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CHAPTER ~ I I GEODETIC INSTRUMENTS D. L. PARKHURST U. S. Coast and Geodetic Survey INTRO DUCT ION The accurate results obtained by the geodesist in the determination of distances and elevations and in the Axing of geographic positions over the earth's surface, are due largely to the perfection of geodetic instru- ments. The instruments now employed are the result of a gradual but steady development from the accurate but unwieldy instruments used a century or more ago. Many of the researches of the physicist., the metal- lurgist and the astronomer have been of assistance in the development of geodetic instruments and methods. The astronomical transit and the zenith telescope are the instruments used in determining longitude and latitude from observations on the stars. The long inva,r ribbon or wire is now employed in measuring, accurately the length of a side of a, triangle, called a base line, in an arc of tria.ngu- lation; the angles of the triangles, are measured by means, of theodolites. The spirit level and a. rod or staff are used in the determination of elevations. The plane of reference for the elevations is derived from observations made with the tide gauge. The values of' gravity are determined by means of the invariable free swinging pendulum which is described by C. H. Swick in Chapter X. The use of the data obtained by the instruments mentioned is set forth in other chapters of this boor<. This chapter will be devoted to a brief description of the instruments used in astronomical determinations of latitude and longitude, and in the execution of triangulation and level- in~,. References are given to reports and papers in which detailed de- scriptions of the instruments appear ASTRONOMICAL INSTRUMENTS Transit arid accessories.-The transit is used in the determination of local sidereal tine, in connection with the determ.ina.tion of the a.stro- nomical longitude of a station. The local time thus obtained is com- pa,red with the time signals sent through a radio station from the Naval 13 191

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192 FIGURE OF TTIE EARTH Observatory at Washington, or from some other observatory whose astro- nomical longitude is known. The transit hats a heavy metal base with two upright arms ha,nTing notches or V's at the tops in which. rest the pivots, or cylindrical ends, of the horizontal axis of the telescope. The base is fitted with three ver- tical screws, for making the instrument level, and with a slow-motion screw for placing the telescope in the meridian. A lifting device is fitted to the base for raising the telescope from its, supports. The telescope can be turned IS0 in azimuth after lifting and the pivots of the horizontal axis may thus he interchanged in. the vertical supports. This reversing is done either at the middle of an observing list of from 10 to 12 stars composing, a time set, or at the middle of the observations on each star, depending on the instrument used. Attached to the eye end of the telescope is an " impersonal microme- ter " or " transit micrometer " with oldish an automatic record is made on a chronograph sheet as the star moves across Else field of the telescope. The screw of the micrometer moves a carriage to which is fixed a single wire, or strand of spider web. In observing, this, wire is kept as nearly as possible bisecting the star as it moves across the held of view. Mounted on the axis of the micrometer screw is an ebony wheel into which are set 10 strips of metal. This. ebony wheel moves, under a, metal brush and completes an electric current at each, contact of a, metal strip, the tines of these contacts being registered by a chronograph. The mean of' all the recorded micrometer contacts is. the time of transit of' the star across the center of' the f~elcl of the telescope. The scaling is clone to the nearest tenth of a second of time. The Deld of view of the telescope its illuminated by the bigly -from ail electric bulb placed in a bracket fastened to one of the supports of the telescope. The light passes through. the perforated horizontal axis to ~ small mirror set into the center of the telescope and is then reflected to the cross-wires which appear black on a bright held. The brightness o-t' the field can be varied to suit the magnitude of the star observed on. A stride level which rests on the pivots. of the horizontal axis., the rea,d- ings of which are recorded at frequent intervals, enables the observer to cletermine, and correct for, the inclinations of the telescope :from the plane of' the mericlian. The angular value of one division of the level vial, usually 2 mm. in length, is about I.3o seconds of arc. The determination of the local time at a station depends usually on obser~ra.tions. made upon 12 to 2a stars. When. this is known and the local time of the time spinals sent by radio' are also known, it is a simple matter to obtain the difference in time between the geodetic or field sta- tion and the fixed astronomical observatory from which the time signals

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GEODETIC INSTRUME1VTS 193 are sent. This diff'eren.ce applied to the longitude of the observatory fur- nishes the longitude of the field station. Practically all astronomical longitudes. throughout the world are now referred to the zero' meridian at Greenwich, England. Special radio apparatus is used in longitude determinations by measles o:t' which the radio signals, are received and. recorded automatically on the chrono,ra.ph sheet. The lag of the receiving set is determined and then applied as a correction to the difference in time. A correction is also 1 1 ~ ~ 1 ~ 1 ~ 0 1 1 _ ~ ~ _ _ 1 ~ a,ppl~ecl to take account of the transmission lime of one radio signals, assumed to be that of the velocity of light. The strai,ht-telescope type of astronomical transit was generally used until within recent years. With it excellent, results can be obtained. It is being replaced, however, by the broken-telescope type in which the eyepiece is in one end. of the horizontal axis The latter hats the advan.- ta.ge of greater stability, and greater ease and rapidity of reversing. The telescope its reversed on each star in order to eliminate the effect of the collimation error. The usual telescope employ-cd has an objective of' about 24- inches aperture and a focal length of about 27 inches. The ma.gnif'y- ing power of the eyepiece is about 60 diameters. This instrument may also be used for the determination of the a.stro- nomica.1 latitude by the l:Iorrebow-Talcott method, in a manner similar to that employed in zenith telescope work. (See below.) Zero telescope. The zenith telescope is the instrument principally used in determining the a.stro~omi.cal latitude of' a ~,eodet,ic station. The method ordinarily used, known as the Horrebow-Talc.ott method, de- pends upon the micrometric measurement of the difference in zenith distances of' two stars, one north and one south of the zenith, which form a pair. An accurate level mounted on the telescope in the plane of the meridian its an essential part of an instrument to be used with this method. The zenith telescope has a vertical column risings, above a three-arm base provided with three foot-screws for leveling. The column forms a vertical axis which supports eccentrically a telescope which may be rotated in a vertical plane and also about the vertical axis. The base is provided with a slow-motion screw for placing, the telescope in the meri~l- ian plane, and lugs which may be set to define the position of the merid- ian. The objective of the telescope has an aperture of' about 3 inches and its focal length varies from 4.o to 46 inches. The magnifying power of the eyepiece generally used is 100 diameters. By means of a vertical circle and the level already mentioned the tele- scope may be set at any desired vertical angle. ~ micrometer screw with a, frame holding, a wire or strand of spider's web is fitted to the eye end .

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194 FI CURE OF THE EAR TH of the telescope. This wire, when the instrument is ready for the ob- servations, can be moved towards or away furor the zenith. The image of the star is bisected by the wire until it crosses a. fixed wire defining, the center of the telescope and the meridian. The position of the movable wire with reference to the zero of the comb is then read from a comb ire the telescope which indicates full turns of the micrometer screw. The Tractional portion of a turn is read from the graduated head of the mi.- crometer drum. Then the position of the bubble in the level vial is. read. The telescope is next rotated 180 about the vertical axis for the second star of the pair and the procedure outlined is repeated. From the star catalog (usually the Boss Preliminary Catalog) two stars are selected which cross the meridian within 3 to 15 minutes of each others a.ncl have zenith distances difI:'ering not, more than about 20 minutes of arc. The program of observing makes possible the determination of flee dif- ference in the zenith distances of the two stars, which, combined with the mean declina,tions, or angular distances, of the stars above or below the equator, furnishes a value of the latitude of the station. A latitude de- termination usually depends upon observations of from 15 to 20 pairs of stars. The work can be done on a clear flight in from 3 to ~ hours. A chronometer or clock is used in placing the telescope in the meridian and to give the times. that the stars will appear in the telescope. Azirnq~th instrument. The astronomical transit enables one to deter mine the meridian with great accuracy, but the theodolite is used almost exclusively in determining, azimuths of triangulation lines. In northern latitudes an azimuth is determined by measuring the angle between Polaris and a line of the triangulation. After observing on Polaris, the position of the bubble of the striding level is read to obtain the inclination of the horizontal axis of the telescope. The ob- served angle between Polaris and the mark or line of triangulation is corrected for this inclination. When a pointing is made on Polaris the time of the observation is noted on a clock, chronometer, or watch, whose error and rate on local sidereal time have been determined by radio time signals or by observa- tions on the stars with the astronomical transit or with the theodolite. The observations on Polaris are reduced to the true pole. TRIANGUL ATION INSTRUMENTS Bass apparatus. - -The evolution of base measuring apparatus hats been most interesting. Bars of wood, of glass, and.of many different metals have been used in the past. :Now, however, tapes or wires of invar are used exclusively in accurate base measurements.. Steel tapes or wires will ,ive excellent results when work is done at night or on cloudy days, but

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GEODETIC INSTRUMENTS 195 they are now seldom used. Since the principle involved is the same for wires as for tapes, the latter only will be described. The invar tape used in different countries varies in length from 24 to 50 meters between end graduations and has extensions of one to two meters at each end. It has a thickness of about 0.02 inch and a width of about 0.25 inch. The coefficient of expansion is usually not greater than about 0.000001 per degree Centigrade. Invar, as is well known, is not a stable alloy. However, by a special treatment (involving heating, and whipping), the tendency to change by appreciable amounts is lessened. The effect of any slow changing which may occur can be offset by having the tapes standardized just before and after their use on the base measurements. In the United States the tapes are standardized at the Bureau of Standards in Washington. As a part of the first standardization of a tape the coefficient of expansion is determined. In the field, tapes are supported at the ends and at intermediate points by posts or stakes set firmly in the ground in the exact line between base ends. The stakes are set ahead of the taping and are lined in with a transit or theodolite. The base is divided into kilometer sections and the section ends are marked by concrete or heavy wooden posts. A metal plus, indicates the point on the post to which the measurement in each direct-ion is referred. The portions of the tape between the supports' swing free, forming cate- naries. In malting the measurements the rear mark is brought into coin- cidence with the mark on the strip on the rear stake, and then the gradu- ation at the forward end of the tape is transferred to a strip of soft metal fastened to the top of the forward stake. The transfer to the strip is made with a sharp pointed scriber or awl, the error seldom being greater than + 0.! mm. A tension of Io kilograms is applied to the tape during measurements by a weight and pulleys or by a spring balance. The tem- perature of the tape is obtained by reading, for each tape length, two thermometers attached to the tape near its ends. During standardization the same number of supports and the same tension are used as during measurements in the field. With a knowledge of the weight of the tape per unit length, and of the modulus of elasticity, corrections can be computed for those cases where the tension applied in the field differs from the normal tension. Each section of the base is measured at least twice with different tapes. The probable error of the measure of length is seldom greater than one part in a million. The actual error is usually less than one part in three hundred thousand. This accuracy is sufficient for standard first-order triangulation, but greater accuracy can be obtained, as was done when

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196 PI CURE OF THE EAR TH the Pasadena. Ba.se near Pasadena, Cali.I'ornia, was measured, from which the Michelson Base between Mt. Wilson and San Antonio Peak was derived. The appliances used in holding the tape during measurement vary. The Coast and Geodetic Survey employers simple staves to which the tape ends are attached. Heliotrope aced signal lamps. Lines of triangulation are usually so long that observations cannot be made economically on poles or targets. This difficulty is overcome by using a heliograph or heliotrope to reflect sunlight during clear days and an acetylene or electric. lamp at night. Elel~otro~?e. The usual type of heliotrope consists of a flat board to which is fastened a, frame carrying a movable plane mirror and two vanes or pointers. The mirror is about 4 inches in diameter for lines up to 75 miles in length for which the visibility is good, and is larger for longer lines or for poorer conditions of visibility. In operation the heliotrope is centered over the station mark and clamped to the top of the observing, tripod or stand. By means. of' the pointers. the apparatus is. directed toward the observer's station. Then the mirror is turned horizontally and vertically until the sun's rays cast a shadow of a ring attached to the rear pointer concentrically on a larger ring on the forward pointer. The rays will then be directed to the ob- server who sees. them as a bright lilt. Owing to the movement of the sun the mirror must be adjusted three or four times a minute. When the horizontal angle between the sun and the triangulation line exceeds a certain amount an auxiliary mirror must be used, and the sunlight re- Hected twice in order that it may be directed to the observer. Larry. Many types of lamps have been used in triangulation, but the one most generally employed is the electric lamp. This consists of' an automobile headlight reflector with a special contracted-filament bulb at its focus. The reflector is in a box which can be centered and fastened to the tripod or stand over the station. The apparatus has adjustments for focusing the light. and for directing the beam horizontally and verti- cally. In actual practice it is found that the beam of light will change direction and require readjustment whenever the bulb is changed. Usually there is an attendant for the lamp at each station, but occasionally the lamps at two or more stations are placed in position and oriented by a. single member of the party. In order to economize on the consumption of the dry cells used to supply the electric current, a switch operated by a clock is used to turn the current on and oh. The clocl: will run eight days and will turn the light on for two, four, or any desired number of hours each night. When the observer snores to another station the lamp must be visited and changed to point to his new station.

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GEODETIC INSTRUMENTS 197 Bulbs of varying amperage and voltage are provided for each lamp. For short lines and clear atmosphere a one-volt bulb with one or two dry cells will give a light of required intensity, butt for lone, lines and hazy atmosphere larger bulbs are required. Over difficult lines two lamps are sometimes used, one lamp being, placed on top of' the other to avoid horizontal eccentricity. In the Ignited States an electric light has been observed upon over a triangulation line 1,53 miles long. Heliotropes leave been observed upon for distances up to 192 miles. Theodol~te. In principle the theodoli.te is, similar to the s.urve:-or's transit with which all are familiar The essential differences, are the rev finements in workmanship, optics, graduation of the circle arid in the read . ~ . 1n`~ devlee. It lla,s a three-arm base, resting Ol1 le~7eli.n`~, screws, which holds the ~,ra,duated circle and in which is set the vertical axis. The axis carries a framework which has. two upri.~,hts. terminating, in V-shaped slots in which rest the pivots or ends of the, horizontal axis of the telescope. Attached totthe uprights are two micrometer microscopes by which the horizontal circle is read. The circle varies in diameter for different makes and calibers of theoclo- lites but the tendency has been to decrease the diameter of the circle. At the present time, a. 9-inch circle is held to be large enough for even the Posit e2:a.ct angle Cork. The plate of the circle is, usually of bronze with a ring of silver set into it on which the graduations are made. The surface of the ring, navy be either a. plane or OF. a, cone depending, upon whether the micrometer microscopes are vertical or inclined. The ~raclu- ati.ons are usually spaced at intervals, of ~ minutes. Each degree is num- l~ered and the 15, 30 and 4,~ minute marls are indicated by lodger lines to :fa.cilita,te reading. The upper part of the theodolite, called the alidade~ and consisting. o:t- the telescope and. its support,, can be moved separately from the gradu- ated circle. It can be turned in azimuth, by loos,enin~t, a, clamp, and the object can be centered between the two vertical sighting wires by means of a slow-motion screw. As a, result of experiments it has, been found that. a pair of vertical wires spaced about So seconds apart gives better results than a single wire when observing, on heliotropes and lamps. The micrometer microscopes are attached rigidly to the uprights sup- porting the telescope, and are placed as nearly as practicable 180 apart. By readings, two micrometers for each pointing, o:t' the telescope the effect of eccentricity of centers. of' the alidade and base is eliminated. The effect of systematic errors in the graduation of the circle is practically elimi

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~8 FIGURE OF THE EARTH Hated by repeating the observations with the initial reading made, on different parts of the circle. The objective of the telescope varies from 1-4' to 2 inches in diameter and has a focal length of from 16 to 24 inches,. There is, no uniformity in the optics of theodolite telescopes. The field work is done under great differences in atmospheric and terrain conditions and a telescope satis- fac.tory for triangulation with short lines where atmospheric conditions are excellent, may not be suitable for mountain work with long lines partly obscured by smoke and haze. As the world is, done mostly at night the field of the telescope is illumi- nat,ed by a small electric lamp, the light from which. is carried through the perforated horizontal axis of' the telescope to the cross, wires. The method of illumination is the same as that used in the astronomical transit. Electric bulbs fixed in place are now used on some types of t,heo- dolites to illuminate the graduated circle and the micrometer head. The vertical axis which is of very satisfactory form consists of a. shingle piece ot iorgect tool st,eei with an acute cone (frustum) at its upper end and an obtuse cone (frustum) at. its lower end, with the apexes of the two cones coincident. This design insures free motion of the vertical axis in its socket regardless of the temperature during observations or of the difference in the coefficients of' expansion of the materials of the axis. and its socket. The circle supported by the base of the theodolite is held in position by either a sprin;, nut or a clamp, and can be turned in azimuth on the .j . p ,~ base. In the first-order triangulation done by the Coast and Geodetic Survey thirty-two observations are made over each line. The accuracy of the work is such that. the average closings, error of a. triangle (the difference between the observed angles and 180 plus the spherical excess) is only about one second. The probable error of an observed angle averages about 0.60 second. Greater accuracy can be obtained if desired for special pur- poses, by increasing the number of observations and by observing on a renumber of days or nights under various atmospheric conditions. LEVEL AND ROD Level. There are many models of leveling instruments used for pre- eise leveling. The one more generally used is the model of E. G. Fischer, first made in the office of'' the Coast. and Geodetic Survey. It is, the only one which limited space permits of' describing. A three-arm base with leveling screws rests. on a portable tripod. Into the base extends a vertical axis on which is mounted horizontally a tube

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GEODETIC INSTRUMENTS 199 about two inches in diameter and S~ inches long. The observing telescope is mounted inside of this tube and is supported by two' pivots just above the vertical axis and by the end of' a. micrometer screw set into the tube at a distance o:t' about four inches from the vertical axis. A spring, near the eye end of the outer tube holds the telescope down on the micrometer screw. A sensitive level vial is set in the top of the telescope tube and is covered with a glass plate. There is a capstan screw at one end of the vial container which is used. in brin~,in', the axis of the bubble parallel to the line of sight. An optical system reflects and refracts the image of the level vial to the eye of the observer through an auxiliary tube which, is fas,tenecl to the tube supported by the vertical axis. The telescope is provided with one vertical and three horizontal wires, the latter being equally spaced. In practice the observer levels the instru- ment and turns the telescope horizontally until the vertical wire falls on the leveling rod. Then with one eye! to the auxiliary tube and the other ~o me telescope ne brings one outrode as nearly as possible to the center of the level vial and holds it there by the micrometer screw while reading the position of each of the three horizontal wires on the rod. The readings are estimated to the nearest millimeter. 1 ~ 1 ~ ~ The latest model of' this level has, all metal parts of the telescope made of invar to reduce the effect of irregular expansion due to changes in t,em- perat.ure or irre,ula.r heating, of its parts. The other parts of the instrll- ment may be made of any desired metal. Rod. The ordinary type of rod used for precise leveling has a strip:) of invar between three and four meters in length, two centimeters in width and one millimeter in thickness. This strip is fastened ri~,-;dly :to ~ foot piece which terminates in a plane at. right angles to the length of the invar strip. The foot piece is rigidly secured to one end of' a wooden staff along, the face of which a channel is cut to receive the invar strip. Screws with wide heads along the sides. of the strip prevent it from pro- jectin~ beyond the face of the sod. By means of a, light sprints, at the upper end of the rod, buckling, of' the strip is prevented when the rod is held vertically during observations. On the invar strip are two columns of centimeter graduations with the black and white squares. staggered. The face of the wooden staff carries numbers indicat.in~, distances above the foot of the rod in meters arid decimeters. At the bacl: of the rod are a universal level, used in plumbing, the rods and a mercury thermometer for obtainin`, the temperature of the invar strip. The thermometer is bent in order that the bulb may be placed close to the bacl: of the strip through a hole in the staff.

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200 FIGURE OF THE EARTH S U G GESY'I O. ~ S FOR ADDI TI O1VAL READI VG Bowie, William. Determination of time, longitude, latitude, and azimuth (fifth edition). U. S. Coast and Geodetic Survey Special Publication No. 14: 5-17, 52-53, 10~107, 139-141 (1913). Breed, Charles B., and Hosmer, George L. The principles and practice of survey- ing. Vol. II, Higher surveying. John Wiley & Sons, Inc., New York, p. 1-443 (1923). Cowie, George D., and Eckhardt, E. A. Wireless longitude. U. S. Coast and Geodetic Survey Special Publication No. 109~: 3-16 (1924). Morse, Fremont, and French, O. 13. Determination of the difference in longitude between each two of the stations Washington, Cambridge, and Far Rockaway. U. S. Coast and Geodetic Survey Special Publication No. 35: 6-12 (1916). Parkhurst, D. L. Geodetic level and rod. U. S. Coast and Geodetic Survey Special Publication No. 129~: 1-11 ( 1927) . A new first-order theodolite. J. Franklin Inst., Philadelphia, 206: 623-629 ( 1928) . The United States Coast and Geodetic Survey, its work, methods and organization. U. S. Coast and Geodetic SurveY Sceeia1 Publication No. 23:1-130 (1929).