REPORT ON THE COAST SURVEY

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To obviate this source of error, Professor Bache designed an apparatus, which was constructed in the office of the Coast Survey, under his direction, and with which the subsequent bases have been measured. In this apparatus the measuring bars are arranged upon the plan of compensation for the effects of temperature, which was first used by Colonel Colby in Great Britain, and afterwards in this country by Mr. Borden, in the Trigonometrical Survey of the State of Massachusetts; but the mode of obtaining the compensation is entirely different. A principle is also introduced, which, though of sufficiently obvious importance when once suggested, had not been previously recognized; or had not, at least, been previously applied in practice. It is matter of observation that if a bar of brass and a bar of iron of equal dimensions be exposed to the same source of heat, they will not always undergo equal changes of temperature in equal times; but that, after a short interval, a difference will be found to exist, the amount of which will depend on the different conducting properties of the two metals, their different specific heats, and the different powers of absorption possessed by their surfaces. Accordingly, two such bars, if of equal cross-sections, will not form a system compensating during progressive changes of temperature, however perfectly te compensation may be ultimately effected, when the temperature shall have become stationary, and uniform throughout the system. In order therefore that a combination of such bars may answer the purpose aimed at, their sections must be so proportioned to their conducting power and specific heat, that their fluctuations of temperature under different exposures may go on at precisely the same rates. As to the absorbing powers of their surfaces, that is easily made identical, by giving to both bars the same external coating.

The lever of contact and level, first used in the adjustment of standard measures by Bessel, has been adapted to this apparatus, the contact between two sets of bars being made by a blunt knife-edge against a plane, both of agate. Those who desire to study this beautiful and delicate arrangement are referred to the Coast Survey Report for 1854, where it is described and figured. The mechanical arrangements by means of which the bars are adjusted in line, height and inclination, are also worthy of admiration; and such is the rapidity with which the apparatus can be used, that on favorable ground a mile has repeatedly been measured in a single working day of ten hours. It is so arranged that the measurement may be made at inclinations up to 3° with the same facility and accuracy as on level ground.

The accuracy of its results has been practically tested by repeated measurements of the same distance, from which it appears that the probable error in measuring a mile is about two hundredths of an inch. This base apparatus was designed in 1845, and first used in 1847 on Dauphine Island, on the coast of Alabama. Since then base-lines have been measured with it in North and South Carolina, in Florida, and in Maine. All these measurements have been conducted by the Superintendent in person, aided by some of his assistants. The average length of the primary base-lines measured thus far is about six miles.

Many laborious and delicate experiments were requisite to perfect the adjustments of the apparatus. Before and after the measurement of each base-line, the length of both sets of bars, which is six metres or nearly twenty feet, is carefully compared with a standard bar of iron. The rate of expansion of this standard has been ascertained by experiment, and its length at 32° Fahr. has been verified by means of six single metres abutting endwise, each of which has been compared with an authentic standard metre– one of those originally made by the French committee on weights and measures. The possession of this valuable standard, which was brought to this country by Mr. Hassler, and by him presented to the American Philosophical Society, was one of the chief reasons for using the metre as the unit of length in the Coast Survey, especially in the absence of any legally established standard of the country. The length of the English yard, which is our customary unit of length, has but recently been definitively settled in Great Britain; and the fact that the dimensions of the earth have hitherto been best known in metres, makes the latter measure one of great convenience in geodetic operations. The distances in the Survey are, of course, also given in yards, and miles, for common use.

The comparisons of length are made by means of Saxton’s pyrometer, an instrument of great simplicity, and affording the highest degree of accuracy. A small mirror, movable about a vertical axis, reflects into the field of a telescope, placed at a distance of 20 feet, the divisions of a long curved scale fixed directly under the telescope; by means of a small abutting piece attached to the mirror, any difference in length to be measured causes a corresponding rotation of the mirror, by which different scale-divisions appear on the wires in the telescope, and a greatly magnified indication is thus obtained by an index equal in length to twice the distance of the mirror from the scale. The quantity to be measured is thus readily magnified 2,000 times, without any loss from inertia and flexure, which would be unavoidable in obtaining a similar result by means of mechanical levers.

The necessity for the greatest attainable accuracy in such operations is apparent when we remember, that an error in the base-line will affect the whole distance depending upon it by triangulation in the same ration: thus, if the base-line were in error by but its ten-thousandth part, a distance of 100 miles depending on it would be in error, from that source alone, by one hundredth of a mile or 53 feet.

The Fire Island base, on the south side of Long Island, and the Kent Island base in Chesapeake bay, are connected by a primary triangulation. These are the bases alluded to in a former part of this report, where it is mentioned that the Kent Island base has served to verify the others. This Kent Island base is five miles and four-tenths long, and the original Fire Island base is eight miles and seven-tenths. The shortest distance between them is two hundred and eight miles; but the distance through the triangulation is three hundred and twenty. The number of intervening triangles is thirty-two; yet the computed and measured lengths of the Kent Island base exhibit a discrepancy no greater than four inches.

On some portions of the coast, where the pressing wants of commerce made it desirable to commence the work in advance of the regularly primary triangulation, local surveys have been executed based on preliminary baselines, which were measured with wooden or iron bars, and some simple auxiliary apparatus, generally devised by the assistants having immediate charge of the work. Some of these contrivances have been described in the annual reports of the Superintendent, and will be found very useful to persons wishing to execute local surveys with some degree of accuracy. See particularly C.S. Report, 1857. All such preliminary measurements will in time be superseded by measurements with the compensating apparatus above described.

MEASUREMENT OF ANGLES.– In measuring the angles of the primary triangulation, theodolites of various sizes and construction are employed. The largest instrument of this class belonging to the Coast Survey has a circle of 30 inches in diameter, graduated five minutes, and reading to single seconds of arc on three micrometer-microscopes; it is provided with a telescope of great power, which is partly supported by springs within the upright columns, so as to relieve the bearings in a great degree from friction. The weight of the whole upper or movable portion is in great part secure the latter against wear and to obtain a very free motion about the axis. This instrument was designed by Mr. Hassler, and constructed by Troughton & Simms, of London. It is used by the Superintendent in the execution of the primary triangulation of the north-eastern part of the coast, where the country presents considerable natural elevations and admits of long lines of sight, ranging from twenty to eighty miles in length. The accuracy of pointing and reading attained with this instrument is such, that, notwithstanding the varying condition of the atmosphere, the probable error of a single measure of an angle is about one second and a quarter, which in the mean of thirty such measures, the usual number taken, is reduced to about one-fourth of a second. The observations are made under all conditions of visibility of signals, varying from a well-defined and steady image, to a nearly obliterated, trembling blur. For each observation, the appearance of the signal observed has been carefully noted; and the means have been thus obtained for a discussion of the results with reference to the conditiosn of vision. The results arrived at justify the conclusion that the mean of observations taken in various states of the atmosphere, is probably preferable to the mean of such as have been obtained under circumstances apparently the most favorable; there being in the former case less of correction required to fulfil the geoemtrical conditions of the work; while a given limit of probable error can generally be reached by that method, in much less time than by the other. This result may be readily accounted for, by supposing that, under the conditions which appear most favorable to accuracy of observation along a line of considerable extent, there may regularly occur a slight lateral deflection, which, in the mean of observations taken under different conditions of the atmosphere, is sensibly eliminated.

A theodolite nearly similar in construction with the one described, but having only twenty-four inches diameter, is likewise used in the primary triangulation. Besides these, repeating theodolites with circles varying from twelve to six inches are employed in the different classes of triangulation. On the Atlantic coast south of New York, and on the shores of the Gulf of Mexico, where the country presents no considerable eminences, and is in general densely wooded, the instruments frequently require to be elevated on wooden structures, in order to overcome the curvature of the earth, and to get above the most heated statum of air. These structures, which range from twenty-five to fifty feet in height, have been constructed on various plans by the assistants of Professor Bache, and have proved amply steady for measurements with the repeating instruments.

The signals generally employed to mark station-points are straight poles, supported by a tripod, and surmounted by a cone or bell-shaped cap of bright tin, on which the reflection of the sun shows a luminous spot to the observer. On the long lines of the primary triangulation, however, heliotropes are used in addition to the single-poles. The heliotrope, invented by Gauss, is an instrument in which a mirror of a few square inches surface is so mounted in connexion with a telescope, that the reflection of the sun may be thrown to any desired direction. It is very effective, and it is not unusual to observe on heliotropes on the summit of mountains 80 or 90 miles distant, when the outlines of the mountains are invisible through the hazy atmosphere.

The number of observations taken for the different classes of triangulation is so apportioned to the quality of the instruments used, and to the agreement of the individual observations among themselves, that the error of the sum of the angles in a primary triangle will not exceed three seconds, or nine seconds in a triangle of the second order. These limits of error, however, are seldom reached in fact. The average correction required for an observed angle in the eastern section, where the stations are natural elevations and the sides average over forty miles in length, is about four-tenths of a second. In the southern sections it is rather larger.
OBSERVATIONS OF LATITUDE.— In order to fix the situation of the whole network of triangles on the surface of the earth, it would suffice to determine the latitude and longitude of some one point, and the direction with reference to the true meridian of one of its lines– its azimuth– if the figure of the earth were precisely known. But owing to the irregularities of the latter, it is found necessary to repeat those determinations very frequently, by which means the work is checked, and any accumulation of error avoided, while at the same time the figure of that portion of the earth covered by the survey is accurately ascertained. Observations of latitude are made at numerous stations of the primary triangulation. Different methods and different instruments have been employed, and the results have been carefully discussed in order to determine which are best and most available. A two foot vertical circle, and several twelve-inch repeating reflecting circles, by Troughton & Simms; and also six-inch and ten-inch repeating theodolites by Gambey, were tried successively, but the results were found to be liable to considerable instrumental errors, and the degree of their accuracy proved to be insufficient to repay the labor which had been bestowed upon them. Finding a larger class of instruments to be indispensable, Mr. Bache had recourse to the prime vertical transit, the zenith telescope of equal altitude instrument, and the zenith sector; each provided with a telescope of forty-five inches focal length.

The method of determining latitude by observations of transits of stars over the prime vertical, first used by Bessel, is admirable in theory, but in practice a great loss of time and labor is often occasioned by clouds, which interfere with obtaining corresponding sets of eastern and western transits; and for operations in the field this method is found to present less advantages than others.

The zenith telescope, or equal altitude instrument, was first applied to the determination of latitude by Capt. A. Talcott, late an officer in the United States army, and has been remodeled and specially adapted to the purpose in the Coast Survey, where it has become the favorite instrument on account of the great number and accuracy of the results that can be obtained in a given time, and the facility with which it is used. It is employed in determining latitudes by measuring, with an attached micrometer, the differences of zenith distance of stars culminating within a short time of each other, at nearly the same altitude, on opposite sides of the zenith. From the star catalogue of the British Association may be selected any desirable number of pairs of stars having the required relative positions. If, after pointing the micrometer wire in the telescope to a star at its meridian passage south of the zenith, and revolving the instrument about its vertical axis, the telescope remaining at a fixed inclination, we find that a star culminating north of the zenith passes precisely on the same wire, we infer that the zenith is exactly midway between the two stars, and consequently that its distance form the celestial equator, or the latitude of the place, is equal to the mean or half sum of the declinations of the two stars observed. If, furthermore, the second star does not pass precisely on the wire, but still in the field of the telescope, we are able to measure the difference of zenith distance by means of the micrometer, and correct by half that amount the half sum of the declinations. By means of a delicate level attached to the instrument we keep account of its deviation from the true vertical. The whole observation thus consists of pointing and reading the micrometer, and noting the level, in each position of the instrument.

This method possesses also the great advantage that the result is nearly free from the effects of refraction, which enters only so far as the difference of zenith distance is affected by it; the correction for refraction never exceeds a quarter or a second.

The observations with the zenith telescope being considerably more accurate than the positions of the stars in the British Association’s catalogue, it has been preferred rather to increase the number of pairs employed, than to multiply observations on the same pairs. In practice, from twenty-five to forty pairs of stars are observed, at a station; with from four to six observations on each pair, on different nights. The probable error of a single observation with the zenith telescopes used in the Coast Survey is from three to five-tenths of a second; while the probable error of the catalogue places considerably exceeds one second. The Greenwich observations, and other recent catalogues, frequently supply better places than the larger catalogue just referred to; and thus contribute to improve the result.

Prof. Bache has at various times communicated to the American Association notes on the use of the instrument in question, and at the Baltimore meeting read a paper showing the remarkable result that when at a station the same stars are observed by the same observers with different zenith telescopes, and by different observers with the same instrument, results almost identical were obtained; setting at rest the question of any residual personal or instrumental errors. It may safely be predicted that this simple and effective instrument is destined to supersede all others for the determination of latitudes in the field, and it is proper here to state that the recent assertion of Mr. Porro, a French engineer, that the method used in America is merely Gauss’ method of equal altitudes, is founded on an entire misconception of the method and instrument as used in this country.

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