U.S. Corps of Topographical Engineers

Mode of Determining the Astronomical Positions
and the
Elements of Magnetism at Temporary Camps.1


Amiel W. Whipple

U S Corps of Topographical Engineers



Having completed a series of observations at Isleta, we proceeded seven miles down the right bank of the river to Las Lunas, a military station commanded by Capt. Ewell, of the dragoons. That officer had a thorough knowledge of the country in this vicinity, and was kind enough to accompany us upon an excursion to look at the route esteemed favorable for crossing over into the valley of Rio Puerco. It was decided to adopt this course for the survey. Lieut. Ives, with the party despatched from Washington before us with the design of reaching this place in advance of the survey, in order to make the necessary preparations for facilitating our progress westward, was detained in Texas for the want of an escort across the plains to El Paso, and therefore did not arrive here until the 6th of October. He succeeded in obtaining at El Paso the instruments loaned by the Department of the Interior, which have much increased the facilities for making scientific observations. Among them were an astronomical transit, and a "Fox" dip-circle, for measuring the elements of magnetism. The latter instrument was invented by Mr. Fox, of Falmouth, England, who has given instructions its use in obtaining the magnetic inclination of the needle, and relative intensity of magnetism at different points of the earth's surface. The transit was made by Troughton & Simms, of London, after a plan furnished by Col. Graham, of the Topographical Engineers. Upon three foot-screws rests a circular base, to which are attached, by movable screws, the vertical uprights forming the Y's. The telescope has a focal length of twenty-two inches. The whole is light and portable. We have had a pine stand made for it, the parts firmly fastened together with wooden pins. Iron was excluded, in order that it might serve also for the magnetic instrument. Lieut. Ives was directed to commence a series of observations at this place, to serve as a basis for comparison with succeeding stations. In none of our text-books can be found detailed instructions upon the mode of adjusting and using these instruments with the rapidity required for field service. As, hereafter, only slight notice will be taken of this portion of our operations, it may not be deemed out of place to insert the method which experience, upon similar surveys, had suggested as proper to adopt. It will serve also to show what value should be accorded to the results obtained from the observations.

Upon arriving at camp, usually from 3 to 5 p. m., a firm stool, about two and a half feet high, will be placed on solid ground, from whence a clear view of the heavens, and particularly of the meridian, can be obtained. A trench from one and a half to two feet deep will be dug surrounding the stand, about eighteen inches from the point beneath the centre, leaving an isolated column of earth, free from the vibratory motion communicated by the ordinary movements of the men and animals about camp. There should be a platform for the observer north and south of the stand, resting entirely outside the trench. It must be recollected that the value of the observations greatly depends upon the isolation of the instrument. Hence a fiat rock should never be selected as a foundation, in case the observer is obliged to stand upon the same himself. Cooking-fires should be at least 300 feet distant, and to the leeward, that the smoke may not vitiate the results.

The stand being prepared, the "Fox" magnetic dip and intensity instrument will be placed upon it and adjusted; the recorder will take the note-book; the instrument-attendant his ivory disc, and the observer make the usual observations upon the needles and azimuth circle for the magnetic meridian, inclination, and intensity. This operation, and a record of the usual barometric and meteorological observations, will be completed at sunset. With the estimated latitude of the place, the telescope of the dip-circle will be set to the altitude of Polaris, which will be observed at the intersection of the two wires as soon as it appears, and the time of observation and readings of altitude and azimuth circles recorded. The telescope will be now depressed to the same angle below the horizon, and the star observed as reflected from an artificial horizon of mercury. The face of the instrument being set in the opposite direction, similar observations on Polaris will be recorded; first by reflection, and then direct. We have now, provided the error of chronometer be known, data for determining the reading of the azimuth circle when the telescope is in the true meridian; which, compared with observations previously recorded for the magnetic meridian, gives, approximately, the magnetic declination. The altitudes read will give the latitude of the place to the nearest minute.

The magnetic instrument, the adjustments of which have remained undisturbed during the preceding operations, now gives place to the astronomical transit. Polaris being visible, the first approximation to the meridian will be to direct the telescope towards that star. By the striding level the stand will be approximately levelled, and the telescope again directed towards Polaris, if supposed near its upper or lower culmination. If the error of the chronometer be entirely unknown, adjust the axis by the foot-screws, until the reversals of the striding level prove that the telescope moves in a vertical plane; then elevate, and observe the chronometer time of passage over the middle wire of the first known star near the zenith. The difference between this time and the right ascension of the star for the night, will give the approximate error of the chronometer. Apply this error to the right ascension of the first known circumpolar star that approaches the meridian. The estimated latitude of the place, plus or minus the star's polar distance, according as the star happens to be above or below the pole, will give the altitude at which the vertical circle should be set, in order to find the star sought. This should be done several minutes before the computed time of the star's meridian passage. If the star does not then appear in the telescope, sight along the upper edge of the tube; and if it can be seen with the naked eye, one may judge whether the instrument needs to be moved in azimuth east or west. This motion should, if possible, be communicated by the micrometer screw attached to the Y. The star at length having been brought into the field of the telescope, the recorder, who watches the chronometer, states how many minutes are wanting to the time of computed meridian passage. The observer then turns the azimuth micrometer screw until the middle wire of the telescope is in advance of the star's place, about equal to the distance over which he imagines the star will move during the time specified. Now, if able, while awaiting the signal from the recorder, who repeats the distance from the meridian in minutes of time by the chronometer, the observer, by the aid of the striding level, makes the axis of the instrument horizontal. He then places his eye to the telescope; and, as the star approaches the meridian, turns the azimuth micrometer screw; and, as the recorder repeats successively, "two minutes," "one minute, " "thirty seconds, ""fifteen seconds, brings the middle wire closer to the star and when the recorder cries "time," makes the middle wire bisect the star. The transit is now probably very nearly in the meridian. To test this, observe the passage of the next two known stars that pass the meridian; one high, near the zenith; the other differing thirty or forty degrees from the first in declination. If nearly equal differences be found between the observed times of passage of these stars over the middle wire, and their right ascensions, respectively that is, if the difference between the AR. and time of passage of the first star over the middle wire agrees, within half a second or less, with the difference of AR. and chronometer time of the second star's transit-the instrument is sufficiently near the meridian for the night's work. The adjustments should not, therefore, after this be disturbed until a complete set of observations has been obtained. This set consists in a record of the times of transit of every Nautical Almanac, or well known star that approaches the meridian, until one high and one low star, or two circumpolar stars, one above and one below the pole, have been observed for deviation of instrument, and about five near the equator for time. A record of the readings of the level should frequently be made for data to correct for inclination of axis. Should the moon appear, her bright limb will be observed when tangent to the wires; and the culminators of the Nautical Almanac will be added to the list. The error in collimation of the optical axis is supposed to be small, before the commencement of the observation. To insure this, the telescope, when first set up and levelled, may be directed to some distant clearly defined point, and so adjusted that the middle wire may bisect and thread the object. The axis then being reversed, and the telescope again turned to the point, the apparent lateral distance of the wire from it is equal to twice the collimation error; which may be nearly corrected by the screws that hold the diaphragm. The residual error should be nicely determined, at leisure, after the night's usual observations have been completed. Polaris, or some other close circumpolar star, should be observed upon the first three wires, "A," "B," "C," with illuminated end of axis east; then reverse the axis in the Y's, and observe the star's passage over the same three wires "C," "B," "A," the error in level having been recorded for both positions of the axis. This operation will give data for the determination of error in collimation; for which, unless very small, the results for time should be corrected. The distance from each lateral to the middle wire, called the equatorial interval, should be obtained on first commencing the use of the instrument. Circumpolar stars are supposed best for this' determination, because a small error in the time of noting the observation does not appreciably affect the result. Upon a clear night, and with a steady instrument, Polaris or some other star should be observed upon each wire consecutively, from A to G, if the illuminated end of the axis be east, and from G to A, when reversed. The observed interval from a lateral to the middle wire, divided by the secant of the star's declination, will give the equatorial interval. The mean of several results should be taken in order to insure accuracy. Having the equatorial interval, a catalogue of stars should be constructed; giving, according to the declination of each, the true distance in time from each lateral wire to the middle wire. Having this list before him, the observer may at once convert the observation upon any one wire to what it should have been upon the middle wire itself. And there is also this advantage in acquiring thus by induction the mean of all the wires observed: that, in case an error has occurred in one observation, the rest will visibly combine to prove that it ought to be rejected.

The meridional transit observations having been completed, the observer will revolve his instrument ninety degrees,* and observe the transit of stars over the prime vertical for latitude. For this purpose, from an assumed approximate latitude of the place, should be prepared a catalogue of the zenith distances, and times of passage of stars over the first wire, on the prime vertical, east and west. To determine the deviation, it will be preferable to select stars that cross the prime vertical near the horizon. Only those that cross near the zenith will-be used in the direct computations for latitude. Set the transit so as to catch the star to be observed upon; take four readings of the striding level, direct and reversed; and, should the instrument not be accurately placed in the.prime vertical, the first wire may be made to bisect the star at its computed time of passage; the signal being given by the recorder. The illuminated end of axis being north, wire A will first thread the star; and afterwards will be accurately noted the times of passage over B and C. The motion of the star being slow, there will be time to reset the striding level, and have four more readings of level error recorded. The axis of the telescope will now be reversed, and four readings again taken with the level. The star will then be watched, and the times noted when it passes the same wires, C, B, A, with the illuminated end of axis south. With another set of readings for level, the observations upon the east prime vertical will be completed. At the same altitude as the last observation east, the telescope will be directed west, in time to catch the star upon the first wire; and the times of passage over A, B, and C will be noted, with level readings, as before, preceding and following the observations. Then reverse the telescope axis and repeat the operation; first with the level, then observing the star upon the wires C, B, and A; a final levelling completes the process, which will give three results for latitude. Observations should be made on several stars crossing the prime vertical near the zenith, and the mean of the results taken for the true latitude.

Latitude and longitude have been obtained by the preceding methods, with one transit instrument, in a single night. With a sextant and an artificial horizon of mercury, similar results may be accomplished as follows:

Place the artificial horizon where the meridian and prime vertical are visible from thirty degrees altitude to the zenith. Dig a slight trench to isolate the cube of earth on which the mercury rests. Watch for bright stars to attain nearly equal altitudes of from thirty to sixty degrees, near the prime vertical, east and west, upon which to observe for time; and upon the meridian, north and south, for latitude. In places between thirty degrees and sixty degrees north of the equator, Polaris will always, when not concealed by clouds or mist, be available for latitude. Upon a clear night the observer may, therefore, be employed in observing that star, whenever compelled to wait for others to arrive in position. He will place a stool south of the artificial horizon and move his seat, and the direction of the glass roof till the star appears reflected from the mercury. Then, with the sextant clasped in his right hand, and elbow resting on his thigh, he will look through the telescope at the reflected image. Keeping the plane of the sextant truly vertical, with a sweep of the index with his left hand, twice the angle of elevation of the star, he will bring also into the field of view its image, as reflected from the index mirror. These two images being brought by the tangent screw directly in contact, so as to appear coincident, the signal "time" will be given to the recorder, who will be on the watch, and notice the instant required. Opposite to this record of the chronometer time, should be noted the double altitude or reading of the sextant. Fifteen such observations upon a star north, and a like number upon a star south, of nearly the same altitude, both taken within ten minutes of the meridian, should give the latitude within 10" of arc. Another set of stars nearly equal in altitude, one east and the other west, will give a result for time; and hence, knowing the error and rate of chronometer at any other station, we obtain the difference of longitudes. The greater the number of pairs of stars observed upon, the more accurate will be the result. Index error should be observed each day or night. The diameter of the sun may be measured by bringing its reflected image tangent first upon one side, then upon the other; and half the difference of the readings will give the index error. Or the reflected image of a star may be brought in contact with that seen through the telescope; and the zero of the vernier will then indicate the point which should be the zero of the arc. Hence, the reading will denote the index error, to be added to the altitudes observed when the reading is off the arc, and vice versa.

If observations be made for latitude upon one star north, and upon another south of the zenith, of very nearly equal altitudes, and those observations, corrected for index error, be computed, the difference in the results should be due to eccentricity of the instrument. One half this difference may be adopted as the eccentricity for that angle, and may be applied to future observations.



Polaris, being near the pole, may be observed for latitude at any hour of the night when visible.

All instruments should be handled lightly and delicately. No clamp screws should be tightly pressed. Every part of an instrument not absolutely necessary should be dispensed with; as, for instance, clamps on the vertical circle of a meridian transit, or bars to hold its axis in position. Sufficient care in the manipulation supersedes the necessity of such appliances.

Lists of occultations will be frequently examined; and if the moon is above the horizon at the time when the occurrence of an occultation is predicted, the large telescope, four feet focal length, will be mounted, and the moment of the disappearance of the star behind the moon's limb will be noticed. During the moon's first quarter, and until full moon, this occultation will take place behind the dark limb. Afterwards the star will be occulted by the bright limb, and the time of emersion from the dark side should then be marked.

The error of chronometer being determined at one station, and its rate approximately known, for the succeeding date and station apply the rate, and the estimated or measured distance due east or west, reckoning plus or minus four seconds of time to the mile. In this latitude, this will generally give the error of chronometer with sufficient accuracy to set the transit in the meridian by a circumpolar star. Formulae and methods of computing the results of the foregoing observations may be found in the "Tables" prepared by Capt. Thomas J. Lee, Topographical Engineers, for the use of the corps. This admirable and comprehensive work contains almost all that is necessary for field and office computations, and is now an indispensable companion of the topographical engineer.

* The transit used would have been much more convenient for this purpose, had it rested upon an azimuth circle.

1  from:  Reports of Explorations and Surveys, to ascertain the most practicable and economical route for a railroad from the Mississippi River to the Pacific Ocean. Ex. Doc. No. 91, Vol III, A O P Nicholson, 1856


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