p CD
U.S. Coast and Geodetic Survey
Geodesy
CO
n
No. Ill J
DEPARTMENT OF COMMERCE
U. S. COAST AND GEODETIC SURVEY
E. LESTER JONES, SUPERINTENDENT
GEODESY
iNERAL INSTRUCTIONS FOR PRECISE AND
SECONDARY TRAVERSE
U. S. COAST AND GEODETIC SURVEY
PRICE, 10 CENTS
old only by the Superintendent of Documents, Government Printing Office
Washington, D. C.
WASHINGTON
GOVERNMENT PRINTING OFFICE
1919
Serial No. Ill
DEPARTMENT OF COMMERCE
U. S. COAST AND GEODETIC SURVEY
E. LESTER JONES, SUPERINTENDENT
GEODESY
GENERAL INSTRUCTIONS FOR PRECISE AND
SECONDARY TRAVERSE
U. S. COAST AND GEODETIC SURVEY
Special Publication No. 58
PRICE, 10 CENTS
Sold only by the Superintendent of Documents, Government Printing Offloe
Washington, D. C.
WASHINGTON
GOVERNMENT PRINTING OFFICE
1919
r^i
f(= %> ^'^.:.
llL
CONTENTS.
Page.
Introduction 5
General statement 6
Location of traverse stations 6
Measurement of distances 7
Check measurement 10
Angle measurements 12
Azimuth stations 14
Marking stations 14
Descriptions of stations 15
Inclination corrections 16
Records and computations 19
Traverse measurement 20
Check measurement 21
Y levels over stakes 21
Precise levels 22
Sample computations and tables 23
Computation of inclination correction 24
Inclination correction table 25
Inclination correction table for 50-meter tape lengths 28
Computation of Savannah to Norfolk traverse line 33
Certificate of standardization 34
Temperature corrections 36
Tape corrections for tape No. 552 when supported through-
out. . ., 36
Tape corrections for tape No. 552 for various methods of sup-
port 37
Projection computation 38
Computation to close loops 39
Computation of angle closure for loop 40
Computation of distance for loop 40
General instructions for secondary traverse 41
Inclination correction table 42
Factors for inclination correction 44
Measurement of angles 45
Azimuth stations 46
Index 47
3
ILLUSTRATIONS.
Page.
Figure 1. Section of traverse line 19
Figure 2, Diagram for projection computation, one offset sta-
tion 37
Figure 3. Diagram for projection computation, both stations
offset on same side of track 38
Figure 4. Diagram for projection computation, stations offset
on opposite sides of track 39
Figure 5. Diagram for loop computation 40
4 .
GENERAL INSTRUCTIONS FOR PRECISE AND SEC-
ONDARY TRAVERSE, U. S. COAST AND GEO-
DETIC SURVEY.
INTRODUCTION.
During the early part of 1917 the United btiiu-^ < un^t and (Jeodetic
Survey started work on a system of precise traverse lines in Georgia
and Florida, which have since been extended into other States along
the Atlantic coast. This work was called for by the Corps of Engineers
of the United States Army to give the necessary primary control for
various military maps in that section of the country. Traverse was
used instead of triangulation as the general lay of the land and the
prevalence of high timber would have made high scaffold signals
necessary to give clear lines for triangulation. The traverse lines
followed the railroads, and so required but little signal building or
cutting of timber.
Although traverse has been used in place of triangulation by the
United States Coast and Geodetic Survey at various times in the past
it has never been used on so large a scale as in the recent work. The
methods employed in the work were largely experimental at first,
but they have been gradually changed and improved until they have
become practically standard.
It has been thought advisable to publish these general instructions
in order to preserve the knowledge that has been gained, to standardize
any future field work as much as possible, and to prevent the continued
use of any methods which have been found inefficient or unwise.
Wlien a precise traverse is to be run over country roads or along
beaches, separate instructions supplementing these general instruc-
tions will be issued to the officer in charge of the general operations.
Changes iu these general instructions will undoubtedly be made
from time to time as better methods are developed. The members
of the field and office forces of the Survey engaged on the precise
traverse and its computations are invited to offer suggestions which
may make it possible to do the work more expeditiously without
decreasing the accuracy or increasing the cost.
5
6 TT. S. COAST AND GEODETIC SURVEY.
GENERAL STATEMENT.
Precise traverse will, in general, be done in those sections of the coun-
try where the topographic conditions make it impracticable to carry
on primary triangulation. The work will supplement the primary
triangulation in furnishing the fundamental control for the surveys and
maps made by federal, State, or other organizations and by private
individuals. The conditions which make it more desirable to carry
on precise traverse than primary triangulation are flatness of the
land and presence of timber. Under these conditions it is neces-
sary to have comparatively short lines in the primary triangulation, and
to erect high scaffold signals at the stations in order to make them inter-
visible.
These instructions are designed for the highest class of traverse, equal
in accuracy to primary triangulation, and for secondary traverse com-
parable in accuracy with secondary triangulation. Should it be
necessary to carry on tertiary traverse for the control in local areas,
special instructions will be furnished to officers in charge of the field
work.
LOCATION OF TRAVERSE STATIONS.
1. In general the traverse will be run along a railroad track. The
stations should usually be at the intersection of two contiguous tan-
gents of the railroad. Occasionally when the tangent is particularly
long and the profile of the road between its ends such that it would
be difficult to get a line clear between the ends of the tangent, one or
more intermediate stations should be placed at the side of the road.
The profile of the road along the tangent will be the deciding factor in
the location of the intermediate stations. If the ground is practically
level along such a tangent, the stations may be placed almost anywhere,
and should be located near a crossroad, if convenient.
2. In general the stations along any tangent should not be more than
4 or 5 miles apart, as delays caused by observing longer lines will more
than offset the time gained by having fewer observations. It is also
true that stations should be placed fairly close together, so as to be
of the maximum benefit for public and private surveys.
3. A traverse station should be placed near each railroad crossing or
point where a branch line makes off from the line followed by the trav-
erse. Also a traverse station should be located at or very near each
town along the route of the traverse, and when at all practicable a
second traverse station should be located ^vdthin 2 miles of the town
in order to enable local engineers and surveyors to obtain an azimuth
with little difficulty.
GENERAL INSTRUCTIONS FOR TRAVERSE. 7
4. When curves are numerous for any given distance and the tangents
very short, it will be well to lay out comparatively long lines extending
over several curves in order that the azimuth may be carried forward
with greater strength than if it had to be carried through a number of
short lines. The distance between the ends of such a long line can be
carried by measurement and angles along the track. This latter work
would be considered in the nature of a subsidiary scheme of angles.
Care must be taken that each end of such a long line is carefully tied
into the scheme running along the railroad between its ends.
MEASUREMENT OF DISTANCES.
6. The lengths in the traverse will depend on measurements made
with 50-meter invar base tapes, standardized at the Bureau of Stand-
ards before and after use in the field.
6. The length should depend upon one measurement in one direction
only, unless a blunder has been made. There should be three primary
tapes in the party, two used in measurement and one used as a stand-
ard. About one-half of the measurement of any considerable portion
of the travei*se should be made with each of the working tapes. A com-
parison should be made of the three tapes at intervals along the trav-
erse in order to detect any changes that might occur in the length of one
or both of the working tapes. No tape should be used ior more than
15 kilometers of measurement without being recompared. The com-
parison of the three base tapes can best be made on the stakes used in
the traverse measurement between a point of tangency and a traverse
station, A distance of at least 100 meters should be used in making the
comparison. Metal strips should be used on the top of the stakes em-
ployed for the comparison to prevent parallax in marking. The com-
parison of the tapes with a record of temperatures, etc., should be
entered in the traverse record.
7. A tape should be sent to the office for restandardization if it differs
by more than 1 part in 75 000 from the standard tape.
8. As soon as a new tape has been received from the office a compari-
son of this tape should be made with the standard tape and the other
working tape or tapes. No actual field work should be done with the
new tape until such a comparison has been made.
9. Do not straighten out kinks in the tape. If such exist and the tape,
in consequence, can not be used for measurement, send the tape to the
office with a letter explaining in detail this condition, giving date on
which the injury or injuries occurred.
8 U. S. COAST AND GEODETIC SURVEY.
10. The base tapes used in the field should have a tension applied
of 15 kilograms, and this same tension will be used during the standardi-
zation at the Bureau of Standards.
11. Two thermometers should be attached to the tape, one at each
end, during measurement, and they should be read and recorded at
each tape length. Special centigrade thermometers, for use during
traverse or base measurement, will be furnished by the office on appli-
cation. In attaching the thermometers to the tape suitable cases
should be used which will insure good contact with the tape and pre-
vent the breaking of the thermometer. They should be attached to the
tape beyond the end graduations in order to guard against any tendency
to kink the working part of the tape. The cases can be fastened to
the tape by means of adhesive tape, and this will make it possible to
detach them easily when the tape is wound on the reel.
12. A second measurement, with a primary tape, will be made over
any section of the line of traverse which is to be used as a base line from
which to start an arc of primary triangulation.
13. When measuring along a railroad, the distances along the tan-
gents will be measured with the 50-meter tape, supported throughout
its length on top of a rail of the track. The distances from the points
of tangency to the traverse stations at the intersection of tangents,
should be measured over stakes especially set to support the tape.
14. In measuring up to or away from a station the record should indi-
cate clearly whether the tape was held on the station mark itself or on
the bench or table built over the station mark. In this connection do
not use the word "tablet" for the station mark, as it is easily confused
with th e word ' ' table . ' '
15. In measuring the offset distance between the point on the rail
and the station itself, for stations along tangents, the record should
show whether the measurement was made horizontally or on an incline,
and in the latter case the difference in elevation must be given,
16. The record should also indicate clearly whether the traverse was
measured to a rail station, to the rail opposite a station, or to the station
itself. A rail station proper is one which is actually on the rail itself
and is occupied with a theodolite for observations of the same degree
of accuracy as for the regular scheme. A rail station is usually put in
to aid in determining some point at some distance from the track. It
is very rare that there will be another traverse station within one or two
hundred meters of the rail station.
17. ^\^lile measuring along the top of a rail, the position of the for-
ward end of the tape can be transferred to the rail with an ordinary
cheap glass cutter. In measuring over stakes, the forward end of the
GENERAL INSTRUCTIONS FOR TRAVERSE. 9
tape will be marked directly on the top of the stake by means of a
knife cut or a mark Avith a glass cutter. If the top of the stake is badly
battered, an ordinary pin may l^e driven in to mark the end of the
tape.
18. The rear contact man must use the same end of the small scratch
on the rail as was used by the forward contact man. This will be
brought about by the two contact men always standing on the same
side of the tape.
19. Great care must be exercised in counting and recording the
number of tape lengths in a section. At least one other man in the
party besides the recorder should count the tape lengths entirely
independently. It is suggested that a system of counting tape lengths
similar to the one used in ordinary surveying be tried out by the
taping party. Small tin or aluminum rings or harness rings two or
three inches in diameter could be used for the purpose. For each
tape length one of these rings could be left beside the rail close to the
mark on the rail by the forward contact man and later picked up by
the rear contact man. Twenty one rings could be used and 20 of them
passed to the forward contact man at the end of each kilometer. A
piece of colored rag tied to the ring will enable the rear contact man
to find it readily. The rings can be carried by means of a spring
attached to the handle of each of the tape stretchers.
20. To av(nd gross errors, all fractions of a tape length less than
about 49.9 meters, which enter into a section, should be measured as
set-ups. The set-ups will be measured with a standardized pocket
steel tape or metal scale, except as provided for in paragraph 21.
21. Wlien a fraction of a tape length is greater than 25 meters, it
should be measured as two set-ups; the first one as half a tape length
and the balance as a set-up to be measured with the pocket steel tape.
A half tape length can easily be measured by placing a mark with a
pencil or otherwise near the center of the base tape. Then the dis-
tance from the stake ending the last full tape length to a point on a
stake set approximately 25 meters can be measured twice, once with
each half of the tape, and the error in marking the middle of the tape
can thus be eliminated.
22. In setting stakes on the prolongation of tangents it will be of
advantage to begin at the station and work toward the rail in either
direction, for this will bring the minimum number of set-ups on the
stakes, and all half tape lengths on the stakes will be eliminated.
When measuring by this method, ail necessary large set-ups will occur
on the rail, where they are easily measured.
114585' 19 2
10 U. S. COAST AND GEODETIC SURVEY.
23. A railroad curve often occurs in a deep cut, which makes it
necessary to put the traverse station at the top of a high bank and
renders the staking and taping difficult. If a saving of time can be
made, it is permissible to compute the distance from the stake,
beyond which the taping would be difficult, to the station by means
of a triangle. A small base should be measured from this stake to
another stake at some convenient point along the curve which will
give a triangle with a good angle of intersection at the station. The
angles should be measured with such accuracy as to insure against an
error as great as one-half centimeter in the computed distance. The
same method may be used in going ahead from the station.
24. During the measurement with the base tape, indicate in the
record the distance from the initial point of the section to crossroads,
railroad stations, water towers, section houses, semaphores, bridges,
culverts, mileposts, banks of rivers, State and county lines, decided
changes of grade and possibly some other objects, in order that the
traverse may be properly connected with the alignment of the rail-
road, and thus make it possible to utilize the railroad surveys in
making maps of the country through wliich the traverse runs. These
measurements will also be utilized in making a determination of the
geographic positions of some of the objects to which distances are
measured. The record must show whether the taping is along the left-
hand or right-hand rail. Instructions in regard to the angles to be
measured to objects along the road are given on another page.
25. The designations of the points of tangency and their distances
from the initial station of the section should be carefully recorded;
as, for example, P. T. 42=24-f-4. (24+4 means 4 meters beyond the
end of the 24th tape length). In case the precise leveling precedes
the taping, the designation of all permanent and temporary bench
marks along the track, and their distances from the initial station,
should also be recorded, as for example, 6+20=T. B. M. 115.
26. No measurement should be made with the primary tape when
the rail is wet, and when it is damp measurements should be made
with caution. It is the experience of those engaged on measurement
along railroad tracks that the tape tends to stick to the rail when the
latter is wet, and therefore errors will result.
CHECK MEASUREMENT,
27. A single check measurement will be made of each section of
the traverse with a 300-foot tape. The best means of recording the
number of full tape lengths is to read and record the temperature each
time. Only one thermometer need be used. Counters may be used
GENERAL INSTRUCTIONS FOR TRAVERSE. 11
as a check on the number of tape lengths. ^Tien measuring from the
P. T. point to the station the tape may be supported on the stakes
that were used for the invar tape, but no other regard should be
given to these stakes. Plumb lines should be used at the ends of
the tape, the same as in ordinary chaining, and the point marked
on the ground with an iron pin.
28. The 300-foot tape may be supported along the top of the rail
or on the ties close to the rail while measuring between tangent
points. The position of the forward end of the tape may be indi-
cated on the top of the rail by a pencil mark. The location of the
pencil mark may be indicated by a cross made with chalk or keel
on the rail or a tie. The distances between the points of tangency
and the traverse stations should be measured as in ordinary chain-
ing without reference to the original stakes.
29. A moderate pull only should be used with the 300-foot tape. It
is believed that five kilograms is sufficient. The object of having a
light pull is to make it possible to have the measurement made with
a very small party. A heavy pull would require the use of stretchers
at the forward and rear ends of the tape. The lengths of the tapes
under the standard pull and temperature must be known.
30. During the check measurement, distances should be indicated
in the record from the traverse station at the beginning of the section
to the country road and railroad crossings, to bridges, water tanks,
mileposts, and other objects, as given in paragraph 24, in order that a
check may be made on the determination of the distance of these
objects from the traverse station. Designations of all points of tangency
and all bench marks along the track and their distances from the
initial station should be carefully recorded; as, for example, l-t-235=
P. T. 42, and 11+135=T. B. M. 115.
31. Measurements with the 300-foot tape may be made under any
conditions of the weather.
32. If the temperature is not recorded for each tape length, as smg-
gested in paragraph 27, the approximate temperature of the tape should
be entered in the record at least once for each section.
33. If the measurement with the 300-foot tape differs by more than
a few decimeters in any section from the distance given by the meas-
urements with the 50-meter base tape, a second measurement with the
300-foot tape will be made. If this second measurement agrees closely
with the first one made with the 300-foot tape, then a second measure-
ment will be made with the 50-meter tape.
12
IT. S. CX)AST AND GEODETIC SURVEY.
ANGLE MEASUREMENTS.
34. In general, the highest type of instrument will be used in meas-
uring the angles of the main line of traverse stations. When a direction
instrument is used which is read by micrometer microscopes, the
angles will be measured in eight positions of the instrument. The
initial settings for these positions are as follows:
Position
No.
Reading.
00 40
30 01 60
60 03 10
90 04 20
125 00 40
155 01 50
185 03 10
215 04 20
36. When the measurement of an angle in the main line of traverse
stations is made with a 7-inch repeating theodolite, a sufficient number
of observations should be made to obtain the same degree of accuracy
as can be obtained by measuring the angle in eight positions with the
direction theodolite. It is probable that about three sets, each con-
sisting of six repetitions of the angle with the telescope direct and six
repetitions of the explement with the telescope in the reversed posi-
tion, will be needed to secure the degree of accuracy desired.
36. A position for a direction instrument consists of a pointing on
each object in the horizon, in both direct and reverse positions of the
telescope, for one initial setting of the horizontal circle.
37. Observations for angle measurements at the principal stations of
the traverse should be made only when the conditions are favorable.
To^an inexperienced observer this can be determined only by experi-
ment. It will be found that a steady signal does not always mean that
observing conditions are perfect, t<Sr it is possible that there may be
lateral refraction under the conditions that obtain when the signal
appears steady that might be absent when the signal is tremulous or
jumpy. Excellent observations can be obtained on a signal that is
moderately unsteady when a number of repetitions of the angle or
direction is made. The amount of unsteadiness that will still permit
good observations to be obtained can be determined approximately
by the observer. He can observe some one direction under various
GENERAL INSTRUCTIONS FOR TRAVERSE. 13
weather conditions and note the agreement in the angle or direction
obtained under each condition.
38. The 7-inch repeating theodolite should be used in measuring all
angles at subsidiary traverse stations which are not used for carrying
the main azimuth ahead. One set of six repetitions of the angle with
the telescope in the direct position, followed by a set of six repetitions
of the explement of the angle with the telescope in the reversed posi-
tion, is sufficient.
39. The instrument and the object sighted upon should be accu-
rately centered, or, if they are eccentric to the traverse stations, the
eccentric distance and direction should be carefully measiured and
entered in the records. The direction from the eccentric instrument
station to the true station, or from the station to the eccentric object,
should be entered in the list of directions and should be referred to
the same initial station as the other directions from that station.
Confusion is caused by recording the eccentric as "2.5 centimeters
right."
40. One of the greatest sources of error in triangulation or other angle
measurements is what is known as phase. This is caused by uneven
illumination of the object sighted on, thus causing the observer to
point his cross wires to the right or left of the center of the object.
When the sun is shining, a round or square pole \^'ill always have
phase unless the sun is exactly in line with the instrument and the pole,
except that a square pole will not have phase if one face of the pole is
at right angles to the line to the observer. ^ Phase may be eliminated
almost entirely by having a thin strip of board centered directly over
the station mark. It is prt)bable that the signal on which the instru-
ment will be mounted can be made in such a way that a pole 4 inches
square can be set into the top of the tripod. This pole can be con-
structed of two pieces of 2 by 4 inch material, and between the two
pieces at the upper end can be placed the thin piece of board on which
the observations are to be made.
41. At each traverse station observe directions to such objects along
the track as mileposts, water towers, semaphores, railroad stations, sec-
tion houses, and any other objects that may be \isible. (See paragraph
24.) With the angle or direction to these objects and the distances
measured during the determination of the distances along each section,
the geographic positions of a number of objects which may be of great
geographic value may be determined. It is particularly important
that angles or directions should be observed to objects distant from the
railroad which may be determined by observations from several traverse
stations. Each object of a more or less permanent nature whose geo-
14 U. S. COAST AND GEODETIC SURVEY.
graphic position can be computed from the angles and distance measure-
ment made by the traverse increases the engineering and geographic
value of the work.
AZIMUTH STATIONS.
42. Owing to the fact that errors in angle observations on a traverse
tend to accumulate, it is necessary to observe frequent astronomic
azimuths. The observations should be made on Polaris.
43. In general, an azimuth station of primary accuracy will be
established at intervals of about 30 or 35 traverse stations. Observa-
tions for azimuth should be made only at main line traverse sta-
tions (see par. 46). The locations of the Laplace azimuth stations
will be given in the special instructions for each particular piece
of work.
44. The azimuths may be observed by the method of repetitions
with a 7-inch theodolite. For any instrument double the number of
obsei'vations should be made for azimuth as for a horizontal angle at a
main traverse station. The probable error of a primary azimuth
should not exceed 0.^^50 and for a Laplace station should not exceed
0.^^30.
45. At intervals of about 10 traverse stations secondary azimuth
stations should be established between the primary azimuth stations.
The accuracy of the secondary azimuths should be that represented by
a probable error of about 6^\
46. In order that the geodetic azimuth may be carried along the
traverse with a minimum ewor, it will be well to have stations on or
off the road or railroad along which the traverse is measured which are
intervisible for much longer distances than between the regular traverse
stations. The azimuth can be carried through these extra stations;
but whenever used, the extra stations should be connected in azimuth
and distance with the regular traverse stations and should always be
used instead of one of the regular stations for the azimuth observations.
The angles measured at regular stations along any portion of the line
where there are extra stations should be adjusted to the angles meas-
ured at the extra stations. The extra stations, rather than the regular
stations along the same piece of traverse, will be used in determining
where an azimuth station will be located.
MARKING STATIONS.
47. The standard triangulation and reference marks should be used
in marking the traveree stations. (See p. 42 of Special Publication
No. 26.) They should be set into heavy blocks of concrete or stone to
iiasure permanency.
GENERAL INSTRUCTIONS FOR TRAVERSE. 15
48. On the standard station and reference marks should be stamped
the name of the traverse station, and, if the station mark is used as a
bench mark, the letter and number designating the bench mark should
also be stamped on the tablet.
49. All traverse stations should be marked when each two contiguous
stations are a mile or more apart. When the track along which the
traverse is made has numerous curv'es and short tangents, some of the
traverse stations need not be marked in a permanent manner. In
general, there should be a permanently marked station at least every
3 miles along the traverse, except, of course, when a section of the
traverse along a tangent is more than 3 miles in length. Wlien a sta-
tion is marked in a permanent manner, the next station back of it or
ahead of it must be marked also in a permanent manner, in order that
anyone using the traverse may be able to obtain an azimuth. The
station should be marked with an underground as well as a surface
m?,rk. The underground mark may be a bottle or some other object,
preferably set in a small block of concrete. It is frequently the case
that the underground mark will be left intact when the surface mark
is destroyed .
50. At each station marked in a permanent manner there should be
placed a reference mark. This reference mark should consist of con-
crete or rock, into which is set a standard inscriljed reference m'ark.
It should be so accurately connected in distance and azimuth vnth the
station mark that it may be used as the station mark if the latter should
be destroyed. It should be placed in such a position that it will not
be liable to be destroyed by the same agency that might destroy the
station mark itself.
51. Traverse stations which are not marked in a permanent manner
should be marked temporarily with a suitable wooden or other kind
f stake in order that the station may be available for several years
after its establishment. Wood which resists decay, such as cedar or
Georgia pine, should be used if it can be obtained easily.
DESCRIPTIONS OF STATIONS.
52. All stations of the traverse, whether marked permanently or in
a temporary manner, should be described in such a way that they may
be recovered easily. The descriptions should include the distance
from the nearest milepost and railroad station and also the offset dis-
tance from the nearest rail of the railroad track. The station mark and
the reference mark should be described by notes, as given on pages 42
and 43 of Special Publication No. 26. If a new type of station mark
is used which is not covered by one of those notes, a new note should
16 U. S. COAST AND GEODETIC SURVEY.
be added and given a number. The Chief of the Division of Geodesy
should be notified that a new note is being used, and the wording of the
note and its number should be furnished him as soon as practicable
after its adoption,
63. It is often desirable in writing descriptions of stations to give
approximate distances to various near-by objects which are not impor-
tant or definite enough to justify an accurate measurement to them.
Whenever possible, these distances should be paced, as gross errors are
often made in estimating, and erroneous distances cause confusion
when the station is recovered .
54. The descriptions should be made on the cards furnished by the
office for the descriptions of triangulation stations. The writer of the
descriptions should have in mind that the descriptions will be pub-
lished in the near future, and they should be in such a condition, there-
fore, that the minimum amount of editing will be necessary in pre-
paring the manuscript for the printer. Any facts essential to the re-
covery of the station should be given, but those features of only a tem-
porary nature should not bfe mentioned in the description.
INCLINATION CORRECTIONS.
66. In general, a line of precise levels will be run along the line of
traverse at the same time that the traverse is measured. This leveling
will be connected with such points of the traverse as will make it pos-
sible to compute the inclination corrections of the measured distances.
Precise leveling will be carried on in accordance with the general in-
structions for precise leveling contained in Special Publication No. 22
of the United States Coast and Geodetic Survey, or in later leveling
publications, except as may be modified by the instructions for car-
rying on primary traverse.
66. There will be determined by the precise leveling party the
elevations of any points of decided change in grade along a tangent.
There will also be determined the elevation of the rail opposite all
mileposts, water towers, section houses, railroad stations, and over all
bridges and culverts. There will also be determined the elevation of
all points of tangency which have been indicated by the traverse
measuring party or which may be indicated by the leveling party, if
the leveling precedes the measurement. Points of tangency should
be marked on the rail or ties of the track by a cross, or otherwise. A
designation or number should be given to the point of tangency as,
for example, P. T. 42 ^in order that there may be no doubt as to the
identification of the records of the measuring and leveling parties for
any one section.
GENERAL INSTRUCTIONS FOR TRAVERSE. 17
57. The traverse stations which have been marked in a permanent
manner will be used as the bench marks on the line of levels. In
addition, the leveling party \v411 establish bench marks in each of the
towns and cities through which the line passes, in order that the city
surveyors and engineers may have sufficient bench marks to control
the elevations of their various public works.
58. None of the reference marks should be used as bench marks in
the line of levels, as it has been found in the Office, when making the
final computations, that the records are apt to be confusing when two
bench marks are so close together as a traverse station and its reference
mark. The precise leveling done in connection with the primary
traverse along a railroad should follow the setting of the station marks
of the traverse stations. This will make it possible to use the traverse
stations as bench marks and mil avoid the necessity for setting other
bench marks. If the leveling party should be held back at all on
this account, the members of the leveling party can assist the traverse
party in any way that is possible and work on their ovm records until
the marking of the traverse stations has been carried ahead. The
traverse party should do everything that is possible to keep the
stations marked ahead of the leveling, in order that the leveling party
may not be delayed.
69. When carrying the line of levels from the railroad into a town
for the purpose of connecting with the bench marks established on
masonr>', brick, concrete, or other structures, the place where the
leveling left the track should be indicated in the records. When the
leveling has returned to the track, the rod should be held as nearly
as possible on the same turning point that was last used when the line
of levels left the track and a proper note should be made in the
record. If this is done, it will be possible to get a continuous profile
of the track over which the traverse is run, for use in computing the
inclination corrections.
60. Two rod readings should be taken on the rail opposite each trav-
erse station or bench mark which has been established on the side
of a tangent. One of those readings should be made from the instru-
ment station just before getting to the point opposite the traverse sta-
tion or bench mark, and the second rod reading should be made from
the first instrument station after passing the traverse station or bench
mark. This will make it possible for the computer to get a continuous
profile between traverse stations and also obtain a rough check on the
measured distances. It should be borne in mind that distances as
well as elevations are computed from the precise levels. If the
114.58.5" 19 3
18 U. S. COAST AND GEODETIC SURVEY.
leveling is done according to these instructions, gross errors in the
taping will be discovered in computing the distances for the grade
corrections.
61. At all times when an extra rod reading is taken it should be
indicated in the record by the letters F or B according to whether the
reading was taken in front of the instrument or back of it.
62. There should be noted in the record the points in the line of
levels at which decided changes of grade occur.
63. Care should be taken to show clearly in the record when
readings are made opposite a railroad station if there is a traverse
station near-by having the same name.
64. In carrying on precise leveling one rod may be kept ahead for
a whole section, and then for the next section the other rod can be
kept ahead. By alternating the rods for successive sections no
appreciable error will enter into the leveling, and in many cases the
work will be expedited. This method should be used only if better
progress can be made than by the usual method of ha\ing the same
rod at a rod station for both the fore sight and the back sight.
65. Except in special cases the inclination corrections for the
distance from the points of tangency to the traverse stations should
be determined by levels run especially for the purpose and separate
from the precise leveling. The leveling over the stakes need have
only such accuracy as is necessary to obtain the grade correction for
any one tape length with an error not in excess of one millimeter or
one part in 50 000. There should be both a forward and backward
running with different instrument stations.
66. In recording the levels over the stakes care should be used to
give the stakes the same designation as in the traverse record.
67. A leveling rod graduated to meters should be used for the Y
levels in order to avoid the necessity for the conversions from feet to
meters in joining the Y levels with the precise levels. It is recom-
mended that a Y level equipped with stadia wii'es be used on this
work in order to give an additional check on the distances measured
over the stakes. The offset distance of each instrument station not
in the line of stakes should be paced and noted in the record in order
that proper allowance can be made in computing the check distances
over the stakes.
GENERAL INSTRUCTIONS FOR TRAVERSE. 19
RECORDS AND COMPUTATIONS.
68. There are given below samples of records, abstracts, computa-
tions, and results in connection with primary traverse. These sam-
ples should be followed unless authority has been given by the Super-
intendent to deviate from them.
69. The following samples of records and computations, with the
exception of the computation of loop closure, are all for the same
section of the traverse, namely, from station North to station Douglas
of the Savannah-Norfolk traverse line. This makes it possible for
Fig. 1. Section of traverse line.
anyone desiring to do so to follow through the various steps of the
computation and see how each value is obtained. The section
selected is a typical one with one station at the intersection of two
tangents and tho other an offset station on a long tangent.
70. All angles of the traverse are measured and recorded as in
triangulation, instructions for which have already been published in
Special Publications Nos. 19 and 26. No samples of the angle
measurements are included in this publication.
20
U. S. COAST AND GEODETIC SURVEY.
71. Traverse measurement.
From station North to station Douglas, forward measurement.
Department op Commerce
U. S. COAST AND GEODETIC SURVEY
Form 590.
[Date, 5-11-18; time, 10.30 a. m.; tape No. 552; bal. No. 266.]
Section.
Temp.
Set-up.
Setback.
Tape
sup-
port.
From
To-
For-
ward.
Rear.
Remarks.
Rail North.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24'
25
26
Table Douglas.
tid totals
43.5
41.3
40.2
39.1
37.0
36.1
35.0
36.8
36.6
36.4
36.4
37.3
38.0
38.6
38.4
38.4
39.3
39.2
38.5
39.2
43.5
41.4
40.0
40.0
44.0
41.0
39.8
38.9
38.6
38.5
34.9
.36.4
36.1
35.9
34.9
36.9
37.1
37.3
38.4
39.6
39 7
39.8
39.9
41.0
44.3
44.5
43.9
42.9
Meters.
Meters.
aT
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
3
3
3
1
Left-hand rail.
1
2
3
4
5
/6+20m.=T.B.
t M. 115.
6
7
8
9
fll-f7m-WR
10
X. (wagon-
11
12
ing)
13
14
15
16
17
18
19
20
21
22
23
S. U.=55' 111"
24+4 m.=P.
^ T. 42
24
17.0565
24'
37.4
36.7
34.8
34.8-
35.1
32.9
0.0445
25
Chief of trav-
26
0.0110
ing subparty:
J Smook
Means a
17.0675
0.0445
o A "T" in this column means that the tape is supported throughout, a "3'
'5" means the number of equally spaced supports.
GENERAL INSTRUCTIONS FOR TRAVERSE.
21
72. Check measurement.
From station Douglas to station North, backward measurement.
[Date, 5-13-18; time, 9 a. m.; tape No. 251 (300-foot).]
Section.
Tem-
pera-
ture.
Set-
up.
Set-
back.
Remarks.
From
To-
Table Douglas.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
RaU north.
"C.
37.1
36.5
35.4
35.0
34.8
34.6
34.3
34.1
34.2
34.6
34.9
35.2
35.5
36.1
36.4
Feet.
Feet.
1
1-1-235'- P. T. 42.
2
3
4
5
6
7
8
8+257'- W R X.
9
(wagon road cross-
10
ing).
11
11+135' T. B. M. 115
12
13
14
284.8
Totallengtli=44S4.8 fect= 1366.97 meters; original measuremcnt= 1367.02 meters.
The check measurement may be recorded in the regular traverse book, Form 590, by
making a few changes in the headings.
73. Y levels over stakes.
Station Douglas.
[Date, 5-14-18; time, 11.30 a. m.; Y level, 93.J
Forward running.
Rod station.
Backward running.
Mean
Rod station.a
Back
sight.
Fore
sight.
Differ-
ence of
eleva-
tion.
Back
sight.
Fore
sight.
Differ-
ence of
eleva-
tion.
differ-
once of
eleva-
tion .
P. T. 42
Feet.
1.04
y::::.
Feet.
Feet.
P. T. 43
3
2
1
Mark at Doug-
las
Feet.
6.75
Feet.
Feet.
Feet.
24'
25
26
Table at Doug-
las
1.38
1.20
0.83
2.84
-0.34
+0.18
+0.37
-2.01
6.89
5.80
6.15
3.54
-0.14
+1.09
-0.35
+2.61
+ 0.16
- 1.10
+ 0.34
- 2.60
Mark at Doug-
las
}
3.93
-1.09
Table at Doug-
las.
2.45
+1.09
- 1.09
1
2
3
P. T. 43
6.52
6.18
7.29
7.12
-2.59
+0.34
-1.11
+0.17
26
25
24'
P. T. 42
0.43
0.80
0.98
0.60
+2.02
-0.37
-0.16
+0.36
- 2.02
+ 0.37
+ 0.17
- 0.35
a Y level readings should be recorded in the same order as the points sighted on actu-
ally occur along the traverse line, in the direction of progress.
V
22
17. S. COAST AND GEODETIC SURVEY.
74. For convenience in printing, the backward and forward runnings
of the Y levels over the stakes are given together in the preceding table.
In the field the two runnings should be recorded on different pages,
separated by a page or two in order to avoid duplication of errors by
the recorder. A third running should be made if the first two fail to
check.
75. Precise levels.
T. B. M. 115 to B. M, Aa (forward).
Rail at T. B. M. 115 (B)
42 3*
^
t5 ^
Si -^
^ 1
.a' bo
% 1
a o
m f^
pq ^
223500000
2003
233600000
2136
243800000
2269
720
70900000
820
84300000
921
97700000
\1479Ha
(153871
h579?e
Rail at A Douglas (F)
hoQln
U680
(158471
281
. 128700000
428
140500000
575
152300000
258200000
1100
273100000
1219
288000000
1338
256300000
jl539
271100000
P. T, 43 (F)
{1549W
286000000
ll5597
504
954
651
1025
799
1097
814
225400000
962
232700000
1110
240000000
249300000
j 148171
264200000
RaOatB.M. AaT)
h552n
279100000
Il6237i
120400000
133700000
4899828710
147000000
Difl. of siiTns= +20288
2180
Diff. of sums divided by 3
=.-
2328
DifE. of elev.= +6762.7
2476
181871
1890W
,1963
P. T. 42 (F)
a AW numbers in this table marked with an "t?" are not included in the total, as
they were put in the adding machine with the "non-add" key depressed.
GENERAL INSTRUCTIONS FOR TRAVERSE. 23
SAMPLE COMPUTATIONS AND TABLES.
76. The various steps in making a traverse computation are as
follows:
(a) Checking list of directions from the original angle records.
(6) Computation of gi-ade corrections and mean elevations of sections.
(c) Computation of lengths on Form 589, including temperature,
tape, and sea-level corrections.
(d) Projection computation or computation of lengths between the
true stations when the tape measures were made to a point on the
rail opposite the station at either or both ends.
(e) Closm-e of loops when the azimuth is carried through long lines
extending past several stations. (See par. 46.)
(/) Computation of geographic positions. As there is no check on
this computation, it must be made in duplicate.
(g) Final least square adjustment to make the traverse lines con-
sistent with each other and with the triangulation with which they
connect.
77. Various tables which are useful in making the computations
are given on the following pages just after the computation in each
case for which they are needed. The first one of these tables giving
the inclination correction for different lengths of section and differ-
ences of elevation will be found on page 25. This is used for com-
puting the inclination corrections when these corrections depend
upon the precise levels. Following the computation of lengths on
page 33 are several tables of tape corrections for tape No. 552 for
various methods of support. These tables can be used only for this
one standardization of this particular tape. Each tape and each
new standardization requires new tables. Whenever a tape is used
for any considerable length of time it will be found to save much
work in the long run to construct tables similar to the ones published
here.
24 U. 8. COAST AND GEODETIC SURVEY.
78. Computation of inclination correction.
From station North to station Douglas.
Bench mark.
Differ-
ence of
eleva-
tion.
Dis-
tance.
Inclination
correction.a
Eleva-
tion.
Remarks.
Rail North-....
-RailllS
Rail 115-
-P.T.42
Meters.
-0.01
-0.59
0.15
+0.76
-f-2.30
+ 2.06
+ 1.68
-0.55
-0.11
+0.05
+0.11
-0.62
Meters.
16
199
102
134
197
197
198
137
13
50
50
50
Millimeters.
0.0
0.9
0.1
2.2
13.4
10.8
7.1
1.1
0.5
0.0
0.2
3.8
Meters.
103.051
i62.'29J
::::::::
107. 98
Preciselevel record, Vol. 15
{see page 22).
Traverse record, Vol. 6 (see
page 20) .and wye-levelrecord,
Vol. I(epage21).
2628.
ao f Table
^^'XDouglas....
Total .
1343c
40.1
Meaneleva
tion . .
105.3
a The corrections in this column were obtained from the table on page 25, except for
the last part of the section, shown in italics, for which the corrections were obtained
from the table on page 28.
b The mean of these two elevations was used in computing the mean elevation for the
whole section.
c Due to the use of a convenient but slightly inaccurate value of the stadia constant
for the precise level, this distance fails to check the measured distance. The percentage
of error is qiute small, and by comparing several sections its value can be obtained
quite accurately and allowance made for it. If the precise leveling has been done
according to the instructions in this pubhcation, this check on the distance should
locate any bluuder of a tape length in the tape measurement.
79. With regard to the preceding computation it should be noted
that the table on page 25 differs from the one on page 28 in this respect,
that in the former the known measured distance, I, is the horizontal
distance or leg of the right triangle, while in the latter it is the inclined
distance or hypotenuse of the right triangle. This distinction should
be kept in mind in computing any values which fall outside the limits
of the tables.
80. In computing inclination corrections outside the limits of the~
table on page 25 for the precise-leveling work it will be found that the
first term only of the series formula at the top of the table, namely,
^-j, will give sufficient accuracy. The same formula may also be used
for the Y-level work when the lengths are other than the 25 or 50
meters for which the table on page 28 is computed and when the
GENERAL INSTRUCTIONS FOR TRA^T^RSE.
25
grades are under 5 per cent. Of course h must be expressed in meters
instead of feet. Other values outside the limits of the tables can be
obtained readily by actually computing -the right triangle. Barlow's
tables of squares will be found useful in this connection.
81. Inclination correction.
^- . ,'h*
[Correction=i Vp+^^= iT~+i7i (always negative).]
Length
of sec-
Difference of elevation in meters.
tion in
meters.
0.0
0..
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
10
mm.
0.0
mm.
0.5
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.0
mm.
2.0
1.0
0.7
0.5
0.4
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
20
2.2
1.5
1.1
0.9
0.8
0.6
0.6
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.2
0.2
4.0
2.7
2.0
1.6
1.3
1.1
1.0
0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.5
0.4
0.4
3o:....
4.2
3.1
2.5
2.1
1.8
1.6
1.4
1.2
1.1
1.0
1.0
0.9
0.8
0.8
0.7
0.7
0.7
6.0
4.5
3.6
3.0
2.6
2.2
2.0
1.8
L6
1.5
1.4
1.3
1.2
1.1
1.1
1.0
0.9
8.2
6.1
4.9
4.1
3.5
3.1
2.7
2.4
2.2
2.0
1.9
L7
1.6
L5
1.4
1.4
1.3
10.7
8.0
6.4
5.3
4.6
4.0
3.6
3.2
2.9
2.7
2.5
2.3
2.1
2.0
1.9
1.8
1.7
40
10.1
8.1
6.8
5.8
5.1
4.5
4.0
3.7
3.4
3.1
2.9
2.7
2.5
2.4
2.2
2.1
12.5
.50 ..
10
60
8.3
70
7.1
80.....
6 2
90
5.6
100
5
110
4.5
120
4 2
130
i
3 8
140
i
3 6
150
'
33
ICO
3.1
2.9
2 8
170... .
180
..
190
2 6
200
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.4
0.4
0.4
0.9
0.9
0.8
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.6
1.2
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.9
0.8
0.8
1.6
1.5
1.5
1.4
1.3
1.3
1.2
1.2
LI
1.1
LI
2.0
1.9
1.8
1.8
L7
L6
L6
L5
1.4
L4
1.3
2 5
210
220
2.4
2.3
2 2
230
240
2.1
2
250
260... .
1
270.
1.8
L7
L7
280
290
300
26 U. S. COAST AND GEODETIC SURVEY.
Inclination correction Continued .
Length
Difference of elevation in meters.
of sec-
tion in
meters.
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
40
15.1
18.0
50 .
12.1
14.4
16.9
19.6
22.5
25.6
60
10.1
12.0
14.1
16.3
18.8
21.3
24.1
27.0
30.1
33.3
70
8.6
10.3
12.1
14.0
16.1
18.3
20.6
23.1
25.8
28.6
80
7.6
9.0
8.0
10.6
9.4
12.2
10.9
14.1
12.5
16.0
14.2
18.1
20.2
22.6
20.1
25.0
22.2
90
6.7
100
6.0
7.2
8.4
9.8
11.2
12.8
14.4
16.2
18.0
20.0
110
5.5
6.5
7.7
8.9
10.2
11.6
13.1
14.7
16.4
18.2
120
5.0
6.0
7.0
8.2
9.4
10.7
12.0
13.5
15.0
16.7
130
4.7
5.5
6.5
7.5
8.7
9.8
11.1
12.5
13.9
15.4
140
4.3
5.1
6.0
7.0
8.0
9.1
10.3
11.6
12.9
14.3
150
4.0
4.8
5.6
6.5
7.,5
8.5
9.6
10.8
12.0
13.3
160
3.8
4.5
5.3
6.1
7.0
8.0
9.0
10.1
11.3
12.5
170
3.6
'i.2
5.0
5.8
6.6
7.5
8.5
9.5
10.6
11.8
180
3.4
4.0
4.7
5.5
6.3
7.1
8.0
9.0
10.0
11.1
190
3.2
3.8
4.4
5.2
5.9
6.7
7.6
8.5
9.5
10.5
200
3.0
3.6
4.2
4.9
5.6
6.4
7.2
8.1
9.0
10.0
210
2.9
3.4
4.0
4.7
6.4
6.1
6.9
7.7
.8.6
9.5
220
2.7
3.3
3.8
4.5
6.1
6.8
6.6
7.4
8.2
9.1
230
2.6
3.1
3.7
4.3
4.9
5.6
6.3
7.0
7.8
8.7
240
2.5
3.0
3.5
4.1
4.7
5.3
6.0
6.7
7.5
8.3
250
2.4
2.9
3.4
3.9
4.5
6.1
5.8
6.5
7.2
8.0
280
2.3
2.8
3.2
3.8
4.3
4.9
5.6
6.2
6.9
7.7
270
2.2
2.7
3.1
3.6
4.2
4.7
5.4
6.0
6.7
7.4
280
2.2
2.6
3.0
3.6
4.0
4.6
5.2
6.8
6.4
7.1
290
2.1
2.5
2.9
3.4
3.9
4.4
6.0
5.6
6.2
6.9
300
2.0
2.4
2.8
3.3
3.7
4.3
4.8
5.4
6.0
6.7
GENERAL INSTRUCTIONS FOR TRAVERSE.
Inclination correction Continued.
27
Length
of sec-
tion in
meters.
Difference of elevation in meters.
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.0
3.0
70
80
90
100
110
120
130
140.
150,
160,
170
ISO
190,
200,
210,
220,
230,
240.
250
260,
270,
280,
290.
300.
mm.
31.5
27.6
24.5
22.0
20.0
18.4
17.0
15.7
14.7
13.8
13.0
12.2
11.6
11.0
10.5
10.0
9.6
9.2
8.8
8.5
8.2
7.9
7.6
mm.
34.6
30.2
26.9
24.2
22.0
20.2
18.6
17.3
16.1
15.1
14.2
13.4
12.7
12.1
11.5
11.0
10.5
10.1
8.7
9.3
9.0
8.7
8.3
8.1
mm.
37.8
33.1
29.4
2S.4
24.0
22.0
20.3
18.9
17.6
16.5
15.6
14.7
13.9
13.2
12.6
12.0
11.5
11.0
10.6
10.2
9.8
9.4
9.1
8.8
mm.
41.1
36.0
32.0
28.8
26.2
24.0
22.1
20.6
19.2
18.0
16.9
16.0
15.2
14.4
13.7
13.1
12.5
12.0
11.5
11.1
10.7
10.3
9.9
9.6
34
31.2
28.4
26.0
24.0
22.3
ly.o
18.4
17.4
16.5
15.6
14.9
14.2
13.6
13.0
12.5
12.0
11.6
11.2
10. S
42.2
37.6
33.8
30.7
28.2
26.0
22.5
21.1
19.9
18.8
17.8
16.9
16.1
15.4
14.7
14.1
13.5
13.0
12.5
12.1
11.7
10.4 11.3
45.6
40.5
36.4
33.1
30.4
28.0
26.0
24.3
22.8
21.5
20.2
19.2
18.2
17.4
16.6
15.8
15.2
14.6
14.0
18.5
13.0
12.8
12.1
49.0
43.8
39.2
35.6
32.7
30.2
28.0
26.1
24.5
23.1
21.8
20.6
19.6
18.7
17.8
17.0
16.3
15.7
15.1
14.5
14.0
13.5
13.1
46.7
42.0
3<S.2
35.0
32.3
30.0
28.0
26.3
24.7
23.4
22.1
21.0
20.0
19.1
18.3
17.5
16.8
16.2
15.6
15.0
14.5
14.0
50.0
45.0
40.9
37.5
34.6
32.1
30.0
2<<.l
26.5
25.0
23.7
22.5
21.9
20.5
19.6
18.7
18.0
17.3
16.7
16.1
15.5
15.0
28
U. S. COAST AND GEODETIC SURVEY.
82. Inclination corrections for 50-meter tape lengths. -
[Cor. = .01h2 .OOOOOlh*.]
Difference in
Correc-
Difference in
Correc-
Difference in
Correc-
elevation.
tion.
elevation.
tion.
elevation.
tion.
Meters.
Feet.
mm.
Meters.
Feet.
mm.
MeUrs.
Feet.
mm.
0.00
0.000
0.0
0.50
1.640
2.5
1.00
3.281
10.0
.01
.033
.0
.51
1.673
2.6
1.01
3.314
10.2
.02
.066
.0
.52
1.706
2.7
1.02
3.346
10.4
.03
.098
.0
.53
1.739
2.8
1.03
3.379
10.6
.04
.131
.0
.54
1.772
2.9
1.04
3.412
10.8
.05
.164
.0
.55
1.804
3.0
1.05
3.445
11.0
.06
.197
.0
.56
1.837
3.1
1.06
3.478
11.2
.07
.230
.0
.57
1.870
3.2
1.07
3.510
11.4
.08
.262
.1
.58
1.903
3.4
1.08
3.543
11.7
.09
.295
.1
.59
1.936
3.5
1.09
3.676
11.9
.10
.328
.1
.60
1.968
3.6
1.10
3.609
12.1
.11
.361
.1
.61
2.001
3.7
1.11
3.642
12.3
.12
.394
.1
.62
2.034
3.8
1.12
3.675
12.5
.13
.427
.2
.63
2.067
4.0
1.13
3.707
12.8
.14
.459
.2
.64
2.100
4.1
1.14
3.740
13.0
.15
.492
.2
.65
2.133
4.2
1.15
3.773
13.2
.16
.525
.3
.66
2.105
4.4
1.16
3.806
13.5
.17
.558
.3
.67
2.198
4.5
1.17
3.839
13.7
.18
.591
.3
.68
2.231
4.6
1.18
3.871
13.9
.19
.623
.4
.69
2.264
4.8
1.19
3.904
14.2
.20
.656
.4
.70
2.297
4.9
1.20
3.937
14.4
.21
.689
.4
.71
2.329
5.0
1.21
3.970
14.6
.22
.722
.5
.72
2.362
5.2
1.22
4.003
14.9
.23
.755
.5
.73
2.395
5.3
1.23
4.035
15.1
.24
.787
.6
.74
2.428
5.5
1.24
4.068
15.4
.25
.820
.6
.75
2.461
5.6
1.26
4.101
15.6
.26
.853
.7
.76
2. 493
5.8
1.26
4.134
15.9
.27
.886
.7
.77
2. 526
6.9
1.27
4.167
16.1
.28
.919
.8
.78
2.559
6.1
1.28
4.199
16.4
.29
.951
.8
.79
2.592
6.2
1.29
4.232
16.6
.30
.984
.9
.80
2.625
6.4
1.30
4.265
16.9
.31
1.017
1.0
.81
2.657
6.6
1.31
4.298
17.2
.32
1.050
1.0
.82
2.690
6.7
1.32
4.331
17.4
.33
1.083
1.1
.83
2.723
6.9
1.33
4.3&4
17.7
.34
1.115
1.2
.84
2.756
7.1
1.34
4.396
18.0
.35
1.148
1.2
.86
2.789
7.2
1.35
4.429
18.2
.36
1.181
1.3
.86
2.822
7.4
1.36
4.462
18.5
.37
1.214
1.4
.87
2.854
7.6
1.37
4.495
18.8
.38
1.247
1.4
.88
2.887
7.7
1.38
4.528
19.0
.39
1.280
1.5
.89
2.920
7.9
1.39
4.560
19.3
.40
1.312
1.6
.90
2.953
8.1
1.40
4,593
19.6
.41
1.345
1.7
.91
2.986
8.3
1.41
4.626
19.9
.42
1.378
1.8
.92
3.018
8.5
1.42
4.659
20.2
.43
1.411
1.8
.93
3.051
8.6
1.43
4.692
20.4
.44
1.444
1.9
.94
3.084
8.8
1.44
4.724
20.7
.45
1.476
2.0
.95
3.117
9.0
1.45
4.757
21.0
.46
1.509
2.1
.96
3.150
9.2
1.46
4.790
21.3
.47
1.542
2.2
.97
3.182
9.4
1.47
4.823
21.6
.48
1.575
2.3
.98
3.215
9.6
1.48
4.856
21.9
.49
1.60P
2.4
.99
3.248
9.8
1.49
4.888
22.2
GENERAL INSTRUCTIONS FOR TRAVERSE. 29
Inclination corrections for 50-meter tape lengths Continued.
Difference in
Correc-
Difference in
Correc-
Difference in
Correc-
elevation.
tion.
elevation.
tion.
elevation.
tion.
Meters.
Feet.
mm.
Meters.
Feet.
mm.
Meters.
Feet.
mm.
1.50
4.921
22.5
2.00
6.562
40.0
2.50
8.202
62.5
1.51
4.954
22.8
2.01
6.594
40.4
2.51
8.235
63.0
1.52
4.9S7
23.1
2.02
6.627
40.8
2.52
8.208
63.5
1.53
* 5.020
23.4
2.03
6. 600
41.2
2.53
8.301
64.0
1.54
5.052
23.7
2.04
6.693
41.6
2.54
8.333
64.6
1.55
5.085
24.0
2.05
6.726
42.0
2.55
8.366
65.1
1.56
5.118
24.3
2.06
6.759
42.5
2.56
8.399
65.6
1.57
5.151
24.6
2.07
6.791
42.9
2.57
8.432
66.1
1.58
5.184
25.0
2.08
6.824
43.3
2.58
8.465
66.6
1.59
5.217
25.3
2.09
6.857
43.7
2.59
8.497
67.1
1.60
5.249
25.6
2.10
6.890
44.1
2.60
8.530
67.6
1.61
5.282
25.9
2.11
6.923
44.5
2.61
8.563
68.2
1.62
5.315
26.2
2.12
6.955
45.0
2.62
8.596
68.7
1.63
5.348
26.6
2.13
6.988
45.4
2.63
8.629
69.2
1.64
5.381
20.9
2.14
7.021
45.8
2.64
8.661
69.7
1.65
5.413
27.2
2.15
7.054
46.2
2.65
8.694
70.3
1.66
5.446
27.6
2.16
7.087
46.7
2.66
8.727
70.8
1.67
5.479
27.9
2.17
7.119
47.1
2.67
8.760
71.3
1.68
5.512
28.2
2.18
7.152
47.5
2.68
8.793
71.9
1.69
5.545
28.6
2.19
7.185
48.0
2.69
8.825
72.4
1.70
5. -.77
28.9
2.20
7.218
48.4
2.70
8.858
73.0
1.71
5.6iO
29.2
2.21
7.251
48.9
2.71
8.891
73.5
1.72
5.643
29.6
2.22
7.283
49.3
2.72
8.924
74.0
1.73
5.676
29.9
2.23
7.316
49.8
2.73
8.957
74.6
1.74
5.709
30.3
2.24
7.349
60.2
2.74
8.989
75.1
1.75
5.741
30.6
2.25
7.382
50.7
2.75
9.022
75.7
1.76
5.774
31.0
2.26
7.415
51.1
' 2.76
9.055
76.2
1.77
5.807
31.3
2.27
7.447
61.6
2.77
9.088
76.8
1.78
5.840
31.7
2.28
7.480
52.0
2.78
9.121
77.3
1.79
5.873
32.0
2.29
7.513
62.5
2.79
9.14
77.9
1.80
5.906
32.4
2.30
7.546
52.9
2.80
9.186
78.5
1.81
5.938
32.8
2.31
7.579
53.4
2.81
9.219
79.0
1.82
5.971
33.1
2.32
7.612
53. 9>
2.82
9.252
79.6
1.83
0.004
33.5
2.33
7.644
54.3
2.83
9.285
80.2
1.84
6.037
33.9
2.34
7.677
54.8
2.84
9.318
80.7
1.85
6.070
34.2
2.3.5
7.710
55.3
j 2.85
2.86
9.350
81.3
1.86
6.102
34.6
2.3^^
7.743
65.7
9.383
81.9
1.87
6.135
35.0
2.37
7.776
56.2
2.87
9.416
82.4
1.88
6.168
35.3
2.38
7.808
56.7
2.88
9.449
83.0
1.89
6.201
35.7
2.39
7.841
57.2
2.89
9.482
83.6
1.90
6.234
36.1
2.40
7.874
57.6
2.90
9.514
84.2
1.91
6.266
36.5
2.41
7.907
68.1
2.91
9.547
84.8
1.92
6.299
36.9
2.42
7.940
68.6
2.92
9.580
85.3
1.93
6.332
37.2
2.43
7.972
59.1
2.93
9.613
85.9
1.94
6.365
37.6
21.44
8.905
59.6
2.91
9.646
86.5
1.95
6.398
38.0
2.45
8.038
60.1
2.95
9.678
87.1
1.96
6.430
38.4
2.46
8.071
60.6
2.96
9.711
87.7
1.97
6.463
38.8
2.47
8.104
61.0
2.97
9.744
88.3
1.98
6.496
39.2
2.48
8.136
61.5
2.98
9.777
88.9
1.99
6.529
39.6
2.49
8.169
62.0
2.99
9.810
89.5
30 U. S. COAST AND GEODETIC SURVEY.
Inclination corrections for 50-meter tape lengths Continued .
::::
Difference in
Correc-
Dlflerence in
Correc-
Difference in
COTrec-
elevation.
Uon.
elevation.
tion.
elevation.
tion.
Meters.
Fed.
mm.
Meters,
Feet.
mm.
Meters.
Feet.
mm.
3.00
9.842
90.1
3.50
11.483
122.7
4.00
13.123
160.3
3.01
9.875
90.7
3.51
11.516
123.4
4.01
13. 156
161.1
3.02
9.908
91.3
3.52
11.549
124.1
4.02
13. 189
161.9
3.03
9.941
91.9
3.53
11.581
124.8
4.03
13. 222
162.7
3.04
9.974
92.5
3.64
11.614
125.5
.4.04
13. 255
163.6
3.05
10.007
93.1
3.55
11.647
126.2
4.05
13. 287
164.3
3.06
10.039
93.7
3.56
11. 680
126.9
4.06
13.320
165.1
3.07
10.072
91.3
3.57
11.713
127.6
4.07
13.353
165.9
3.03
10.105
95.0
3.58
11.745
128.3
4.08
13.386
166.7
3.09
10.138
95.6
3.59
11.778
129.0
4.09
13. 419
167.6
3.10
10.171
96.2
3.60
11.811
129.8
4.10
13. 451
168.4
3.11
10.203
96.8
3.61
11.844
130.5
4.11
13. 484
169.2
3.12
10.236
97.4
3.62
11.877
131.2
4.12
13.517
170.0
3.13
10. 2G9
98. 1
3.63
11.909
131.9
4.13
13.550
170.9
3.14
10.302
98.7
3.64
11.942
132.7
4.14
13.583
171.7
3.15
10.335
99.3
3.65
11.975
133.4
4.15
13.615
172.5
3.16
10.367
100.0
3.66
12.008
134.1
4.16
13.648
173.4
3.17
10.400
100.6
3.67
12.041
131.9
4.17
13.681
174.2
3.18
10.433
101.2
3.68
12.073
135.6
4.18
13.714
175.0
3.19
10. 466
101.9
3.69
12. 106
136.3
4.19
13.747
176.9
3.20
10.499
102.5
3.70
12.139
137.1
4.20
13.780
176.7
3.21
10.531
103. 1
3.71
12. 172
137.8
4.21
13.812
177.6
3.22
10.564
103.8
3.72
12. 205
138.6
4.22
13.845
178.4
3.23
10.597
104.4
3.73
12. 238
1.39.3
4.23
13.878
179.2
3.24
10.630
105.1
3.74
12. 270
140.1
4.24
13.911
180.1
3.25
10.663
105.7
3.75
12.303
140.8
4.25
13.944
181.0
3.26
10.696
106.4
3.76
12.336
141.6
4.28
13.976
181.8
3.27
10.728
107.0
3.77
12.369
142.3
4.27
14.009
182.7
3.28
10.761
107.7
3.78
12. 402
143.1
4.28
14.042
183.5
3.29
10.794
108.4
3.79
12. 434
143.8
4.29
14.075
184.4
3.30
10.827
109.0
3.80
12.467
144. 6
4.30
14.108
185.2
3.31
10.860
109.7
3.81
12.500
145.4
4.31
11.140
186.1
3.32
10.892
110.3
3.82
12.533
146.1
4.32
11.173
187.0
3.33
10.925
111.0
3.83
12.566
146.9
4.33
1 !. 206
187.8
3.34
10.958
111.7
3.84
12.598
147.7
4.34
14.239
188.7
3.35
10.991
112.4
3.85
12.631
148.4
4.35
14.272
189.6
3.36
11.024
113.0
3.86
12.664
149.2
4.36
14.304
190.5
3.37
11.056
113.7
3.87
12. 697
150.0
4.37
14.337
191.3
3.38
11.089
114.4
3.88
12.730
150.8
4.38
14.370
192.2
3.39
11.122
115.1
3.89
12.762
151.6
4.39
14.403
193.1
3.40
11.155
115.7
3.90
12.795
152.3
4.40
14.436
194.0
3.41
11.188
116.4
3.91
12.828
153.1
4.41
14.468
194.9
3.42
11.220
117.1
3.92
12.861
153.9
4.42
14.601
195.7
3.43
11.253
117.8
3.93
12. 894
154.7
4.43
14.534
196.6
3.44
11.286
118.5
3.94
12.926
155.5
4.44
14.567
197.5
3.45
11.319
119.2
3.95
12.959
156.3
4.45
14.600
198.4
3.46
11.352
119.9
3.96
12.992
157.1
4.46
14.633
199.3
3.47
11.384
120.6
3.97
13.025
157.9
4.47
14.665
200.2
3.48
11.417
121.3
3.98
13.058
158.7
4.48
14.698
201.1
3.49
11.450
122.0
3.99
13.091
159.5
4.49
14.731
202.0
GENERAL INSTRUCTIONS FOR TRAVERSE. 31
Inclination corrections for 50-meter tape lengths Continued.
Difference in
1 Corree-
Difference in
Correc-
Difference in
Correc-
elevation.
! tion.
elevation.
tion.
elevation.
tion.
Meters.
Feet.
mm.
Meters.
FeeL
mm.
llfeters.
FeeL
mm.
4.50
14.764
202.9
5.00
16. 404
250. 6
i 5.50
18.045
303.4
4.51
14.797
203.8
5.01
16.437
251.6
1 5.51
18.077
304.5
4.52
14.829
204.7
5.02
16.470
252.6
5.52
18,110
305.6
4.53
14.862
205.6
5.0;?
16.503
253.6
5.53
18.143
306.7
4.54
14.895
206.5
5.04
16.535
254.7
5.54
18.176
307.9
4.55
14.928
207.5
5.05
16.568
255.7
5.55
18.209
309.0
4.56
14.961
208.4
5.06
16.601
256.7
5.56
18.241
310.1
4.57
14.993
209.3
5.07
16.634
257.7
5-57
18.274
311.2
4.58
15.026
210.2
5.08
16.607
258.7
5.58
18.307
312.3
4.59
15.059
211.1
5.09
16.699
259.8
5.59
18.340
313.5
4.60
15.092
212.0
6.10
16.732
260.8
6.60
18.373
314.6
4.61
15.125
213.0
5.11
16.765
261.8
5.61
18.405
315.7
4.62
15.157
213.9
6.12
16.798
262.8
5.62
18.438
316.8
4.63
15.190
214.8
6.13
16.831
263.9
5.63
18.471
318.0
4.64
15.223
215.8
6.14
16.863
264.9
5.64
18.504
319.1
4.65
15.256
216.7
5.15
16.896
265.9
5.65
18.537
320.2
4.66
15.289
217.6
5.16
16.929
267.0
5.66
18.570
321.4
4.67
15.321
218.6
5.17
16.962
268.0
5.67
18.602
322.5
4.68
15.354
219.5
5.18
16.995
269.0
5.68
18.635
323.7
4.69
15.387
220.4
5.19
17.028
270.1
6.69
18.668
324.8
4.70
15.420
221.4
5.20
17.060
271.1
5.70
18.701
326.0
4.71
15.453
222.3
5.21
17.093
272.2
6.71
18.734
327.1
4.72
15.486
223.3
5.22
17.128
273.2
6.72
18. 766
328.3
4.73
15.518
224.2
o.Zi
17.159
274.3
5.73
18.799
329.4
4.74
15.551
225.2
5.24
17.192
276.3
5.74
18.832
330.0
4.75
15.584
226.1
5.25
17.224
276.4
5.75
18.865
331.7
4.76
15.617
227.1
5.26
17.257
277.4
5.76
18.898
332.9
4.77
15.650
228.0
5.27
17.290
278.5
6.77
18.930
334.0
4.78
15.682
229.0
5.2S
17.323
279.6
5.78
18.963
335.2
4.79
16.715
230.0
5.29
17.356
280.6
5.79
18.996
836.4
4.80
15.748
230.9
6.30
17.388
281.7
6.80
19.029
337.5
4.81
15.781
231.9
6.31
17.421
282.8
5.81
19.062
338.7
4.82
15.814
232."9
5.32
17.454
283.8
5.82
19.094
339.9
4.83
15.846
233.8
5.33
17.487
284.9
5.83
19.127
341.0
4.84
15.879
234.8
5.34
17.620
286.0
5.84
19.160
342.2
4.85
15.912
235.8
6.35
17.652
287.0
5.85
19.193
343.4
4.86
15.945
236.8
5.36
17.585
288.1
5.86
19.226
344.6
4.87
15.978
237.7
5.37
17.618
289.2
5.87
19.268
345.8
4.88
16.010
238.7
6.38
17.651
290.3
5.88
19.291
346.9
4.89
16.043
239.7
5.39
17.684
291.4
5.89
19.324
348.1
4.90
16.076
240.7
5.40
17.716
292.5
5.90
19.357
349.3
4.91
16.109
241.7
5.41
17. 749
293.5
5.91
19.390
350.5
4.92
16. 142
242.7
5.42
17.782
294.6
5.92
19.423
351.7
4.93
16.175
243. 6
5.43
17.815
295.7
5,93
19.465
a52.9
4.94
16.207
244.6
6.44
17.848
296.8
5.94
19.488
364.1
4.95
16.240
245.6
6.45
17.881
297.9
6.95
19.521
355.3
4.96
16.273
246.6
5.46
17.913
299.0
5.96
19.554
356.5
4.97
16.306
247.6
5.47
17.946
300.1
5.97
19.587
357.7
4.98
16.339
248.6
5.48
17.979
301.2
5.98
19.619
358.9
4.99
16.371
249.6
5.49
18.012
302.3
5.99
19.652
360.1
32 U. S. COAST AND GEODETIC SURVEY.
Inclination corrections for 50-meter tape lengths Continued.
Difference in
Correc-
Difference in
Correc-
Difference in
Correc-
elevation.
tion.
elevation.
tion.
elevation.
1
tion,
Meters.
Feet.
mm.
Meters.
Feet.
mm.
Meters.
Feet.
mm.
6.00
19.083
361.3
6.50
21.325
424.3
7.00
22. 966
492.4
6.01
19.718
362.5
6.51
21.358
425.6
7.01
22. 999
493.8
6,02
19. 751
363.7
6.52
21.391
426.9
7.02
23.031
495.2
6.03
19.783
364.9
6.53
21.424
428.2
7.03
23.064
496.6
6.04
19.816
366.1
6.64
21.457
429.5
7.04
23.097
498.1
6.05
19.849
367.4
6.55
21.489
430.9
7.05
23.130
499.5
6.06
19.882
368.6
6.56
21.522
432.2
7.06
23.163
500.9
6.07
19.915
369.8
6.57
21.555
433.5
7.07
23.195
502.3
8.08
19.947
371.0
6.58
21.588
434.8
7.08
23.228
503.8
6.09
19.980
372.3
6.59
21.621
436.2
7.09
23.261
505.2
6.10
20.013
373.5
6.60
21.654
437.5
7.10
23.294
506.6
6.11
20.046
374.7
6.61
21.686
438.8
! 7.11
23.327
508.1
6.12
20.079
375.9
6.62
21.719
440.2
1 7.12
23.360
509.5
6.13
20.112
377.2
6.63
21.752
441.5
7.13
23.392
511.0
6.14
20.144
378.4
6.64
21.785
442.8
7.14
23.425
512.4
6.15
20.177
379.7
6.65
21.818
444.2
7.15
23.458
513.8
6.16
20.210
380.9
6.66
21.850
445.5
7.16
23.491
615.3
6.17
20.243
382.1
6.67
21.883
446.9
7.17
23.524
616. 7
6.18
20.276
383.4
6.68
21.916
448.2
7.18
23.556
518.2
6.19
20.308
384.6
6.69
21.949
449,6
7.19
23.589
619.6
G.20
20.341
385.9
6.70
21.982
450.9
7.20
23.622
521.1
6.21
20.374
387.1
6.71
22. 014
452.3
7.21
23.655
622.5
(5.22
20.407
388.4
6.72
22.047
453.6
7.22
23.688
524.0
6.23
20.440
389.6
6.73
22.080
455.0
7.23
23.720
525.5
6.24
20.472
390.9
6.74
22. 113
456.3
7.24
23.753
526.9
6.25
20.505
392.2
6.75
22.146
457.7
7.25
23.786
528.4
6.26
20.538
393.4
6.76
22. 178
459. 1
7.26
23.819
529.9
6.27
20.571
394.7
6.77
22.211
460.4
7.27
23.852
531.3
6.28
20.604
395.9
6.78
22.244
461.8
7.28
23.884
532.8
6.29
20.636
397.2
6.79
22.277
463.2
7.29
23.917
634.3
6.30
20.669
398.5
6.80
22.310
464.5
7.30
23.950
535.7
6.31
20.702
399.7
6.81
22.342
465.9
7.31
23.983
637.2
6.32
20.735
401.0
6.82
22.375
467.3
-7.32
24.016
538.7
6.33
20.768
402.3
6.83
22.408
468.7
7.33
24.049
540.2
6.34
20.800
403.6
6.84
22.441
470.0
7.34
24.081
541.7
0.35
20.833
404.9
6.85
22.474
471.4
7.35
24.114
643.1
6.36
20.866
406.1
6.86
22.507
472.8
7.36
24.147
644.6
6.37
20.899
407.4
6.87
22.539
474.2
7.37
24.180
546.1
6.38
20.932
408.7
6.88
22.572
475.0
7.38
24.213
547.6
6.39
20.965
410.0
6.89
22.605
477.0
7.39
24.245
549.1
6.40
20.997
411.3
6.90
22.638
478.4
7.40
24.278
550.6
6.41
21.030
412.6
6 91
22.671
479.8
7.41
24.311
552.1
6.42
21.063
413.9
6.92
22.703
481.2
7.42
24.344
553.6
6.43
21.096
415.2
6.93
22.736
482.6
7.43
24.377
655.1
6.44
21. 129
416.5
6.94
22.769
484.0
7.44
24.409
656.6
6.45
21.161
417.8
6.95
22.802
485.4
7.45
24.442
558.1
6.46
21.194
419.1
6.96
22.835
486.8
7.46
24.475
559.6
6.47
21.227
420.4
6.97
22.867
488.2
7.47
24.508
561.1
6.48
21.260
421.7
6.98
22.900
489.6
7.48
24.541
562.6
6.49
21.293
423.0
6.99
22.933
491.0
7.49
7.50
24. 573
24.606
564.1
565.7
GENERAL INSTRUCTIONS FOR TRAVERSE.
33
P
IS
&I
CO
02
O
o
I
I
o
is
1.5
^ in to Pico Ci o* Oi ^
Coo to to ceo r t~
IS! iS O O ^M 00
^iS SoS8
^ I I I I I I I I
t ii s IS s i
^ o
"' I I I I Mil
liii
" + +
=18
0*000
I ++
^?A
+ 1 I
+ +
o8S
io S8
'+I+ + + +
+ I I
88l
+ + + + +
III + 1
it>.e> t>-o
g2 gis53^ rl^
:ssi 8i 8;5S s
8^^^
u5>cu5 uStfiio tS>iiu5 u6>o
^iHp^ Pht^ft, a<&M(zi fc[ii
3 >.o
1^
S
a tco
i,o eg
O O
Isq ^Is
cb22
SCQOQ
ii
:
go
si
2
o i3
o p.
1^
1^1
Sot?
** 'Sb^
02 .r-1 g>
fe s ^
lis
tag
2 fl.o
o w o ^
a ^|2
d o "^^
2 "'f
S >H s
fl a e
"-" o <y T:
^ ^^ Ph
If o M .2
g ^^
7. S '
CO
s.
^
0) 00
CJ
00
25
5 .^3
'is ^
si
II
^ " ^ .
r* 2 fl d t:'
^ :2 .2 o -S
II *
O 0)
1
zl
8 2 S
ill
a a ^
^ - i a a
03 ?Q ^
S =2 03 0)
rt u g ^
M -^ ^ ?^
01
-CI '^ a
11 O) 0) -fJ
till
34 U. S. COAST AND GEODETIC SURVEY.
(6) For the tape correction see the certificate of standardization
below and the tape-standardization tables on page 36. The caten-
ary correction is included in the tape correction, as the tapes are
supported in the field in the same manner as when standardized.
(c) For the inclination correction, see page 24.
(d) The sea-level correction or the correction for reducing the
length to sea level is computed by the formula,
Sea level cor.=
r
in which J.=the length of section in meters, imcorrected except for
set-up or setback to the nearest meter, /t=mean elevation of section to
nearest meter (see p. 24) and r=mean radius of the earth. Log r is
obtained from the tables on pages 55-60 of Special Publication No. 26.
The arguments for use in these tables are obtained by estimating the
mean latitude and azimuth for each part of the traverse line in which
the various sections have the same general direction. For the com-
putation above, log r was computed for that part of the traverse line
extending from the Savannah River to Columbia, as the line is prac-
tically straight for that whole distance. Log r=G. 80312.
86. Certificate of standardization (invar base tape No. 552.)
December 5, 1910.
Supported horizontally at 0, 25, and 50 meter points under tension
of 15 kilograms:
(0 to 50 m.)=50 m. -2.815 mm.+(i-27.4 0.) 0.0282 mm.
(probable errors) 0.020 mm. 0.0008 mm.
Supported horizontally at 0, 12.5, 25, 37.5, and 50 meter points under
tension of 15 kilograms:
(0 to 50 m.)=50 m. +0.113 mm.+(i-27.3 C.) 0.0282 mm.
(probable errors) 0.019 mm. 0.0008 mm.
Mass per meter=25.8 grams. ;;
GENERAL INSTRUCTIONS FOR TRAVERSE. 35
86. Additional computed values of tape corrections (invar base tape
No. 652.)
AL=the amount the tape is shortened by supporting it at
equidistant intervals instead of supporting it through-
out.
n=number of sections into which the tape is divided by
equidistant supports.
/=Iength of such section.
w;= weight of tape per unit of length.
f=the applied tension.
Supported throughout under tension of 15 kilograms:
(0 to 50 m.)=50 m. +1.060 mm.+(-27.4 0.) 0.0282 mm.
Supported horizontally at and 50 meter points under tension of
15 kilograms:
(0 to 50 m.)=50 m.-14.:^71 mm.-f (-27.4 C.) 0.0282 mm.
87. To obtain the tape correction when a part of the tape is supported
on stakes and the remainder is supported throughout, use combinations
of the proper fractional parts of the corresponding corrections given
above. For example, if the tape is supported horizontally at the
and 25 meter points and throughout from the 25 to 50 meter points under
a tension of 15 kilograms, the tape correction is computed as follows:
Taperor. = i (-2.815 mm.)+H+l 060 mm. )= -0.878 mm.
and the formula for the length becomes
(0 to 50 m.)=50 m. -0.878 mm.+(t-27.4 C.) 0.0282 mm.
36
TJ. S. COAST AND GEODETIC SUR^^:Y.
88. Temperature corrections, tape No. 662.
[Cor.=+(f-27.*'4 C.) 0.0000282 meters per tape length.]
Tem-
perature.
Correction.
Tem-
perature.
Correction.
Tem-
perature.
Correction.
Proportional
parts.
"C.
"C.
"C.
2S 29
-0.000773
744
15
16
-0.000350
321
30
31
+0.000073
1
102
2
716
17
293
32
130
1
3
3
3
688
18
265
33
158
2
6
6
4
660
19
237
34
186
3
8
9
5
631
20
209
35
214
4
11
12
6
603
21
180
36
243
5
14
14
7
575
22
152
37
271
6
17
17
8
547
23
124
38
299
7
20
20
9
519
24
96
39
327
8
22
23
10
491
25
68
40
355
9
25
26
11
462
26
40
41
384
10
28
29
12
434
27
-0.000011
42
412
13
406
28
+0.000017
43
440
14
-0.000378
29
+0.000045
44
45
468
+0.000496
89. Tape corrections for tape No. 662 when supported throughout.
Tape
Correc-
Tape
Correc-
Tape
Correc-
Tape
Correc-
lengths.
tion.
lengths.
tion.
lengths.
tion.
lengths.
tion.
Meters.
Meters.
Meters.
Meters.
1
+0.0011
26
0.0276
51
0.0541
76
0.0806
2
.0021
27
.0286
52
.0551
1 77
.0816
3
.0032
28
.0297
53
.0562
! 78
.0827
4
.0042
29
.0307
54
.0572
1 79
.0837
5
.0063
30
.0318
55
.0583
' 80
.0848
6
.0064
31
.0329
56
.0594
81
.0859
7
.0074
32
.0339
57
.0604
82
.0869
8
.0085
33
.0350
58
.0615
83
.0880
9
.0095
34
.0360
59
.0625
84
.0890
10
.0106
35
.0371
60
.0636
85
.0901
11
.0117
36
.0382
61
.0647
86
.0912
12
.0127
37
.0392
62
.0657
87
.0922
13
.0138
38
.0403
63
.0668
88
.0933
14
.0148
39
.0413
64
.0678
89
.0943
15
.0159
40
.0424
65
.0689
90
.0954
16
.0170
41
.0435
66
.0700
91
.0965
17
.0180
42
.0445
67
.0710
92
.0975
18
.0191
43
.04.56
68
.0721
93
.0986
19
.0201
44
.0466
69
.0731
94
.0996
20
.0212
45
.0477
70
.0742
95
.1007
21
.0223
46
.0488
71
.0753
96
.1018
22
.0233
47
.0498
72
.0763
97
.1028
23
.0244
48
.0509
73
.0774
98
.1039
24
.0254
49
.0519
74
.0784
99
.1049
25
0.0265
50
0. 0530
75
0.0795
100
0.1060
GENERAL INSTRUCTIONS FOR TRAVTJRSE. 37
90. Tape corrections for tape No. 552 for various methods of support.
Correction, tape supported
at and
at 0, 121,
at 0, 25,
Tape
lengths.
25 m.
and 25 m.
and 37i
at 0, 25,
and 50 m.
points.
at0,12i,
25,37i,
and 50 m.
at 0, 25.
points
and
through-
points
and
through-
m. points
and
through-
at and
50 m.
points.
points.
points.o
out from
out from
out from
25 to 50
25 to 50
37J to 50
m.b
m.c
m.d
.\feter8.
^^eters.
MettTs.
Meiers.
Meters.
Meters.
Meters.
1
-0.0028
+0.0001
-0.0014
-0.0009
+0.0006
-0.0011
-0.0144
2
.0056
.0002
.0027
.0018
.00i2
3
.0084
.0003
.0041
.0026
.0018
4
.0113
.0005
.0054
.0035
.0023
5
.0141
.0006
.006S
.0014
.0029
6
.0169
.0007
.0081
.0053
.0035
7
.0197
.0008
.0095
.0061
.0041
8
.0225
.0009
.0108
.0070
.0047
9
.0253
.0010
.0122
.0079
.0053
10
-0.0282
+0.0011
-0.0135
-0.0088
+0.0059
o Equivalent to tape supported at 0, 12* , 25, and 50 meter points.
b F.quivalent to tape supported at 25 and 50 meter points and tliroughout from to 25
meters.
c Equivalent to tape supported at 25, 37J, and 50 meter points and throughout from
to 25 meters.
d Equivalent to taue supported at 12*, 25, and 60 meter points and throughout from
to 12i meters.
t(S3 metjsra
OougUs
Fig. 2. Diagram for projection computation, one olTset station.
38 TJ. S. COAST AND GEODETIC SURVEY.
91. Projection computation, North to Douglas.
(See fig. 2.)
log 7.169=0. 8554586
log sin 92 15^ 45^^= 9.9996613 -10
log dist. North to X=0. 8551199
log 7.169=0. 8554586
log cos 92 15^ 45^^= 8.5963531 -10
log dist. Rail North to X=9. 4518117
Dist. Rail North to X= 0. 2830 meters
Dist. Rail North to Dougla8= 1366. 9858 meters
Dist. Douglas to X=1367. 2688 meters
log. dist. North to X =0.8551199
log. dist. Douglas to X= 3. 1358539
log tan a=7. 7192660-10
log sec. a=0. 0000060a
log dist. Douglas to X= 3. 1358539
log dist. North to Douglas=3. 1358599
Dist. North to Douglas=1367. 2877 meters
^ Raitxl^ ,8069.fl80 ffietera J^ Rail Rlncpo
Fig. 3. Diagram for projection computation, both stations offset on same side of track .
92. If both stations involved are offset from the measured line, a
computation similar to the first half of the computation above must
be made for each end of the line. The distance between the two
"X " points can thus be obtained and will give the length of the base
of the long, slender right triangle by which the final length between
stations is computed. The short side of this right triangle is obtained
by adding together the distances from the ''X" points to the stations
o It is not necessary to take out the value of angle . Find in the log tables the log
tan a just computed, and then on the same page in the corresponding column and line
under the heading of cosine will be found log cos a. The colog of this cosine is the log
secant a desired. The logarithms of the cosine and secant change very slowly for such
small angles and can be obtained readily with little interpolation.
GENERAL INSTRUCTIONS FOR TRAVERSE.
39
in case the stations are on opposite sides of the track or by subtracting
the smaller distance from the larger in case the stations are on the same
side of the track. (See figs. 3 and 4.)
Ra.iCievcianci
Fig. 4. Diagram for projection computation, stations offset on opposite sides of track.
93. In making the projection computations it is very essential that
a diagram similar to one of the figures 2 to 5 be made for each computa-
tion. Much confusion will thus be avoided and gross errors elimi-
nated. As the offset distance is small as compared with the distance
between stations, it is well in making these diagrams to exaggerate
very considerably the distances at right angles to the track and also
to exa^erate the angles when it is necessary for the sake of clearness.
Computation to close loops.
94. As stated in pars^aph 4, it is desirable in hilly or rolling country
where the railroad has numerous curves and short tangents to carry
the azimuth through long lines, extending past several intermediate sta-
tions which are necessarily near together, in order that the resulting
azimuth may have greater accuracy. The loop thus formed gives a
good check on the angle measurements. It also gives a rough check on
the distance measurements, for if an error has been made in the taping
the departures or perpendiculars for the loop will not sum up to zero
unless the error was made on a line very nearly parallel to the long line
through which the azimuth is carried. The error will show up also
in the position computations if they are made both through the long
line and through the short lines.
95. The manner of computing the loop and making the projections
to the main line is shown in the following computation. See also
figure 5. The computation of the departures or perpendiculars men-
tioned in the paragraph above is made in the same manner as the com-
putation of distance for the loop as shown in the table on the following
page except that in column 4 log sin azimuth should be used in place
cf log cos azimuth. The sign of the function must be taken into
account.
40 U. S. COAST AND GEODETIC SURVEY.
96. Computation of angle closure for loop.
Liv^mgston A
L;vlo|ston ^-~ ^~ l^33'^5~7'36r3l
807'I9"99-^ ^C" "^^iS^'ae'DS. /u |65''2S'35"60
Livingston s'l^Wct^ra.T, /-"- \-
825'"0I-' Xivings+on C
311
!?^eO-3535l'l7"6l)
Fig. 5. Diagram for loop computation.
Angles and
azimuths.
Correction
for
closure.
Assumed azimuth Livingston-North .
Angle at Livingston
Azimuth Livingston-Livingston A . . .
Azimuth Livingston A-Livingstou. . .
Angle at Livingston A
Azimuth Livingston A-Li^ingston ]> .
Azimuth Livingston B -Livingston h .
Angle at Livingston B
Azimuth Livingston B-Livingston C.
Azimuth Livingston C-Livingston B
Angle at Livingston C
Azimuth Livingston C-North
Azimuth North-Livingston C
Angle at North
Azimuth North-Livingston
Error of closure
Eri-or of closure per angle
- 8
07
19. 99 1
351
171
222
52
52
04
40.01 !
40.01 1
56. 30 1
33
213
154
57
57
28
36. 31 i
36.31 j
05. 70 1
8
188
165
25
25
25
42.01
42.01 :
35.60 1
353
173
6
51
51
08
17.61 !
17.61
46. 10 j
180
00 03.71
03.71
0.74
Final
corrected
seconds.
00 00 00.00
-0.74
-0.74
-0.74
I -0. 74
-0.75
00.00
20.73
39.27
39.27
55. 56
34. S3
34.83
04.96
39.79
39.79
34. 86
14.65
14.65
45.35
00.00
97. Computation of distance for loop.
Section.
Length.
Azimuth, a
Log cos
azimuth.
Log
length.
Log
projected
length.
Projected
length.
Livingston . . .
Livingston A .
Livingston A .
Livingston B .
Livingston B .
Livingston C .
Livingston C .
North..
Meters.
1247. 9212
1074. 4132
1152. 3746
536. 1025
351 52 39.27
33 57 34.83
8 25 39.79
353 51 14.65
9.9956214
9. 9187803
9.9952848
9. 9974966
3. 0961872
3. 0311713
3. 0918086
2. 9499516
3.0615936 3.0568784
3. 7432041
Computed distance Livingston-Nort
Log distance Livingston-North
3. 7407007
Meters.
1235. 4028
891. 1516
1139. 9304
5504. 2823
8770. 7671
3. 9430376
a These are the azimuths computed in the preceding computation. They are referred
to the line Livingston-North, which was assumed to have the azimuth 00' 00.00",
and the convergence of the meridians was not taken into account. Consequently they
are not true azimuths.
GENERAL INSTRUCTIONS FOR TRAVERSE. 41
GENEBAL INSTBUCTIONS FOR SECONDARY TRAVERSE.
98. Secondary traverse will be used in those areas where secondary
triangulation would ordinarily be carried on except for the configura-
tion of the ground, presence of heavy woods, and extensive swamps
which make triangulation excessively expensive.
99. In general, secondary triangulation and secondary traverse or a
combination of the two, depending on the country to be controlled,
will be used instead of primar>^ triangulation or precise traverse when
the distance between terminal points of the line or arc is less than 150
miles. These classes of work must always be joined at each end of an
arc or line with pre\'iously adjusted horizontal control,
100. The probable error of the length of a line of secondar>' traverse
should, in general, be not greater than 1 part in 25 000. This accuracy
will be obtained if the error of closure in position is less than about 1
part in 10 000 of the distance run.
101. The general instructions for precise traverse will apply to
secondary traverse. ox<"opt whoro thoy conflict \vith the following
considerations,
102. One measurement will ])e made of each section of a line of
traverse with a 50-meter invar tape under the same conditions as
obtained during standardization, except as to temperature. It may be
found desirable to read and record the temperature for each tape length
in order to keep count of the number of tape lengths. Otherwise the
temperature will be read and recorded three times on each section
once near the beginning, once near the end, and once near the middle
of the section. These readings are nece8sar\' to avoid uncertainty in
case one temperature is erroneously read or recorded.
103. The temperature may be read from only one thermometer; but,
should this be done, the thermometer should be carefully examined
and be compared with a standard thermometer once each day in order
to detect any break in the thread of mercury which might have occurred.
104. When measuring along a country road, the forward end of the
tape may be marked by a nail driven into the ground or by a wooden
peg, on which the end of the tape may be indicated by a small nail
driven into the peg. A piece of paper laid on the ground and weighted
down, by a stone or earth, near the peg or nail will enable the rear tape
man to find the nail or peg easily.
106. If any part of the tape is unsupported, a note to this effect should
be made in the record book and a correction for sag or catenary will be
computed and applied when the office computation is made.
106. For measurements along a rail of a railroad no inclinations will
be computed for separate tape lengtlis where the slope is approximately
42
U. S. COAST AND GEODETIC SURVEY.
the same from one end of the section to the other. Under this condition
the inclination correction for the distance mil be taken from the
inclination correction table which follows. There will be computed
for each tape length the inclination correction for portions of a section
which are measured over stakes. This is necessary because the grade
is frequently steep when measuring from a point of tangency on a rail-
road to the station at the end of the section.
107. Inclination correction (see p. 25).
Distance
Difference of elevation in meters.
in meters.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
100
mm.
5
2
mm.
20
5
mm.
45
22
15
11
9
8
6
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
200
40
27
20
16
13
11
10
9
8"
62
42
31
25
21
18
16
14
12
11
10
90
60
45
36
30
26
23
20
18
16
15
14
13
300....
82
61
49
41
35
31
27
24
22
20
19
18
16
15
107
80
64
53
46
40
36
32
29
27
25
23
21
20
19
B
135
101
81
67
58
51
45
40
37
34
31
29
27
25
24
22
21
20
400
125
100
83
71
63
56
50
45
42
38
36
33
31
29
28
26
25
151
121
101
86
76
67
60
55
50
46
43
40
38
36
34
32
30
180
144
120
103
90
80
72
65
60
55
51
48
45
42
40
38
36
500.... .
169
141
121
106
94
84
77
70
65
60
56
53
50
47
44
42
196
600....
163
700
140
800....
123
900
109
1000
98
1100 .
89
1200
82
1300..
75
1400
70
1500...
65
1600.
61
1700
58
1800
54
1900
1
?>f,-
2000
....
49
i 1
1
Distance in
15
16
17
Difference of elevation in meters.
meters.
18
19
20
21
22
23
24
25
26
27
500
mm.
225
187
161
141
125
112
102
94
86
80
75
70
66
62
59
56
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
t
mm.
mm.
600
213
183
160
142
128
116
107
98
91
85
80
75
71
67
64
241
206
181
161
144
131
120
111
103
96
90
85
80
76
72
270
231
203
180
162
147
135
125
116
108
101
95
90
85
81
700
258
226
201
180
164
150
139
129
120
113
106
100
95
90
286
250
222
200
182
167
154
143
133
125
118
111
105
100
315
276
245
220
200
184
170
157
147
138
130
122
116
110
800
303
269
242
220
202
186
173
161
151
142
134
127
121
331
294
264
240
220
203
189
360
320
288
262
240
222
206
900
347
312
284
260
240
223
208
195
184
174
164
156
376
338
307
282
260
241
225
211
199
188
178
169
405
1000
364
1100 . . .
331
1200.
304
1300
280
1400
260
1500
176
165
156
147
139
132
192
180
169
160
152
144
?43
1600
228
1700
214
1800
20?,
1900
^n
2000
182
GENERAL INSTRUCTIONS FOR TRAVERSE. 43
Inclination correction Continued.
Difference of elevation in meters.
Distance in
meters.
28
29
30
31
32
33
34
35
36
37
38
39
40
1000
mm.
392
356
327
302
280
261
245
231
218
206
196
mm.
420
382
350
323
300
280
263
247
234
221
210
mm.
450
409
375
346
321
300
281
265
250
237
225
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
1100
437
400
370
343
320
300
283
267
253
240
465
427
394
366
341
320
301
284
269
256
495
454
419
389
363
340
320
302
287
272
1200
482
445
413
385
361
340
321
304
289
610
471
438
408
383
360
340
322
306
540
498
463
432
405
381
360
341
324
1300
527
489
456
428
403
380
360
342
555
516
481
451
425
401
380
361
585
543
507
475
447
422
400
380
1400
571
1500
533
1600
.son
1700
471
1800
444
1900
421
2000
400
108 . In taking the inclination correction from the tables the difference
in elevation of the two points of tangency of a section can be obtained
from the Y leveling over the stakes at the ends of a section. The
record should show clearly what are the differences in elevation between
the ends of the section and the points of tangency, and there should
be no doubt whatever as to the sign of each difference. These differ-
ences applied to the difference in elevation of the ends of the section
as furnished by the precise leveling will give the difference in elevation
of the points of tangency, which is one of the arguments in obtaining
the correction from the table. The other ailment is the distance
between the tangent points. In most cases the grade corrections
obtained from the table will be too small, owing to irregularities in the
slope of the line, but the error mil in nearly all cases bo less than i part
in 100 000, and therefore may be neglected.
109. Should the grade change decidedly in a section, the distance
of the change or changes from one of the ends of the section should be
noted in the record of tape measurement, and the slope may be meas-
ured by a small transit or theodolite. The correction will be
D (l-cos^),
where D is the measured distance and A is the angl( of inclination.
The foUomng table gives values of 1 cos A for various slopes.
44 U. S. COAST AND GEODETIC SURVEY.
110. Factors for inclination correction.
rCorrection=D (1 cos A).]
Angle
Angle
Angle
Ajigle
ofincli-
1 cos^.
ofincli-
1 oos^.
of incli-
1 cos^.
ofincli-
1-cos^.
nation.
nation.
nation.
nation.
00
0.0000000
r
50
0.0001058
o r
1 40
0.0004230
2 30
0.0009518
01
0.0000000
51
1100
41
4315
31
9645
02
0002
52
1144
42
4401
32
9773
03
0004
53
1188
43
4488
33
0.0009902
04
0007
54
1234
44
4576
34
0. 0010032
05
0011
55
1280
45
4664
35
0163
06
0015
56
1327
46
4753
36
0294
07
0021
57
1375
47
4843
37
0427
08
0027
58
1423
48
4934
38
0560
09
oa34
59
1473
49
5026
39
0694
10
0.0000042
1 00
0.0001523
1 50
0.0005119
2 40
0.0010829
11
OOol
01
1574
51
5212
41
0965
12
0061
02
1626
52
5307
42
1101
13
0072
03
1679
53
5402
43
. 1239
14
00S3
04
1733
54
5498
44
1377
15
0095
05
1788
55
5595
45
1516
16
0108
06
1843
56
5692
46
1656
17
0122
07
1899
57
5791
47
1797
18
0137
08
1956
58
5890
48
1939
19
0153
09
2014
59
5991
49
2081
20
0.0000169
1 10
0.0002073
2 00
0.0006092
2 50
0.0012224
21
0187
11
2133
01
6194
51
2369
22
0205
12
2193
02
6296
52
2514
23
0224
13
2254
03
6400
53
2660
24
0244
14
2317
04
6505
54
2806
25
0264
15
2380
05
6610
55
2954
26
0286
16
2144
06
6716
56
3103
27
0308
17
2508
07
6823
57
3252
28
X)332
18
2574
08
6931
58
3402
29
0356
19
2640
09
7040
59
3553
30
0.0000381
1 20
0.0002708
2 10
0.0007149
3 00
0.0013705
31
0407
21
2776
11
7260
32
0433
22
2845
12
7371
33
0461
23
2914
13
7483
34
0489
24
2985
14
7596
35
0518
25
3057
15
7710
36
0548
26
3129
16
7824
37
0579
27
3202
17
7940
38
0611
28
3276
18
8056
39
0644
29
3351
19
8173
40
0.0000677
1 30
0. 0003427
2 20
0.0008291
41
0711
31
3503
21
8410
42
0746
32
3581
22
8530
43
0782
33
3659
23
8650
44
0819
34
3738
24
8772
45
0857
35
3818
25
8894
46
0895
36
3899
26
9017
47
0935
37
3980
27
9141
48
0975
38
4063
28
9266
49
1016
39
4146
29
9391
GENERAL INSTRUCTIONS FOR TRAVERSE. 45
111. When measuring distances of a secondary traverse along a
country road, slopes may be measured as angles of inclination with a
small transit or theodolite, or the differences in elevation of the tape
ends may be obtained by a single line of ordinary leveling. In order
that there may be no uncertainty as to the identification of the tape
ends, it may be advisable to have the leveling follow just behind the
measuring party.
112. ^^^len measuring over a country road where the ground is nearly
level or where the slopes are low with very small changes in grade, it
will not be necessary to determine the difference in elevation of the
ends of each tape length. Under such conditions it will be best to
measure inclinations as angles.
113. A second measurement must be made of each section of a sec-
ondary traverse with a 300 or 200 foot tape. This measurement made
with a tape of a different unit from that of the tape used in the first
measurement will make it reasonably certain that no tape length has
been dropped or added in the first measurement and will also guard
against a blunder in measuring a set-up. The second measurement is
made only as a check, and no grade, temperature, sag, or other correc-
tions will be made to the distance measured. A second check meas-
urement should be made with the foot tape if the first check measiu*e-
ment does not agree within one part in 1500 with the measurement,
uncorrected for grade, made with the meter tape. If the error was
made in the meter-tape measurement, a second measurement should
be made with that tape. The record must indicate clearly the
accepted length.
Measurement of angles.
114. In general, the angles of the traverse will be measured with a
7-inch theodolite, using the method of repetitions. The requisite
accuracy will probably be obtained if the angle is measured by 6 repe-
titions of the angle and 6 repetitions of the explement of the angle.
The telescope should be reversed in the middle of the set to eliminate
the effect of the coUimation error. If the angles are measured with a
direction theodolite, three or four measures, with the initial readings
equally spaced on the circle, will be sufficient. The angle should be
measured clockwise from the back station.
116. The greatest care should be used to make sure that the pole on
which the angle observations are made is straight, accurately centered
over the station, and vertical. If the line is of such length that the
pole can not be distinctly seen, one face of the signal pole or of any
target used should be placed at right angles to the line of sight to avoid
the effect of phase.
46 U. S. COAST AND GEODETIC SURVEY.
Azlmutli stations.
116. Azimuth stations on secondary traverse lines will be estab-
lished at intervals of from 15 to 20 traverse stations. These azimuths
should have an accuracy represented by a probable error not greater
than 1/^5. This accuracy can probably be obtained by making
double the number of observations that is used in measuring a horizontal
angle of the secondary traverse. Instructions for azimuth observations
will be foimd on page 14.
INDEX
Accuracy: Paragraph.
Angle observations 35, 114
Azimuth obser^-ations 44, 45, 116
Check measurement 33
Secondary traverse 100
Angle:
Inclination of tape Ill, 112
Measurements 34-46, 70, 114
Observations, secondar>' traverse. 114
Angles to additional points 41
Azimuth:
Accuracy 116
Long lines 4, 46
Observations 44, 45
Stations 42,116
Stations, location 43, 45, 46
Base line, second precise measure-
ment 12
Base tapes. See Invar tapes.
Bench marks:
In towns 57
O n traverse stations 57, 68
Bench over station mark 14
Cards for descriptions 54
Catenary 84,105
Catenary correction formula 86
Centering of instnmient and object. . 39
Changes of grade 62
Check measurement:
300-foot tape 27,72
Second 33
Secondary traverse 113
Closure of loop 94, 95, 96
Computations, sample. . 76-so, S3-87, 91-97
Counters for tape lengths 19, 27
Description cards 54
Descriptions of stations 52-54
Designation:
Points of tangencv 25, 30, 56
Stakes ". 66
Direction instrument 34, 36
Direction Instrument, definition of
position 36
Distances:
Approximate for descriptions 53
Between azimuth stations 43,45,46
Between traverse stations 2
By precise leveling 60
Computation of final 84
For loop 97
Measurement for secondary trav-
erse 102
Measurement of check 27, 72
Measurement of precise 5, 71
Offset 15
To points of tangency 25,30
BocentricItIs 39, 115
Elevations: Paragraph.
Additional, by precise leveling 56
Points of tangency 56
Rail opposite stations and bench
marks 60
Reference marks 58
Extra fore sights 61
Factors for inclination correction... 110
Fore sights, extra 61
Grade changes 62
Grade correction. See Inclination
correction.
Inclination:
Angle 111,112
Correction 55-67, 78-80, 106
Correction tables 79-82, 107-110
Injury to tapes 9
Instrument , centering 39
Instruments 34, 67
Invar tapes, 50-meter 5-11, 102
Kinks in tape 9
Length.*!. See Distances.
Level rods:
Alternating 64
For Y levels 67
Leveling:
Preci.5e 55,56,75
Precise, distances 60
Precise, extra fore sights 61
Y, over stakes 65,67,73,74
Y.rods 67
Location:
Azimuth stations 43,45,46
Permanent station marks 49
Traverse stations 1, 2, 3
Loop:
Closure 94,95,96
Distance 97
Lines to form 4, 46
Marks:
At station 47-51
For tape lengths 17,18,104
Reference, elevation 68
Measurement:
Check , secondary traverse 113
Distances , check 27, 72
Distances , precise 5, 71
Distances, second check 33
Distances , secondary traverse 102
Taping in rain 26, 31
To additional points 24, 30
Notes on description of stations 52
Object, centering 39
47
48
INDEX.
Observations: Paragraph.
Angle, secondary traverse 114
Angle, subsidiary stations 38
Angle, weather conditions 37
Azimuth 44
Number required for angle 35
On Polaris for azimuth 42
Offset distances 15
Phase 40,115
Points:
Angles to additional 41
Measurements to ad ditiona ! 24 , 30
Points of tangency 25, 30
Elevations 56
Polaris observations for azimuth 42
Position, definition, dirootion instru-
ment 36
Precise leveling 55, 56, 75
Distances 60
Extra fore sights 61
Profile of track 59
Projection, rail to true station ... 91, 92, 93
Rail elevations, opposite stations
and bench marks 60
Rail station, projection to true
station 91, 92, 93
Rail stations 16
Railway stations, name 63
Records, sample 68-75
Reference marks 50
Elevations 58
Restandardization of tapes 7, 8
Rods, level:
Alternating 64
Y levels 67
Sample computations. . . 76-80. 83-87, 91-97
Sample records 68-75
Secondary traverse 98-116
Setbacks 20, 21
Set-ups 20, 21
Stadia readings, Y levels 67
Stake setting 22
Stakes:
Designation 66
Y 1 e veling 65, 67, 73, 74
Stand over station mark 14
Standard mark for station 47, 48, 50
Standard notes, descriptions of sta-
tions 52
Standardization:
Of tapes 7, 8, 85
Tension of tapes 10
Station marking 47-51
Station stand or bench 14
Stations:
Angle observations at subsidiary . 38
Angles to additional 41
t. Azimuth 42, 116
'^^ Descriptions , 52-54
Stations Continued. Paragraph.
Distances between 2
In towns 3
Location of 1-3
Measurements to additional 24, 30
Projection from rail to true 91-93
Rail 16
Railway, name 63
Traverse, as bench marks 57, 58
Support:
For tapes 13, 28, 105
Tape correction tables, for various
methods of 90
Tables:
Explanation 77
Inclination correction 79-82, 107-110
Tape correction 89, 90
Temperature correction 88
Tangents, location of stations along . 1,2
Tape correction:
Computed values 86,87
Tables 89, 90
Tape lengths:
Counter- 19, 27
Marks 17, 18, 104
Tapes:
50-meter invar 5-11
300-foot 27
Checking lengths in field 6
Kinks 9
Number used 6
Standardization 7, 8, 85
Support for 13, 28, 105
Temperature 11, 27, 32
Tension 10, 29
Tapmg:
On wet rails 26, 31
Triangle to avoid 23
Temperature correction tables 88
Temperature of tapes .... 11, 27, 32, 102, 103
Temporary marks 49, 51
Tension for tapes 10, 29
Theodolite 35
Thermometer attachment 11
Thermometers 11, lOa
Towns:
Bench marks in 57
Stations in , 3
Triangle to avoid taping . . . , 23
Weather conditions for observing
angles 37
Weather, taping in rain ...... , 26, 31
Y level 67
Y leveling:
Over stakes 65,67,73,74
Rods 67
Stadia readings 67
^JNIVERSIT Y OF TORONTO
LIBRARY
PLEASE
:ave this card
IN -eooK
pockeT
