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B. TRIANGULATION
Compiled by E. M. DOUGLAS
GENERAL CONDITIONS FOB MAP CONTROL
The boundary lines of all regular United States Geological Survey
maps are parallels of latitude and meridians of longitude. In order
that these shall be properly located and that intermediate points
shall be placed in correct positions, some system of horizontal con-
trol is required. The method to be adopted for linear control should
be fixed by the character of the country, one of the requirements
being that all control work shall be so accurate that no errors will be
apparent in maps several times as large in scale as those to be pub-
lished. In mountainous regions or in hilly, partly timbered areas hori-
zontal control is effected by a system of triangulation, the whole area
being divided into triangles whose apexes are represented by stations
established on prominent points several miles apart. The angles
between each station and all others visible from it are carefully meas-
ured with a theodolite graduated to read angles by micrometer to
two seconds of arc or by estimation to fifths of a second. One side
of the triangles, called the base line, must be carefully measured
with a steel tape, if its length has not been previously determined,
account being taken of slope of the line, elevation above sea level,
temperature of the tape, and other essential details; and for at
least one station the exact latitude and longitude and also the azi-
muth of one of the lines leading from the station must be determined
by astronomic observations or by a connection with stations previpusly
located.
In heavily timbered areas, where it is difficult to see from any
point more than a mile or two in any direction, horizontal control is
best obtained from distances measured on the ground with a 300-
foot steel tape, a record being made of angles measured with a transit
at each bend in the line. Such control, called transit traverse, must
begin and end at points whose positions have been previously deter-
mined, and regardless of the character of the country such control
must be carried around the edge of each quadrangle and once across
its center east and west.
Because of the great expense involved in base-line measurements
and in the determination of positions from astronomic observations,
47
48
it is generally advisable to connect triangulation systems or traverse lines with positions previously determined, even though they may be a long distance away. There are now few localities in the United States that can not conveniently be connected with known positions, and therefore, before horizontal control work is begun, the records of the Coast and Geodetic Survey, the Lake Survey, the United States Army Engineers, and other Government organizations should be examined in order to ascertain what positions in or near the area to be surveyed have been determined and are available for use in the work in hand. Wherever possible, geographic locations should be based on the North American datum (formerly known as the United States standard datum), for there is in many localities a considerable differ- erence between the standard and astronomic data. The results of triangulation or transit traverse by the Geological Survey can always be obtained by anyone having occasion to use them by applying to the Director, United States Geological Survey, Washington, D. C. The United States Board of Surveys and Maps has fixed require- ments for triangulation control, from which geographic positions are to be computed, as follows:
First order
1 1:25,
Second order
1:10,000^3
Third order
5 1:5,
Triangulation by the Geological Survey as described on the fol-
lowing pages, which is intended for map control only, is classed by
the Board of Surveys and Maps as of the "third order," consequently the triangles should close with an average error of not more than 5 seconds, and the check on the terminal line or base must not exceed 1 part in 5,000 of the length of the line. Triangulation of the two higher orders serves both for geodetic investigations and for map control. At present such work is carried on by the United States Coast and Geodetic Survey in accordance with special instructions prepared by that bureau.
TRIANGULATION FIELD WORK GENERAL REQUIREMENTS
Amount of control. At least three serviceable stations of the third or a higher order must be established for each quadrangle, regardless of the scale of the map, and as many more as may be necessary to afford adequate bases for plane-table control. In addition, a number of secondary points such as church spires, windmills, water tanks,
50 TOPOGRAPHIC INSTRUCTIONS OF GEOLOGICAL SURVEY
of well-proportioned triangles. Overlapping figures or an excess of observed lines beyond those necessary to insure a double deter- mination of each length are undesirable, although a diagonal through some figure may occasionally be valuable as a check. As a rule additional lines of this kind only complicate the main scheme with- out materially adding to its strength, and the numerous observa- tions made for them are discarded by the computers as superfluous. Judgment is to be used in this matter, however, for in many regions the atmospheric conditions are exceedingly uncertain, and the ob- server can not always count on being able to see in both directions over every line that may be essential to the main scheme. In such regions it is well to err on the safe side and obtain too many data rather than too few. Angles should be read to all prominent points outside of the area for use in future expansion, even though the points lack signals or are not sharply defined. Secondary points. In cutting in secondary points for topographic control it should be remembered that locations that depend on two sights only, even if the angles are of adequate size, are likely to be of doubtful value, because of the absence of any check on possible gross errors in observing or computing, or because of the possibility of mistakes in the identification of the points. An endeavor should therefore be made to obtain at least three sights to every secondary point, even if the triangles are not of the best shape. Observers are especially cautioned not to slight the location of secondary points merely because they happen to be of no importance in their scheme of figures. As the topographer may find it expedient to start his control from a secondary point, a blunder in the location of such a point may result in his starting with an erroneous base and having later to make corrections at a great cost. Consent oj owner. Before a site for a station on private land is selected, the written consent of the owner should be obtained, if practicable, for establishing a permanent station mark and erecting the*required signal. If a summit must be cleared of timber, or if lines of sight must be cut, the value of the timber to be cut should be definitely fixed and agreed upon with the owner before cutting is begun. When it is necessary to clear away timber and the owner or agent for the ground can not be reached without great delay, three resi- dents of the locality should be asked to appraise the value of the timber cut and to sign a written statement regarding it. This state- ment should be forwarded to the office of the Survey for consideration if a claim for damage is filed. Station marks. Triangulation stations must be permanently .marked by standard bench-mark tablets, each tablet to be set in
TBIANGULATION 51
rock in place or in the top of a concrete or stone pier. (See pi. 4 and also p. 120 of leveling instructions, for instructions in regard to setting tablets.) When practicable, bottles or other imperishable material should be left as subsurface marks. Two or more permanent reference marks should be established about each station mark. These may consist of holes drilled in rock in place in which a metal reference mark tablet is to be fixed, with the arrow pointing toward the station; spikes in roots of trees; or large stones set solidly in the ground. The azimuth and the distance to each reference mark must be duly entered in the field record. When old stations are revisited and any of the marks are found to be defective or to have been destroyed, new marks must be estab- lished in their places, and a report regarding them must be sent at once to the Washington office. Signals. Triangulation signals must be built with a view to their permanence as well as to their visibility. They may be of various forms, the form selected depending on the locality and the materials at hand. Thus, a signal on a bare mountain peak may be a rock cairn; one on a partly wooded summit may be a straight tree, the surrounding timber being cleared away; one on cleared land may be a tripod or quadripod. (See pi. 1.) Rock cairns should be not less than 8 feet high and should be Avell put together, so that they will withstand strong winds and heavy snows. A pole or a small green tree placed in the top is of advantage in sighting. Signal trees are most satisfactory if stripped of their branches, except a tuft at the top. They form the best of targets when sighted against the sky, but if they are to be sighted against a dark back- ground, they should carry two triangular targets 3 to 6 feet on a side, placed at right angles to each other and covered with white cloth. Tripods or quadripods should be built of sawed lumber if such mate- rial is available. For the legs and center pole 2 by 4 inch scantlings may be used; for the cross braces 1 by 6 inch boards. The base of the pyramid should be large enough to permit a theodolite to be set up under the center pole. In order to increase its visibility, boards may be nailed across the sides about a foot apart and cov- ered with signal cloth, and cross targets may be attached to the center pole above the apex of the pyramid. The best colors for this cloth are white and black or white and red. Most signals stand in exposed places and should be securely anchored to prevent their being blown over. The legs of tripods and quadripods should be placed in the ground at least 2 feet; each leg should be fastened to a "deadman" and the hole filled with thoroughly tamped earth or rocks, or else a stake 4 feet long should be driven into the ground at an angle with each leg and firmly spiked
TJ. S. GEOLOGICAL SURVEY BULLETIN 788 PLATE 1
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WHBfcjsm.'!
1
OBSERVING TOWER AND SIGNALS
U. S. GEOLOGICAL SURVEY BULLETIN 788 PLATE 2
VERNIER TRANSIT-THEODOLITE
U. S. GEOLOGICAL SURVEY (^) BULLETIN 788 PLATE 4
> O E-LEVAT10N
O ABOVE 'A. S A
FEET
ELEVATION ABOVE A SEA
GEOLOGICAL SUKVEY MARKS FOR TRIANGULATION, TRANSIT TRAVERSE, AND LEVELING
TRIANGULATION 53
Heliotroping. The heliotrope outfit commonly used by the Survey
is either the Steinheil or a plane mirror with a screw hinged to the
back to give it universal motion and improvised diaphragms of tin
or wood with round apertures. The plane mirror is generally pre-
ferred to a heliotrope of the more elaborate form.
A heliotrope is usually set up by mounting the mirror on a stake
or board immediately over the center of the station and the diaphragm
on another stake, 10 or 20 feet away, carefully aligned with the distant
station. The operator must constantly watch the reflection from the
mirror and keep it symmetrically over the aperture. If the sun is
back of the observer a second mirror, a foot or two from the first, may
be used to reflect the light into the first.
To the observer the flash should appear as a clearly defined point
of light; if of appreciable size it will be necessary to bisect it, and an
error is thus likely to be introduced. The apparent size of the flash
depends more on the steadiness of the atmosphere than on the size
of the aperture. An aperture greater than 1 inch will not be required
in Geological Survey work.
PERSONNEL AND OUTFIT OP PARTY
In general each party consists of a chief of party, who acts as
observer, and a recorder; also a cook and a teamster (or packer)
when camping is necessary. Additional men are required for helio-
troping, one for each heliotrope station, and local laborers may be
employed to clear timbered summits or to erect large signals.
The following instruments and books are used in Geological Survey
triangulation for map control:
One 8-inch theodolite, with leather carrying case and shoulder straps, or a transit. Two pairs field glasses. One prismatic compass. One protractor (6-inch celluloid, full circle). One boxwood scale, graduated to inches and tenths. One 50-foot steel tape, meters on back. Two electric hand lamps. One 6-foot steel tape. Heliotropes. One plumb bob. Triangulation tablets. Cement, cans. Signal notices, printed on cloth. Climbing irons, for use in wooded regions. Sun umbrella IFor use in regions where improvised sun and wind shelters Wind screen j can not readily be built. Triangulation field notes (9-912). Computation of geodetic distances (9-901). Computation of geodetic coordinates (9-902). Computation book, blank (9-889). Polaris positions for year. Geographic tables and formulas (Bulletin 650). Seven-place logarithmic tables. A good watch must be provided by the chief of party.
TBlANGtTLATION 55
instrument. Most webs taken from grass or bushes are rough,
coarse, and dirty.
To draw the reticule from the instrument, unscrew and remove
the eyepiece slide; then take out two opposite capstan-headed screws
and loosen the other two. Using the latter two as handles, revolve
the cross-wire ring 90°, insert a pointed stick through the end of the
telescope tube into a screw hole in the ring, and, using it as a handle,
remove the other capstan screws and draw out the ring. To replace
it in the telescope, reverse this procedure. When in place the cross
wires should be on the side of the ring toward the eyepiece.
Having pressed a bit of beeswax to each prong of the dividers or'
forked stick, let a small web fall from the end of one of the prongs,
or pick with it from a cocoon a single thread, pressing the thread
into the beeswax, stretch the thread moderately, and attach to the
wax on the other prong. If an old web is used, it should first be
dampened by dipping in water for a few seconds. In place of the
dividers or forked stick, small sticks or lumps of wax may be at-
tached to the web about 2 inches apart. Place the web across the
reticule, using a magnifier to insure its coinciding exactly with the
marked lines. Put a small drop of shellac on each end and leave
until dry.
Cleaning instruments. Instruments having working parts exposed
to air and dust require cleaning from time to time. Such exposed
parts as the threads of tangent screws are particularly liable to collect
dust and grit and should be wiped frequently with an oily rag, then
rubbed dry. Only the best quality of clock or watch oil should be
used for this purpose.
Steel tapes should be cleaned and oiled after use. All moisture
or grit must be wiped from them each time they are reeled, or they
will deteriorate rapidly.
Neither the object glass nor the eyepiece of a telescope should ever
be rubbed with rough cloth or with the fingers, as the glass may
thus be permanently scratched. The lenses should never be removed
from the cell that holds them nor separated from one another.
Packing and shipping. In shipping instruments by freight or
express transit and theodolite boxes must be filled in with paper or
cloth, so that if any part of the instrument should jar loose during
the journey it may not roll around in the box and damage other
parts. Heavy articles, such as compasses, aneroids, or other small
instruments, should never be placed in the instrument box. The
micrometers of theodolites should be wrapped tightly with cloth, as
they are easily jarred loose. The same precautions should be taken
when these instrument are to be transported by pack train.
On no account should any instrument be shipped by express or
freight in its own case only. A wooden box, large enough to permit a
56 TOPOGRAPHIC INSTRUCTIONS OF GEOLOGICAL SURVEY
generous amount of excelsior, hay, or other padding around the instrument case, should be provided. In mountains where pack trains are the sole means of conveyance the triangulator's outfit is most conveniently carried in a pair of canvas pack bags (alforjas), which must be properly balanced. The tripod, umbrella, and wind screens should be placed lengthwise on top, lashed to the saddle, and further balanced by properly disposing them on each side of the center. A canvas pack cover should be thrown over the whole and tucked in on all sides.
ADJUSTMENT OF INSTRUMENTS
PRECAUTIONS
The object glasses and eyepieces of all instruments must be prop- erly focused. The cross wires projected against a distant object should appear immovable when the eye only is moved. Before the adjustments are commenced the instruments must be firmly set up and leveled. An instrument may appear to be out of adjustment simply because some part is loose. The object glass may be partly unscrewed or an adjusting screw may be only partly tightened; level bubbles or cross wires occasionally become loosened. There- fore, before commencing the adjustment of an instrument look out for such defects. When it is thought that an adjustment has been completed, always test it before using the instrument. All adjusting screws should be screwed tight enough to hold, yet not so tight as to injure the threads or put a severe strain on any other part. Espe- cial care should be taken not to strain the cross-wire screws. Adjust- ments should be made in the order given under the following headings,
for some adjustments depend on the accuracy of others previously made, and a change in any one may affect the others.
MICROMETER THEODOLITE
Striding level. Place the level (pi. 3) in the proper position on the telescope axis. Level carefully with the horizontal plates clamped, and rock the level slowly back and forth till the foot pieces strike. If the bubble leaves the center, bring it back by means of the side adjusting screws near one end of the tube. Reverse the level and bring the bubble halfway back to the center by raising or lowering one end of the tube with the screw at that end and the other half with the leveling screws. Repeat these operations till the adjustment is perfect. Standards. After the striding level is in adjustment with the lower horizontal circle clamped, level the instrument hi two posi- tions at 90° from each other. Turn on the vertical axis 180° from one position; if the bubble runs away from the center, bring it halfway
58 TOPOGKAPHIC INSTRUCTIONS OF GEOLOGICAL SURVEY
screw and the distance between the micrometer box and the gradu- ated plate. When the former is longer than it should be, the latter should be made longer, if an adjustment is desired, and vice versa. To make the adjustment, loosen the small capstan-headed screws which clamp the microscope tube; then, if the thread space is long, twist the middle part of the tube (including the micrometer box) back and forth and at the same time pull it upward, thus lengthening the distance to the graduated plate. When by estimation it has moved far enough, which can be roughly determined by the amount of blurring that results from the lower lens being thrown out of focus, clamp the upper capstan-headed screw. The lower part of the micro- scope tube holding the objective lens must now be twisted and gently pushed downward till the graduations again appear in focus. If the movable threads and graduations are not then parallel, the upper screw must be again loosened and the tube turned far enough to make them parallel, after which both screws' must be tightened. Test the adjustment by again measuring a 10' space with the microm- eter. If it is still out of adjustment, repeat these operations till it is satisfactory. When the adjustment has been completed a scratch may be made on the tube below each support and used as a guide in future adjustments. The opposite micrometers may be placed 180° apart by setting one at a reading of 0° 0' 0", with the comb scale exactly centered, and then centering the comb scale of the other micrometer over the 180° mark by means of the capstan-headed screw at the left-hand end of its box. Bring the micrometer threads over the 180° mark also; then, while holding the screw firmly in place, turn the graduated ring till it reads zero.
When setting the micrometer wires on a graduation, it is very important that they be moving toward the right when the turning of the screw is stopped. Should they be moved, the least bit^too far to the right, turn back not less than half a revolution of the screw and then bring them forward again. In general, when a setting is made by means of a screw working against a spring, the spring should always be undergoing compression when the motion stops. Cross wires. The vertical wire should be truly vertical; otherwise an exact adjustment of the cross wires is not essential. After the striding level has been adjusted and the horizontal axis of the telescope carefully leveled, sight a distant point, raise and lower the telescope through an angle of 5° or 10°, and note whether the cross wires follow the point. If not, loosen the cross-wire ring and twist slightly; repeat the adjustment if necessary. Hold the striding level on the telescope parallel to the optical axis and, with the bubble in the center of the tube, set the intersection of the cross wires on a distant point and clamp both plates; lift the
TRIANGUIoATION 59
telescope out of its supports and turn 180° around its optical axis; set it again on the selected point. If the striding level when placed on top of the telescope is horizontal and the vertical wire still cuts the point, the adjustment is complete. If not, shift the cross-, wires in either direction by means of the capstan-headed screws for one-half the apparent error. Repeat the test till the error is nearly all elim- inated. Finally readjust the vertical wire, if necessary; or both wires may be put in place by revolving them in temporary wooden. Y sup- ports. / TEANSIT THEODOLITE / / .. - , The adjustments for striding level, standards, and plate (level are the same for the transit theodolite (pi. 2) as for the micrometer theodolite. Collimation. Level carefully, sight on a point about 500 feet dis- tant, raise or lower the telescope slightly, and note whethervthe ver- tical wire remains on the point; if not, loosen the capstari-headed screw and turn the cross-wire ring till the vertical wire will ;remain on the point when the telescope is raised or lowered. Clamp the instrument, set the vertical wire so that it cuts the point selected* transit the telescope by revolving it 180° on its horizontal axis, and select a second point 500 feet distant in the opposite/ direction from the first. Unclamp the upper plate, turn the transit 180? on the vertical axis, set it on the point first selected, and again clamp the plate. Transit the telescope, and if the vertical cross wire exactly bisects the second point its adjustment is perfect; if it does not, bring it one-quarter of the way back to the second, point by turning the two capstan-headed screws on the sides of the telescope. Eyepiece tube. The eyepiece may be put into/ position over the cross wires by turning the screws that hold the eyepiece ring until the cross wires appear in the center of the field; an exact centering is not required. / Telescope level. If there is a level attached to/the telescope, it may be adjusted by the "peg method" after all the other adjustments are made, as follows. Level the transit and bring the bubble to the center of the tube under the telescope. Take a reacjing on a leveling rod or pole 300 or 400 feet distant, which is held on a stake set firmly in the ground. Revolve the transit 180° on the vertical axis and after again bringing the bubble to the center set a second stake at the same distance as the first and at such an elevation that the rod or pole reading is the same as on the first stake. The tops of the two stakes will then be at the same elevation. Move the transit 25 or 50 feet back of one stake and on a line with the other. Make the tele- scope as nearly horizontal as possible by means of the attached level, clamp it, and then take a reading on the rod held on the near stake and another reading on the distant stake. If the two readings agree, 58515° 28 5
TRIANGULATION 61
that 19 especially distinct and easily sighted and use it as the initial point for all sets of readings. The telescope being set on the initial point, read both micrometers, then sight the other stations in suc- cession in the order of their azimuths (clockwise rotations), closing on the initial point. Then reverse telescope, set on initial point, and sight the stations in reverse order. This completes one set of readings with telescope direct and reverse. Now shift the circle about 45° (examine the plate bubbles after this shift and relevel if necessary) and begin another set. When pressed for time, shift the circle when telescope is reversed. No angle should be considered well determined that has not been measured on at least four different parts of the circle or eight times in all, four with telescope direct and four with telescope reversed. When the telescope is reversed, each end of its axis will rest in the same Y as before. Reversals and releveling are of especial importance where there is an appreciable difference in the elevations of the points sighted. If the observations are made in the afternoon, take all secondary pointings before commencing the observations to stations, and make at least two sets of such pointings; the remaining time for observing can then be devoted to the accurate measurement of the important angles while conditions are the most favorable. The graduated circle should never be placed so that when pointing at any particular station the micrometers will be set to even degrees, except, as before noted, while data are being obtained for "reduction to center." Field record. The field record is to be kept in book 9-912. It must be written in a plain neat hand with a No. 4 pencil or in ink, and no part of it must on any account ever be erased. A single line should be drawn through erroneous records, the corrected figures being written above. If deemed necessary, an explanation should be written in the column for remarks. The memory should not be trusted for data of any kind; the record must be faithfully kept in all particulars and must be made so complete that it can be under- stood by another person at any time. On the flyleaf of each field notebook is a blank in which all infor- mation necessary to identify the book may be recorded. This blank should be filled so far as practicable on or before the first date of entry of field notes, and it must be completely filled before the book is forwarded to the Washington office. Any failure to fill in com- pletely the blank on the flyleaf of a field notebook should be re- ported by the computer to the division engineer. One of the blank flyleaves must contain an index of the contents. The date, name of station, time of observing, and names of observer and recorder should be systematically entered at the head of each page. The position of the instrument with respect to the center of the station must be clearly defined, and if it is set up off the center a full statement must be given of the distance and the angles measured.
62 TOPOGRAPHIC INSTRUCTIONS OF GEOLOGICAL, SURVEY
On the page immediately preceding the record of angles should be written a minute and complete description of the station occupied, the station's marks, character of signal, nearest camping or other stopping places, roads, and trails, also a statement regarding the ownership of the land and such other information as will be helpful to the topographer. The description must be written before the recorder leaves the station and should be accompanied by a rough diagram showing directions to other stations and plan indicating location of instrument or signal if it was not centered on the station. The following is a suitable station description: ELK, LEWIS COUNTY, KT. About 4 miles north of Petersville and 2 miles south of Glen Springs, on a cleared round knob at the head of Elk Lick and Black Lick, branches of Kinni- conick Creek. George Washburn lives at base of hill on north side, and his place can be reached by road up Elk Lick. An excellent view in every direction. Signal: Chestnut oak aboxit 14 inches in diameter; distance 8.3 feet, true azimuth from station mark, 58° 11'. Station mark: Stone post with tablet in top, set 30 inches in ground and rest- ing on bedrock. Underground mark: A + cut in rock. A plat, drawn to scale, should always be prepared and forwarded to the office with the field notes. Reading and recording of angles. When the micrometer wires are set for a reading with the Geological Survey theodolites it is very important that the last movement of the wires be toward the right. The readings on the graduated head are then decreasing, and the spring attached to the slide that holds the wires is being compressed. If the cross wires are moved the least bit too far to the right they must not be turned backward merely to the setting but must be turned backward at least a half turn of the screw and then brought forward slowly to correct setting. When the setting is properly made a division on the graduated plate will appear exactly midway between the two movable cross wires, and an equal amount of white space will show on each side of it. A part at least of the micrometer adjustment in errors can be eliminated by making the settings with less than five turns of the screw; this can always be done if the right-hand part of the comb scale is sometimes used for comb-scale and micrometer- head readings, the 10-minute space being taken from the left. For all precision instruments in which a tangent screw and spring are used together, the setting should be made while the spring is being compressed; otherwise the "slack" of the screw may cause an error. The recorder should not only take down the readings called off by the observer but should without delay compute the angles between successive stations and also the mean readings. The following form is to be used for recording angles by the method of directions:
