if possible without an increase in the time and cost of the triangulation. Or, if the causes of the largest errors can be found and removed, it
might be possible to obtain the present accuracy with fewer observations over each direction
in the scheme of triangulation. It is known to all observers of experience that large errors are likely to occur in observations made on a heliotrope before the late afternoon, when the wind makes the support of the instrument vibrate badly, and when a line passes close to a steep slope or a factory or heated stack. There must be other more obscure sources of error. In the text below are given data which .may help to discover some of the sources of errors in primary

triangulation.
Beginning with the season of 1904 each observer on the northern portion of the ninetyeighth meridian triangulation and on the Texas-California arc kept a record, called the error
"book, in which he made notes of the weather conditions, the character of the line observed over,
and the appearance of the object observed upon. For each period of observations of primary horizontal angles there were entered in the record the date, with the hour; the direction of the wind; the strength of the wind; the station observed; the intensity, size, and degree of steadi-

ness of the image of the heliotrope or lamp; the character of the image, whether symmetrical or asymmetrical; and the character of the line, whether high, low, grazing, or clear only at
night as a result of elevation by refraction. In a column of remarks notes were made regarding
the condition of the atmosphere, whether clear, hazy, or smoky. It has been impossible for
the author, in the limited time at his disposal for such work, to make an analysis of all the
accumulated data. 1

High, low, grazing, and refraction lines. As considered in the error book, a high line is

one with it3 greater portion elevated well above the ground and obstructions. This usually

A occurs when the line crosses a depression or valley.

low line passes over a very flat country

or just over ridges, trees, houses, or other obstructions. Grazing was the term employed to

A describe a line which was barely clear during the day.

refraction line was one which was

A clear only at night as a result of great refraction.

refraction line is, strictly speaking, a grazing

line.

The following table gives certain data regarding the number of high, low, and grazing or refraction lines on the triangulation along the one hundred and fourth meridian and the aver-

age corrections to directions for the different kinds of lines:

PKIMABY TKIANGULATION.

65

The following table gives the number of large corrections to all the directions and the number of them on the several classes of lines :

%

66

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

the observations were mainly made in the late afternoon, the west side of the instrument is undoubtedly warmer than the east side, and the resulting angles opening to the west and to the east should be subject to systematic errors of opposite signs, and therefore twist would develop. If this theory is correct, an east-and-west arc should develop only a small amount of twist, well within the limits for the expected error. Arcs on which the observing was done at night should develop no twist exceeding that allowed by the probable error, for the temperature of the east and west sides of the instrument would be equal. It is expected that this theory will be tested in the near future on all of the arcs of primary triangulation now existing in the United States.
In the following tables are given the data, for each section of primary triangulation in the
United States, which may throw some light upon this deviation in triangulation. It is believed
that if similar data for the primary triangulation of other countries were in print it would be possible eventually to discover the cause or causes of deviation in triangulation, and with this
knowlodge to carry on the work in such a way as to minimize or eliminate its effect. The sections of triangulation between Laplace stations are arranged in two tables. In the
first are given data for the sections whose axes he approximately in the meridian, while in the second table data are given for those sections which run east and west or nearly so.
On page 74 are given the data for three sections of the Eastern Oblique Arc.
Explanation of tables. The data for any section are given in the direction south to north. In columns 1 and 2 are given the names of the Laplace stations at the south and north ends of
the section, respectively.
Column 3 contains the correction necessary to make the computed and adjusted azimuth
agree with the Laplace azimuth at the northern end of the section in question. In each case the triangulation started with a true or Laplace azimuth at the southern end and the difference given is the amount of the accumulated systematic error or the deviation of the triangulation in azimuth at the northern end. This correction results from the figure adjustment and the adjustment for discrepancy in length between bases. It does not include the effects of any adjustment for latitude, longitude, or azimuth.
Where the triangulation had been adjusted without equations for latitude, longitude, or azimuth, the values for the corrections in column 3 were taken from the table on page 20 of the "Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy."
Where an equation for latitude, longitude, or azimuth was used in the adjustment of the triangulation to the North American datum, various expedients were adopted to obtain the values for column 3, and the numbers given are subject to some error.
Column 4 contains the values of the probable error of the adjusted azimuth. The method of deriving these values is explained below in the text relating to column 8.
In column 5 are given for each section the values of the ratio of the deviation itself (col-
umn 3) to the probable error of the deviation (column 4).
If the deviation of triangulation in azimuth were due to accidental errors alone and the probable error in column 4 were free from errors of computation, then the values of the ratio between the value and its probable error for any section should on an average be about unity (theoretically 1.18), with few values as great as 2 or 3. It will be seen in the tables on pages
67 and 69 that the values of this ratio are frequently larger than 3 and the mean is 3.7 without
regard to sign.
In columns 6 and 10 is given the number of lines between the Laplace stations at the ends of the sections for the eastern and the western sides of the scheme of triangulation,
respectively.
In column 7 are given the corrections necessary to make the azimuth carried along the eastern side of the scheme from the south agree with the Laplace azimuth at the second or northern station. The computation starts with the Laplace azimuth at the first station and is carried through the observed directions. These directions are unadjusted, except for any
local conditions at the stations at which they were observed. The above paragraph applies also to column 11, except that in this case the azimuth is
carried through the unadjusted directions on the west side of the scheme of triangulation.

PRIMARY TRIANGULATION.

67

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+i

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t*
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3

OOO d d

n id O -4"

* (9

o

1-4

,-4

C4

<-

TO

ddodo

*So
oo

++ I

+

+

+++++

1

+ + I

I

00 ~H

o Ocod

3-

to co

odd d d

+ 11 + +

.

w pj o
8od3 d8 d d
+++++

5S

d do

+ 4-

I

o'S .J 2 si 3

o o wScccsooio^o

co 3-

r-
***
CO

odd d d

++ I

+

+

odd S 3 3 M --* -4

8

"-J

+++++

Q 50 iO 89s d d o oo + I + +1

o-<

I

I

I

+ I

o i

i-H

I-H

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+ + I

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+ + I

1

~h'cocn

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a. :

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d d h

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_+

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+

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+++++ +1++1 d m h fi eo ^Jpi'-H p4

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U0I133S JO ON

-" CCO ^* Ui

68

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Columns 8 and 12 contain the values of the probable error of the azimuths carried through the observed directions on the eastern and western sides, respectively, of the schemo of triangulation. These are the azimuths referred to in columns 7 and 11.
The probable error, ea, of the azimuth as carried through one side of the scheme is computed by the formula

where is the probable error of a single observed direction and d is the number of directions
used to carry the azimuth.
As there are four independent ways for carrying the azimuth through a scheme of quadri-
laterals with the diagonals also observed, then the probable error of the azimuth carried through the scheme which has been adjusted for figure or for figure and length conditions is obtained by the approximate formula,

eA is the probable error of the adjusted azimuth, and sa is the same as in the preceding
paragraph. In column 9 are given the values of the ratio of the difference between the observed and
Laplace azimuth to the corresponding probable error of the observed azimuth. The observed azimuth referred to is that carried through the observed directions on the eastern side of the triangulation. Column 13 contains similar data for the western side of the scheme.
D The time at which the observing was done is given in column 14, standing for day and N for night.
There are given in column 15 the apparent convergences of the two sides of the scheme of triangulation. This is the value in column 7 minus the value in column 11.
In column 16 are given the values of the probable errors of the apparent convergences.
The probable error is the square root of the sum of the squares of the probable errors of the corrections to the azimuth as carried by the two sides of the scheme of the triangulation.
There are given in column 17 the ratios of the apparent convergence to the probable error
of that convergence.
The last four columns 18 to 21 give the accumulation for a single direction, in the adjusted azimuth, in the azimuth as carried through the observed directions on the eastern side of the scheme, the same for the western side of the scheme, and in the convergence. The figures are obtained by dividing the numbers in columns 3, 7, 11, and 15, respectively, by the sum of the corresponding numbers in columns 6 and 10.

PBIMARY TEIANGULATION.

69

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+ I

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70

U. S. COAST AND GEODETIC SUKVEY SPECIAL PUBLICATION NO. 19.

The explanation on pages 66 to 68 of the table giving data for the north-and-south sections
applies to the above table for the east-and-west sections of triangulation, except that for eastern should be placed the word northern and for western the word southern. It is not necessary to repeat the explanation. The azimuth is carried westward from the east end of
the section. The columns with, the same number in the two tables contain similar data, except
as noted above.
Analysis of data in the above tables. In order that one may fully comprehend and see the
bearing of the data in the above two tables, it was thought advisable to give the summaries contained in the following six tables. The first three relate to the north-and-south arcs and the others to the arcs which run in an east-and-west direction.
The correction to an adjusted or observed azimuth carried from one station to another through the triangulation is positive when the azimuth is smaller than the Laplace or true geodetic azimuth at the second station. As the azimuths are reckoned clockwise, a positive correction indicates that the azimuth as carried through the triangulation has worked to the left, or westward, looking north. If the azimuth had been computed southward, the correction would have been negative, showing that the azimuth had worked to the right, but again westward. It is readily seen that the effect of systematic error in azimuth is to make curved what otherwise might be a straight line. If either end of the curved line is held coincident with the straight line, the other end will go to the westward. If the curvatures are reversed, the line as actually observed will deviate to the eastward regardless of which end is held to a
Laplace azimuth.
The data for the north-and-south sections given in the preceding and following tables were gotten by computing from south to north; hence a positive correction indicates a westerly deviation of the azimuth and a negative correction an easterly deviation.
Summary for all north-and-south sections.

PRIMARY TRIANGULATION.

71

tion of the deviation is about 60 per cent greater for the eastern than the western sides, +0".072 against +0".044.
The evidence is strong that the western side of the scheme is less affected by systematic
error than the eastern side. In the last column in the above table are given data regarding the convergence of the
two sidtvj of the triangulation.
There is given below a summary of azimuth data for those north-and-south sections which
were observed entirely during the day.
Summary for north-and-south sections observed in the day.

72

U. S. COAST AND GEODETIC SUEVEY SPECIAL PUBLICATION NO. 19.

That there is some systematic error present is indicated by the fact that most of the sections have positive corrections to the azimuths, which shows that in general the line deviates to the westward. This is the same direction of deviation as obtains when the observing was done
during the day.
The mean positive values of the accumulation of error to the azimuth are much smaller than
for day observations, and the positive accumulation is only 1".93 against 8".ll for the day work. The largest positive value for the adjusted azimuth is only 6".62, this being the only positive value greater than 4". 00.
For the eastern side of the scheme the largest positive value is only 4".13. The western side has three positive values greater than 4".00, with the largest one 5".79. The negative values are all comparatively small except for one section. That value is more than 10".00 for the adjusted azimuth, the azimuth by the east side and the azimuth by the west side. If that one section were not considered, the mean values for the negative azimuths would be comparable with the mean positive values.
The mean value of the convergence for the night observations is only about one-half that for the day work and is of opposite sign.
Discussion of data for east-and-west arcs. In the following table is a summary of the data
given in the table on page 69 for the sections of triangulation which run in an east-and-west
direction :
Summary for all sections of east-and-west arcs.

PRIMARY TRIANGULATION.

73

Summary for east-and-west sections observed in the day.

Accumu-
lated correction to

Accumulated correction to observed azimuth.

adjusted azimuth. Northern Southern

side.

side.

Convergence
N -S.

Number of sections Number of + values Number of values
Mean values, sign not con-
sidered
Mean + value
Mean value
Mean value, sign considered. . Weighted mean of accumula-
tion per direction

11 5 6
4.10 5.08 3.29 +0.51
+0.019

4.78 4.76 4.83 +2.14
+0.079

11 5 6
5.01 5.20 4.86 -0.28
-0.011

11 8 3
3.89 4.34 2.67 +2.43
+0.090

Number of + ratios (corrn.
top. e.)
Number of ratios Mean of ratios, sign not con-
sidered
Mean of + ratios
Mean of ratios Mean ratio, sign considered.. Probable error of mean ratio.

74

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Deviation of eastern oblique arc in azimuth. The axis of this arc of primary triangulation
runs in a northeast and southwest direction. The arc may be considered in three sections, as
is shown in the small table below.

Eastern oblique arc.

PBIMABY TKIANGULATION.

75

The writer, believing the unequal heating of the circle of the theodolite to be the principal cause of systematic error in the azimuth, recommended to the Superintendent of the Coast and Geodetic Survey, in October, 1913, that the theodolites be equipped with nickel-iron circles instead of circles of brass. The former metal has a coefficient of only 0.000004 per degree centigrade, while the brass has a coefficient of about 0.000018, or more than four times as great. One of the theodolites is now (May, 1914) equipped with a nickel-iron circle and it will be used on the Memphis-Huntsville triangulation. The results should be of great interest.
The observer was also requested to change the circle about 180 in azimuth for each new position by using the settings given in the table below in place of those shown on page 14 of
Special Publication No. 11.
Circle readings for initial directions.

Position.

76

TJ. 8. COAST AND GEODETIC SUBVEY SPECIAL PUBLICATION NO. 19.

In the report on the work done in 1902 its author, Prof. J. F. Hayford, in commenting upon the possible effect of twist, stated that:
About two days were spent by computers at the office in examining the records after the close of the season for evidence of twist. No convincing evidence that any systematic twist occurs could be found. Whatever twisting of the tripod head in azimuth occurs, if refjular and continuous in one direction for considerable periods, is so slow as to be concealed by accidental errors in pointing and reading. There is possibly a very irregular twisting, with frequent reversals or stops, the effect of which is to introduce errors of the accidental class into the results which can not be separated from the other accidental errors.
No further investigations for the effect of twist have been made. It is generally held
that the effect of the sun is to twist the signal in the same direction. If this is true and the motion is continuous and constant in rate, then the mean of two series of observations made in opposite directions and at uniform speed should eliminate the effect of twist. If the motion
is irregular, the effect can be eliminated only if many observations are made. After sundown
the signal should twist in the opposite direction for an indefinite time, and again affect a single series of observations taken in the early part of the night.
It is probable that the effect of twist may increase slightly the sizes of the accidental errors, but there seems to be no reason why it should cause a systematic deviation of triangulation
in azimuth.
EFFECT OF DRAG.

The observed angles or directions at a station may be affected by two sources of error which are sometimes confused or not clearly distinguished. One is the twisting of the signal,
on which the theodolite is mounted, by the sun. If the signal is not protected by screens from the direct rays of the sun, the material of the structure (assumed to be wood in this discussion), is unequally heated or dried and as the sun changes in azimuth during the observations, the
structure may also change in azimuth. This change is probably not at a uniform rate, but by a series of jerky movements. The effect on the mean angles at the station is probably the same as if the motion were uniform. The effect of this torsion will be made negligible by the method of observing in which one-half of the observations in any position of the circle are made in a clockwise direction and the other half immediately afterwards, counterclockwise. The direc-
tions or angles in one case will be too small and in the other too large, but the means should be free from the effect. This will be practically true for the mean of the observations made in
16 positions of the circle.
The other error has its source in the lost motion or nonelasticity of the materials forming
the structure on which the theodolite stands and the base of the theodolite itself. When the
alidade of the theodolite is moved in azimuth, the friction between the movable parts, even though very small, will tend to drag the lower part of the instrument with it. The error due
to this may be termed the effect of drag. It tends to make the measured angle too small
whether the alidade is moved from left to right or from right to left.
When the motion of the alidade ceases the lower part of the instrument will assume its
previous position only if it and the support (all considered as one structure) are perfectly
elastic.
If the elasticity is not perfect then the telescope revolved through 360 should register 360
minus the drag or effect of nonelasticity in the instrument and stand. The alidade of the instrument is assumed to move continuously in one direction. For instance, let it be assumed that the theodolite is graduated clockwise, then if some object is sighted on and the reading of the circle is zero or 360 the reading at the second pointing on the same object, after revolving the alidade 360 should be something less than 360 or zero. Also, if the first reading is zero and the instrument is turned counterclockwise or right to left, the second reading should be greater than zero or 360. These differences in the readings will be the same in amount if the degree of pliability is the same for the two directions.
It would also be reasonable to assume that in a series of angles all of the effect of drag would appear in the first or left-hand angle for the first round of observations (made from left
1 U. 8. Coast and Geodetic Survey Report for 1903, Appendix 4, p. 824.

PRIMARY TRIANGULATION.

77

to right), and on the last angle (the right hand one of the series) for the second round which
would be in a direction opposite to that of the first round. This assumption is based on the idea that after the lower part of the instrument and the support have been dragged as a result of revolving the alidade to the second direction the structure will be perfectly elastic to any further, strains due to the movement of the alidade to the third, fourth, and other directions. That is, after the telescope has been turned to the second direction, all of the drag caused by moving the telescope farther from the initial will be due to the flexibility of the materials of the lower part of the instrument and its support and not to looseness of the parts. The structure should act as if it were perfectly elastic and should recover the same position it had at
the second direction.

If the above theory is correct, one-half the total effect of drag should be present in the angle which lies between the first or initial and the second directions and one-half in the angle formed by the last direction and the initial one (if the horizon were closed in the round). If the horizon is not closed then the first and last angles would each be affected by one-half the amount
of the drag. The intermediate angles should be free from the effect of drag. To test these theories an investigation was made of the work done on the one hundred and
fourth meridian in 1912.

The observers in the United States Coast and Geodetic Survey work do not try to prevent
"overshooting" the mark and therefore it may be assumed that in some cases the telescope
went beyond and had to be brought back, that is moved in the reverse order in which the directions were being made. One therefore will not get as definite an idea of the effect of drag as if the telescope had always stopped exactly on the mark.
Of the stations occupied by Assistant E. H. Pagenhart, there were 17 at which he closed the horizon in each one of the double measurements of the directions. In all the horizon was

closed for 297 such measurements.

Of the 297 times the horizon was closed while revolving the telescope from left to right,

there were 146 cases where the last pointing on the initial was greater than the first, and in

136 cases the reverse was true. The sum of the plus closures was 244".2, while that of the

negative closures was 245".0. The averages were, respectively, 1 ".67 and 1".80.

There seems to be no effect of drag in these observations.

Of the 297 measures closing the horizon when the telescope was swung from right to left,

106 had positive closures, with a total of 174". 8 and an average of 1".65, and 172 had negative

closures, with a total closing error of 290".9 and an average of 1".75. The closure is considered

positive if the second reading passes the first one in the revolution of the telescope.

Why The evidence is strong that the right^to-left measures are affected by drag.

there

should be drag in these measures and not in the left-to-right ones is not clear. The resultant

drag in each position that is, the mean of the two measures of a position is 0".20. The

sum of the angles at a station is affected by this amount, and averages only 359 59' 59 ".80.

Values offirst and last angles of a position, left to right, and the reverse. If the drag is only

on the first angle of a series measured in any one direction, say left to right, then this angle

shouhl be free from drag when measuring this series in the reversed order right to left.

In the work of Assistant Pagenhart on the one hundred and fourth meridian tri angulation

in 1912 he made observations at 49 primary stations and 8 subsidiary ones. Several stations

were occupied a second time. Of the 863 measurements of the first angle of a series (the angle

between the initial and second directions) the second hah of the measurement was greater

than the first in 437 cases. The first hah of the measurement is greater than the second in

426 cases. The sums of the differences are, respectively, 1079". 2 and 1049". 1, and the aver-

ages are 2".47 and 2".46.

The first measure of the last angle of a series was greater than the second in 375 cases with

a total difference of 921". 6 and an average difference of 2". 48. There were 400 cases in which

the second measure ot the angle was greater than the first, with a total of the differences of

985".7 and an average difference of 2".46.

78

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

There is no indication in the above data that there is any systematic effect of drag in the first and second measures of the first and last angles of a series.
Angles measured in series or singly. In Mr. Pagenhart's work there were 28 angles measured partly in a series of angles and partly alone or singly.
The average of the single measures was greater than that of the measures in series in 14 cases and the reverse was true in the other 14 cases. The sum of the positive differences (series minus single) was 11 ".5 and an average difference of 0".82, while the sum of the negative differences was 8".9 with an average of 0".64. Thirty-five of the angles measured by Assistant C. V. Hodgson on the one hundred and fourth meridian triangulation were observed partly in a series of angles and partly singly. In 18 cases the measure in series was greater than the single measure, and in 17 cases the reverse was true. The sum of the differences when the series was larger was 16".4 and the average difference 0".91. The sum of the differences when the single measures were larger was 17 ".0 and the average difference was 1".00.
The above data do not indicate the presence of any systematic effect of drag. If any errors of considerable size, due to drag, were present in the observed horizontal angles these angles would be too small and the sum of the observed angles of the triangles should on the average be less than 180 plus the spherical excess. The custom in the United States Coast and Geodetic Survey has been to take, whenever practicable, the extreme left-hand object as the initial direction, assuming that the observer is facing his scheme of triangulation. This applies only to the side points of the scheme and not to those stations which are within the area covered by the triangulation. Also in general the horizon is not closed, the initial station being observed upon only once in a half series, left to right or right to left. Therefore the angle, which is nearly always about 180, necessary to close the horizon at stations on the sides of the scheme is not measured.
With the methods employed the drag, if present to any extent, should appear in those angles which form the triangles of the scheme.
The following table gives the data in regard to positive and negative closing errors for
several arcs of primary triangulation in the United States.
The plus sign indicates that the sum of the observed angles of a triangle is less than 180 (plus the spherical excess of the triangle). The negative sign has, of course, the opposite meaning, that is, the sum of the three observed angles is more than 180 (plus the spherical excess
of the triangle).

Arc.

PKIMABY TBIANGULATION.

79

sign for the 1314 triangles is ".043. This mean with regard to sign is so small that it can not be attributed safely to any cause except the unbalanced effect of accidental errors.
Conclusion in regard to study of drag. As a result of the above investigations to discover the effect of drag in the observed horizontal directions or angles of the primary triangulation by the United States Coast and Geodetic Survey, it must be concluded that there is no appreci-
able systematic drag. While the above data do not indicate the presence of any systematic error due to drag
there may be some errors of an accidental nature in the results due to that cause. It is believed
that the method of observing employed in India is somewhat preferable though probably slower in operation than that used by the United States Coast and Geodetic Survey. There the observer brings his cross wires up to the object but never overshoots it. The party of this survey now at work on the arc between Huntsville, Ala., and Memphis, Tenn., has been instructed to test the Indian method. After setting the circle for a new position, he will move the telescope to the left of the initial direction and will then bring it up to the initial from the left as will be done for the other directions. Similarly, when making the observations in the reversed order, he will move the telescope from right to left for each of the pointings, including the first.
When using the tangent screw to make the contact he will not limit himself to the direction
in which the observations are being made.
ACCURACY OF THE PRIMARY TRIANGULATION IN THE UNITED STATES.
In the following table, 66 sections of triangulation in the United States, for which the required tabular values can be conveniently obtained, have been arranged in the order of accuracy, the most accurate being placed first. The most severe, and therefore the best, test of accuracy is believed by the writer to be the quantity d, expressing the probable error of the observed direction as derived from the corrections to directions resulting from the figure adjustment before the introduction of equations necessary to hold fixed positions of previously adjusted triangulation. Accordingly the various sections of triangulation have been placed in the order of the values of d. In the few cases in which d is the same to the nearest hundredth of the
second for several sections the next column, a, has been used to decide their relative rank. The methods of computing d and a have already been explained fully on pages 55 and 62.
Sections of triangulation in order of accuracy.

No.

Section.

Probable

error of an

Mean

observed error of an

Average
closing error of a

Maximum Maximum Discrep-

correction

closing

ancy

toa

error ofa between

direction angle=u. -4.

triangle.

direction.

triangle.

bases. 1

Nevada-California series
Stephenville base net to Lampasas I: Yolo base net
Point Isabel base net Elliff-Nolan to Laguna Madre base. .

Dauphin Island base net
New England section

Meades Ranch-Waldo to Shelton base net . .

Deming base net to San Jacinto-Cuyamaca.

Shelton base net to Page base

."

Olney base net Bowie base net to Stephenville 1:
Eastern oblique arc to Augusta. Rocky Mountain series
Stanton base to Deming base

Salt Lake base net Shelton base net Stephen base net to Canada. El Reno base to Bowie base. Fire Island base net

Illinois series
Holton base net
Indiana series Atlanta base net to Dauphin Island base net, IV. Fergus Falls to Stephen base

0.23 0.23 0.24 0.25 0.25
0.26 0.26 0.27 0.28 0.29
0.29 0.29 0.30 0.32 0.32
0.32

0.42 0.45 0.51 0.40 0.62
0.51 0.53 0.35 0.57 0.44
0.54 0.63 0.60 0.57 0.54

80

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

Sections of triangulation in order of accuracy Continued.

Probable error of an

Mean

Average Maximum Maximum Discrep-

No

Section.

obscrvd

error of an

closing error of a

correction
toa

closing error of a

ancy between

direction
-i.

angle a.

triangle. direction. triangle.

bases.

Transcontinental triangulation to Anthony base

Missouri-Kansas series

Atlanta base net
PROVO BASE

tTo ODauApMhiBnRIOslSaEnd

base net.
BA8E

V

Anthony base net to El Reno base net

Brown Valley base net to Royalton base

Ulan la base net to Dauphin Island base net, III

Royalton base net to Duluth

CKyHlEe-YMEcCNlNenEnv

to Stanton
BASE TO

base
PROVO

BASE

Versailles base net

El Paso base net

Seguin base
EL PASO

net to Alice base
BASE NET TO

CHEYENNE

Kent Island base net to Atlanta base net. I

BASE

Yolo base net to Los Angeles base net Kent Island base net Page base net to Brown Valley base Sal ina base net Los Angeles base net
Lampasas base net to Seguin base Ohio series A lleeheny series Epping base net Fire Island base net to Kent Island base net

St. Albans base net Kansas-Colorado series Los Angeles base net to Soledad-Cuyamaca Epping base net to Canadian boundary Dauphin Island westward, I
California-Washington arc Kent Island base net to Atlanta base net, III
A tlan ta base net
Missouri series
Atlanta base net to Dauphin Island base net, II
Coast Range series Eastern Shore series Kent Island base net to Atlanta base net, II
Dauphin Island base net to New Orleans
Atlanta base net to Dauphin Island base net, I American Bottom base net

0.35 0.35 0.35 0.36 0.36
0.36 0.36 0.36 0.37 0.39
0.40 0.40
41 0.41 0.41
0.41 0.41 0.42 0.44 0.44
0.45 0.45 0.45 0.47 0.47
0.47 0.50 0.50 0.51 0.53
0.53 0.62 0.65 0.66 0.67
0.67 0.72 0.72 0.78 0.79 0.82

0.64 0.60 0.68 0.69 0.69
0.70 0.77 0.86 0.71 0.68
0.64 0.68 0.78 0.81 0.88
0.91 0.91 0.77 0.75 0.91
0.82 0.85 0.98 0.63 0.86
1.04 0.75 0.82 0.74 0.78
0.97 0.78 1.00 0.81 0.78
1.37 1.22 1.31 1.20 0.97 1.59

0.79 0.88 0.97 0.94 1.05
0.96 1.10 1.16 1.02 0.96
0.90 0.94 1.04 1.14 1.14
1.16 1.33 1.03 1.13 1.39
1.13 1.14 1.37 0.90 1.29
1.38 1.00 1.16 1.15 1.12
1.22 1.66 1.19 1.09 1.03
1.80 1.75 1.80 1.50 1.35 2.22

1.39 1.12 1.12 1.14 0.84
0.98 0.84 1.22 0.82 0.99
0.95 0.93 1.09 1.33 1.48
1.34 0.75 1.44 1.11 1.22
1.96 1.32 1.37 1.25 2.02
1.53 1.43 1.15 1.12 1.31
2.03 1.72 1.31 1.89 1.84
2.73 1.85 2.05 2.65 2.19 1.80

1.98 2.37 2.87 2.83 2.17
3.84 2.69 4.41 3.11 2.42
2.71 2.60 3.2.5 2.87 3.60
5.52 2.97 3.81 2.37 3.09
3.31 5.08 4.03 2.63 3.35
4.94 3.92 2.53 2.09 2.80
6.35 4.03 4.35 4.64 2.88
6.49 5.24 4.64 5.40 3.44 6.36

+ 41

+ 169

+-

2 40

+7

+ 98

+2

+-

80 11

+ 108

- 144 + 141
- 41 + 65

-7 - 24 + 11 + 46
- 92

+ '79 + 86

+ 24 +2

1 The fixed length Mount Helena-Snow Mountain West of the thirty-ninth parallel triangulation, Willamette base, and Tacoma base, are connected by this aic with discrepancies of +79 and 19, respectively.
Of the 66 sections of triangulation tabulated, the three sections of the one hundred and fourth meridian arc rank as numbers 29, 35, and 39. The mean value of d, 0".38, for the whole arc comes between those for the sections numbered 34 and 35. The average accuracy as shown by this value of d is only slightly lower than the average accuracy for all the 66 sections done in the United States.
THE NORTH AMERICAN DATUM.
Early in the year 1913 the Superintendent of the United States Coast and Geodetic Survey was notified by the director of the Comis6in Geod<jsica Mexicana and by the chief astronomer of the Dominion of Canada Astronomical Observatory that the so-called United States Standard
Datum had been adopted as the datum for the triangulation of those organizations. They also reported that the Clarke Spheroid of 1866, now used in the United States, would be used by them.
Owing to the international character of the datum now adopted by the three countries, the
Superintendent of the United States Coast and Geodetic Survey has changed its designation
from the "United States Standard Datum" to the "North American Datum."

EXPLANATION OF POSITIONS, LENGTHS, AND AZIMUTHS, AND OF THE NORTH AMERICAN DATIM.

The lengths, as already fully explained in connection with the adjustments, all depend upon the Salina, El Paso, Salt Lake, Cheyenne, Provo, and Ambrose bases. The lengths as given are
all reduced to sea level. If the actual length of a line simply reduced to the horizontal is desired,

PRIMARY TRIANGULATION.

81

it may be obtained with all the accuracy ordinarily needed by adding to the sea level length as

given

a

,.
correction

=

n

,,

(length

of{

v
line

as

Jmean
given)
L

elevation

of

the two ends o o7L) UUU

of

the

line

in

me tersl

The

maximum

value

of

this

correction

does

not

exceed

}
14 50

of

the

length for

any

portion

of

the triangulation here published. The maximum error made in the use of the above approxi-

mate

formula

for

the

correction

does

not

exceed

l
45a

of the length for any portion of this

triangulation.
The positions that is, the latitudes, longitudes, and azimuths need special explanation. All of the positions and azimuths have been computed upon the Clarke spheroid of 1866,
as expressed in meters, which has been in use in the Coast and Geodetic Survey for many years.
After a spheroid has been adopted and all the angles and lengths in a triangulation have been fully fixed, it is still necessary, before the computation of latitudes, longitudes, and azimuths can be made, to adopt a standard latitude and longitude for a specified station and a standard azimuth of a line from that station. For convenience, the adopted standard position (latitude and longitude) of a given station, together with the adopted standard azimuth of a line from that station, is called the geodetic datum.
The primary triangulation in the United States was commenced at various points and existed at first as a number of detached portions in each of which the geodetic datum was
necessarily dependent only upon the astronomic stations connected with that particular por-
tion. As examples of such detached portions of triangulation there may be mentioned the early triangulation in New England and along the Atlantic coast, a detached portion of the
transcontinental triangulation centering on St. Louis and another portion of the same triangulation in the Rocky Mountain region, and three separate portions of triangulation in California, in the latitude of San Francisco, in the vicinity of Santa Barbara Channel, and in the vicinity of San Diego. With the lapse of time these separate pieces expanded until they touched or

overlapped.
The transcontinental triangulation, of which the office computation was completed in 1899, joined all of the detached portions mentioned and made them one continuous triangulation. As soon as this took place the logical necessity existed of discarding the old geodetic data used in these various pieces and substituting one for the whole country, or at least for as much of the country as is covered by continuous triangulation. To do this was a very
heavy piece of work, and involved much preliminary study to determine the best datum to be adopted. On March 13, 1901, the Superintendent adopted what was known from that time until 1913 as the United States Standard Datum, but is now known as the North American Datum (see p. 80), and it was decided to reduce the positions to that datum as rapidly as possible. The datum adopted was that formerly in use in New England, and therefore its adoption did not affect the positions which had been used for geographic purposes in New England and along the Atlantic coast to North Carolina, nor those in the States of New York, Pennsylvania, New Jersey, and Delaware. Tho adopted datum does not agree, however, with that used in The Transcontinental Triangulation and in The Eastern Oblique Arc of the United
States, publications which deal primarily with the purely scientific problem of the determina-
tion of the figure of the earth and which were prepared for publication before the adoption of the new datum.
As the adoption of such a standard datum was a matter of considerable importance, it is in order here to explain the desirability of this step more fully.
The main objects to be attained by the geodetic operations of the Coast and Geodetic
Survey are, first, the control of the charts published by the Survey; second, the furnishing of geographic positions (latitudes and longitudes), of accurately determined elevations, and of
distances and azimuths, to officers connected with the Coast and Geodetic Survey and to other organizations; third, the determination of the figure of the earth. For the first anil second
objects it is not necessary that the reference spheroid should be accurately that which most closely fits the geoid within the area covered, nor that the adopted geodetic datum should be

48310 14 6

82

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

absolutely the best that can be derived from the astronomic observations at hand. It is simply desirable that the reference spheroid and the geodetic datum adopted shall be, if pos-
sible, such a close approximation to the truth that any correction which may hereafter be derived from the observations which are now or may become available shall not greatly exceed
the probable errors of such corrections. It is, however, very desirable that one spheroid and one geodetic datum bo used for the whole country. In fact, this is absolutely necessary if a
geodetic survey is to perform fully the function of accurately coordinating all surveys within
the area which it covers. This is the most important function of a geodetic survey. To perform this function, it is also highly desirable that when a certain spheroid and geodetic datum have been adopted for a country they be rigidly adhered to, without change, for all time, unless shown to be largely in error.
In striving to attain the -third object, the determination of the figure of the earth, the
conditions are decidedly different. This problem concerns itself primarily with astronomic observations of latitude, longitude, and azimuth, and with the geodetic positions of the points at which the astronomic observations were made, but is not concerned with the geodetic positions of other points fixed by the triangulations. The geodetic positions (latitudes and longitudes) of comparatively few points are therefore concerned in this problem. However, in
marked contrast to the statements made in preceding paragraphs, it is desirable in dealing with this problem that, with each new important accession of data, a new spheroid fitting the geoid with the greatest possible accuracy, and new values of the geodetic latitudes, longitudes, and azimuths of the highest degree of accuracy, should be derived.
The United States Standard (now the North American) Datum was adopted with refer-
ence to positions furnished for geographic purposes, but has no reference to the problem of the determination of the figure of the earth. It is adopted with reference to the engineer's problem of furnishing standard positions and does not affect the scientist's problem of the
determination of the figure of the earth.
The principles which guided in the selection of the datum to be adopted were: First, that the adopted datum should not differ widely from the ideal datum for which the sum of the station errors in latitude, longitude, and azimuth should each be zero; second, it was desirable that the adopted datum should produce minimum changes in the publications of the Survey, including its charts; and, third, it was desirable, other things being equal, to adopt that datum
which allowed the maximum number of positions already in the office registers to remain unchanged, and therefore necessitated a minimum amount of new computation. These considerations led to the adoption, as the standard, of that datum which had been in use for many
years in the northeastern group of States and along the Atlantic coast as far south as North
Carolina.
An examination of the station errors available in 1903 on the United States Standard
Datum at 246 latitude stations, 76 longitude stations, and 152 azimuth stations, scattered
widely over the United States from Maine to Louisiana and to California, indicated that this
datum approaches closely the ideal with which the algebraic sum of tho station errors of each
class would be zero. 1
The North American Datum, upon which tho positions and azimuths given in this publi-
cation depend, may be defined in terms of the position of the station Meades Ranch as follows:

O

I

If

<=39 13 26.686 A = 98 32 30.506
a to Waldo =75 28 14.52

Points are then said to be upon the North American Datum when they are connected with the station Meades Ranch by a continuous triangulation, through which the correspond-
ing latitudes, longitudes, and azimuths have been computed on the Clarke spheroid of 1866, as expressed in meters, starting from the above data.

' This Is further borne out in the reduction of 765 astronomic stations in connection with the " Supplementary investigation in 1909 of the figure of the earth and isostasy," by J. F. Hayford, published by the Coast and Geodetic Survey.

PBIMARY TRIANGULATION.

83

The principal lists of geographic positions published on the adopted datum throughout the whole United States are contained in the following publications of the Coast and Geodetic Survey and of other organizations:
Appendix 8 of the Report for 1885, positions in Massachusetts and Rhode Island. Appendix 8 of the Report for 1888, positions in Connecticut. \ppendix 8 of the Report for 1893, positions in Pennsylvania, Delaware, and Maryland, Appendix 10 of the Report for 1894, positions in Massachusetts. Appendix 6 of the Report for 1901, positions in Kansas and Nebraska. Appendix 3 of the Report for 1902, positions in Kansas, Missouri, Nebraska, and Colorado. Appendix 4 of the Report for 1903, positions in Kansas, Oklahoma, and Texas. Appendix 9 of the Report for 1904, positions in California. Appendix 5 of the Report for 1905, positions in Texas. Appendix 3 of the Report for 1907, positions in California. Appendix 5 of the Report for 1910, positions in California. Appendix 4 of the Report for 1911, positions in Nebraska, Minnesota, North Dakota, and South Dakota. Appendix 5 of the Report for 1911, positions in Texas. Appendix 6 of the Report for 1911, positions in Florida.
Special Publication No. 11, positions in Texas, New Mexico, Arizona, and California.
Special Publication No. 13, positions in California, Oregon, and Washington. Special Publication No. 16, positions in Florida. Special Publication No. 17, positions in Texas. Special Publication No. 19, positions in Colorado, Utah, Nevada, Wyoming, Montana, South Dakota, and
North Dakota.
Appendix EEE, pages 2905-3031, Annual Report of the Chief of Engineers, 1902, positions of points on and
near the Great Lakes.
Publications of the Massachusetts Harbor and Land Commission.
Various bulletins of the United States Geological Survey.
EXPLANATION OF TABLES OF POSITIONS.
In the tables of positions, the latitude and longitude of each point are given on the North American datum (see p. 80), also the length and azimuth of each line observed over, whether in one or both ways. Along with the latitude and longitude of each point the lengths and
azimuths are given of lines from that point to other points of the triangulation. No lengths or
azimuths are repeated, and for a given line the length and azimuth will generally be found opposite the position of the last mentioned of the two stations involved.
For the convenience of the draftsman a column of "seconds in meters" is given, in which is placed the length (in meters) of each small arc of a meridian or parallel corresponding to the seconds of the given latitude or longitude. To facilitate further the use of the tables, a column is given of the logarithms of the lengths. It must be remembered that it is the logarithm which is derived first from the computation, the lengths given in this table being then derived from the corresponding logarithms.
The rule followed in recent publications of this office has been to give latitudes and longitudes to thousandths of seconds for all points the positions of which are fixed by fully adjusted triangulation. Points, the positions of which are given to hundredths of seconds only, are marked by footnotes as being without check (observed from only two stations) or checked by
verticals only.
In the columns giving azimuths, distances, and logarithms of distances, the accuracy is indicated to a certain extent by the number of decimal places given, it being understood that in each case two doubtful figures are given. In some cases there is very little doubt of the
correctness of the second figure from the right, while in a few cases some doubt may be cast
on the third figuro from the right.
Those tables may bo conveniently consulted by using as finders the 1 1 sketches and the
index at the end of this publication. In the third column of the index will be found for each point a reference to the page on which its description is given, in the fourth column the page on which its elevation above sea level will be found, and in the fifth column the number of the sketch on which it appears.
The following conversion tables are inserted for the convenience of those who may wish
to convert the distances or elevations givon in this publication from meters to feet or from feet
to meters.

84
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U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

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88

U. S. COAST AND GEODETIC SURVEY SPECIAL PUBLICATION NO. 19.

.

GEOGRAPHIC POSITIONS.

One hundred and fourth meridian.

BUtioa.
Principal points. Elbert, 1912 Hilltop, 1912 Morrison' (U. 8. O. 8.), 1912. Douglas, 1912
Indian' (U.S. O.S.), 1912.
Watkins astronomic, 1912 Brighton' (U. 8. O. 8.), 1912. Boulder' (U. S. 0. 8.), 1912.. Horsetooth' (U. 8. G. S.), 1912. Dewey' (U. 8. G. S.), 1912 Warren, 1912 Twin, 1912 Wadill, 1912
Bussell, 1912 Greentop, 1912 Whitaker, 1912 Ragged, 1912
Cheyenne west base, 1913 Cheyenne east base, 1913 Chugwater, 1912 Notch, 1912 Coleman, 1912 Haystack, 1912 Hobbs, 1912

Latitude and
longitude.

Seconds in meters.

Azimuth.

Back azimuth.

To station.

39 14 02. 930 104 34 33. 167

90.5 343 07 56. 47 163 10 20.77 Divide 795.5 42 59 00.56 222 41 19.86 I Pikes Peak..

39 27 19.099 104 38 45. 755

589.0 1093.9

344 49 56.55 346 08 18.69
26 51 45.60

164 55 01.05 166 10 58.83 206 36 41.84

Divide Elbert Pikes Peak..

39 40 09.669 105 13 09. 104

298.2 217.0

295 34 22.98 310 54 07. 84 350 35 37.49

115 56 17. 17 131 18 39.47 170 42 17.31

Hilltop Elbert
Pikes Peak.

/ 39 31 17. 498 539.6 346 31 08.07 166 31 54.95 Hilltop... \104 39 59. 472 1420.5 109 14 48.94 288 53 40.82 Morrison.

39 39 18. 826 104 35 05.801

580.6 13S.3

13 19 47. 36 23 47 37.97 25 17 51.63 59 47 09. 64 91 51 09.32

193 17 27.29 203 30 13. 10 205 14 44. 49 239 12 22. 83 271 26 51. 98

Hilltop. Pikes Peak.
Douglas Bison
Morrison

/ 39 44 43. 813 1351.2 350 US 03.53 170 08 50. 23 Indian . . . \104 36 18.915 450.4 81 04 24.38 260 40 52.36 Morrison.
/ 40 01 37. 866 1167.9 340 19 54.87 160 26 31.41 Indian... \104 45 24.750 586.9 45 01 51.47 224 44 05.02 Morrison .

39 57 37.355 105 17 40. 611

1152.1

260 39 07.01 291 47 49.68 298 54 42.35 348 40 25.56

80 59 51. 20 112 14 20.01 119 21 57.99 168 43 19. 41

Brighton Watkins astronomic. . Indian Morrison

/ 40 32 22. 856 705.0 326 34 17.88 146 51 20. 48 Brighton.

\105 11 46.319 1090.0

7 26 54.96 187 23 06.04 Boulder. .

40 30 25. S68 104 33 16. 100

797.9 379.1

17 58 02. 72 46 17 31.88 94 00 17.52

197 50 11.75 225 48 50- 82 273 35 16.43

Brighton Boulder Horse tooth..

41 01 11.747 104 52 07. 859

362.4 334 54 07. 47 155 06 26. 45 Dewey
183.7 27 29 54.69 207 17 04. 97 Horsetooth.

41 02 54.064 105 16 02.530

1667.9 59.1

275 14 57.94 314 43 30 82 353 54 24. 76

95 30 39. 81 135 11 27.05 173 57 12. 15

Warren
Dewey
Horsetooth.

/ 41 15 12.609 \104 57 18.432

389.0 344 22 09.52 164 25 33.83 Warren. 429.2 49 06 21.40 228 54 01.69 Twin . . .

41 14 12.177 105 19 04.365

375. 7 101.7

266 22 19.71 302 24 34.82 348 31 26.00

86 36 40. 68 122 42 18.07 168 33 25. 63

Wadill.. Warren . Twin...

41 21 01. 198 105 19 48.921

37.0 1137.3

288 46 15.42 351 02 25.01 355 17 56.36

109 01 06. 78 171 04 54. 13 175 18 25. 77

Wadill.. Twin... Russell..

I 41 23 56.362 1738.8 348 33 51.26 168 35 26.95 Wadill.... \104 59 38. 801 901.3 79 14 01.89 259 00 42. 02 Greentop..

41 26 20. 835 105 20 39. 192

642.8 909.8

278 32 31.95 302 12 20. 11 353 14 27. 24

98 46 25.78 122 27 45.47 173 15 00.48

Whitaker. Wadill.... Greentop..

/ 41 17 56. 459 1741.8 198 18 18. 15 18 20 02. 62 Whitaker. \105 02 16.930 393.9 306 00 42. 90 126 03 59.82 Wadill....

41 16 49.077 104 57 45.442

1514.0 1057.5

108 14 19.23 168 42 10.42 348 04 07.26

288 11 20.08 348 40 55.54 158 04 25.07

Cheyenne west 1 Whitaker
Wadill

f 41 48 06. 161 190.1 356 10 17.77 176 11 43.32 Whitaker.

105
1

01

47. 644

1100.0

33 08 55.52 212 56 23.95 Ragged...

[ 42 02 21.540 105 19 46.264

664.6 1064.0

316 36 59.15 338 27 36 65
1 03 .07

136 48 59.78 158 41 00.22 181 02 46.44

Chugwater . Whitaker..
Ragged

r 42 22 03.568 ,105 07 13. 823

110.1 353 10 06.76 173 13 45.38 Chugwater. 316.3 25 23 56.13 205 15 30.66 Notch

42 20 29.575 104 38 04. 961

912.6 113.6

28 44 34.16 59 54 36. 24 94 IS 28. 48

208 28 40.87 239 26 36.36 273 58 50.24

Chugwater. Notch
Coleman . . .

42 34 50. 753 1566.1 104 35 06. 461 147.3

8 44 32. 82 1<*8 42 32.32 Haystack. 61 54 54. 49 241 33 13.02 Coleman..

' Identical with a tertiary

ion of the U. S. Geological Survey.

DLslance

Logarithm.

MeUrt. 18933. 89 59573.16

4.2772388 4. 7750507

44205.34 25286.81 76407. 25

4.6454747 4. 4028941 4.8831345

54688.99 73489.54 93241.38

4.7378999 4. R8622M 4.9696087

7560.25 3.8785359 50230.47 4.7009672

22809.08 98724. 61 16415.27 91149.94 54450. 86

4. 3581077 4.9944254 4. 2152479 4.9597564 4. 7360048

10173.11 4.0074536 53325.64 4. 7269361

43841.69 4.6418873 56071.86 4. 7487449

46520. 13 63635.83 60578. 17 32951. 10

4. 6676409 4.8037017 4. 8424730 4.5178699

68074.92 4. 8329872 64867. 40 4.8120265

560(19.99 87486. 98 54499. SO

4. 7482655 4.9419434 4. 7363949

62822. 61 4.7981160 60064.56 4. 7786183

33661.38 85048.51 56805.20

4. 5271319 4.9296667 4.7543881

26931.76 4. 4302648 34729.35 4. 5406967

30465.35 44737.06 21344.32

4.4838061 4.6506675 4.3292824

33207.90 33949. 22 12660.57

4.5212413 4.5308298 4. 1024531

16484.04 4. 2170637 28636.04 4. 4569130

29607.27 38542. 13
9929.70

4.4713984 4.5859357 3.9969363

11695. 67 4.0680250 8591.41 3.9340644

6650.437 3. 8228501 13442.53 4.1284810
3041.67 3.4831115

44827.29 4.6515425 48041.56 4.6816171

36252. 52 76399. 49 66672. 95

4.5593383 4. 8830905 4.8239497

63307. 03 4.8014519 40319.54 4.6058386

68300.94 66491. 43 40130. 24

4.8344267 4. 8227657 4. 6034718

26883.40 4.4294852 49987.22 4. 6988590