Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/175

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   EODESY (773, the earth, Suite, to divide) is the science of surveying extended to large tracts of country, having in view not only the production of a system of maps of very great accuracy, but the determination of the curvature of the surface of the earth, and eventually of the ﬁgure and dimensions of the earth. This last, indeed, may be the sole object in view, as was the case in the operations conducted in Peru and in Lapland by the celebrated French astronomers Bouguer, La Condamine, Maupertuis, Clairaut, and others; and the measurement of the meridian arc of France by Mechaiu and Delambre had for its end the determination of the true length of the “ metre ” which was to be the legal standard of length of France.

The basis of every extensive survey is an accurate triangulation, and the operations of geodesy consist in—the measurement, by theodolites, of the angles of the triangles 3 the measurement of one or more sides of these triangles on the ground ; the determination by astronomical observations of the azimuth of the whole network of triangles 3 the determination of the actual position of the same on the surface of the earth by observations, first for latitude at some of the stations, and secondly for longitude.

To determine by actual measurement on the ground the length of a side of one of the triangles, wherefrom to infer the lengths of all the other sides in the triangulation, is not the least diﬁicult operation of a trigonometrical survey. When the problem is stated tl1us——To determine the num- ber of times that a certain standard or unit of length is contained between two ﬁnely marked points 011 the surface of the earth at a distance of some miles asunder, so that the error of the result may be pronounced to lie between certain very narrow limits,——then the question demands very serious consideration. The representation of the unit of length by means of the distance between two ﬁne lines on the surface of a bar of metal at a certain temperature is never itself free from uncertainty and probable error, owing to the difﬁculty of knowing at any moment the precise temperature of the bar 3 and the transference of this unit, or a multiple of it, to a measuring bar, will be affected not only with errors of observation, but with errors arising from uncertainty of temperature of both bars. If the measuring bar be not self—compensating for temperature, its expansion must be determined by very careful experiments. The thermometers required for this purpose must be very carefully studied, and their errors of division and index error determined.

The base apparatus of Bessel and that of Colby have been described in. The average probable error of a single measurement of a base line by the Colby apparatus is, according to the very elaborate investigations of Colonel \Valker, C.B., R.E., the Sur- veyor-General of India, :1: 1'5” (,1. meaning “ one millionth”). W. Struve gives =e0'Sla as the probable error of a base line measured with his apparatus, being the mean of the probable errors of seven bases measured by him in Russia 3 but this estimate is probably too small. Struve’s appa- ratus is simple: there are four wrought iron bars, each two toises (rather more than 13 feet) long 3 one end of each bar is terminated in a small steel cylinder presenting a slightly convex surface for contact, the other end carries a contact lever rigidly connected with the bar. The shorter arm of the lever terminates below in a polished hemisphere, the upper and longer arm traversing a vertical divided are. [n measuring, the plane end of one bar is brought into contact with the short arm of the contact lever (pushed forward by a weak spring) of the next bar. Each bar has two thermometers, and a level for determining the inclina- tion of the bar in measuring. The manner of transferring the end of a bar to the ground is simply this : under the end of the bar a stake is driven very ﬁrmly into the ground, carrying on its upper surface a disk, capable of: movement in the direction of the measured line by means of slow-motion screws. A ﬁne mark on this disk is brought vertically under the end of the bar by means of a theodolite which is planted at a distance of 25 feet from the stake in a direction perpendicular to the base. Struve investigates for each base the probable errors of the measurement arising from each of these seven causes:— alignment, inclination, comparisons with standards, read- ings of index, personal errors, uncertainties of temperature, and the probable errors of adopted rates of expansion.

The apparatus used in the United States Coast Survey consists of two measuring bars, each 6 metres in length, supported on two massive tripod stands placed at one quarter length from each end, and provided, as in Colbys apparatus, with the necessary mechanism for longitudinal, transverse, and vertical adjustment. Each measuring rod is a compensating combination of an iron and a brass bar, supported parallel to one another and ﬁrmly connected at one end, the medium of connexion between the free ends being a lever of compensation so adjusted as to indicate a. constant length independent of temperature or changes of temperature. The bars are protected from external inﬂu- ences by double tubes of tinned sheet iron, within which they are movable on rollers by a screw movement which allows of contacts being made within Tn—gw of an inch. The abutting piece acts upon the contact lever which is attached to the ﬁxed end of the compound bar, and carries a very sensitive level, the horizontal position of which de-- ﬁnes the length of the bar. It is impossible here to give a full description of this complicated apparatus, and we must refer for details to the account given in full in the United States Coast Survey Report for 1854. This appa- ratus is doubtless a very perfect one, and the manipulation of it must offer great facilities, for it appears to be possible, under favourable circumstances, to measure a mile in one day, 1'06 mile having been measured 011 one occasion in eight and a half hours. In order to test to the utmost the apparatus, the base at Atalanta, Georgia, was measured twice in winter and on_ce in summer 1872—73, at tempera- tures 51°, 45°, 90° F. ; the difference of the ﬁrst and second measurements was + 0'30 in., of the second and third + 0'31 in.,—the actual length and computed probable_error expressed in metres being 9338'4763az0'0166. It is to be noted that in the account of a base recently measured in the United States Lake Survey, some doubt is expressed as to the perfection of the particular apparatus of this de- scription there used, on account of a liability to permanent changes of length.

The last base line measured in India with Colby’s compensation apparatus had a length of 8912 feet only, and in consequence of some doubts which had arisen as to the accuracy of this compensation apparatus, the measurement was repeated four times, the operations being conducted in such a manner as to indicate as far as possible the actual magnitudes of the probable errors to which such measures are liable. The direction of the line (which is at Cape Comorin) is north and south, and in two of the measure- ments the brass component was to the west, in the other two it was to the east. The differences between the indi- vidual measurements and the mean of the four are + '0017, — '0049, — '0015. + '0045 in feet. The measure-