Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/176

Rh 164 GEODESY ments occupie.l from seven to ten days C3.l'll,-—tll8 average ' be natural objects presenting themselves in suitable posi- rate of such work in India being about a mile in ﬁvc days. The method of .I. I’orro, adopted lll Spam, and by the French in Algiers, is essentially diﬂerent from those' just described. The measuring ro.l, for there is only one, is a thermometric combination of two bars, one of platinum and one of brass, in length 4 metres, furnished with three levels and fo11r thermometers. Suppose A, B, C three micrometer microscopes very ﬁrmly sup- ported at intervals of 4 metres with their axes vertical, and aligned in the plane of the base line by means of a transit instrument, their micrometer screws being in the line of measurement. The measuring bar is brought under say A and B, and those micrometers read ; the bar is then shifted and brought under B and C. By repetition of this process, the reading of a micrometer indicating the end of each position of the bar, the measurement is made. The probable error of the central base of Madridej os, which has a length of 14664600 metres, is estimated at :1: 0'l.7}.L. This is the longest base line in Spain; there are seven others, six of which are under 2500 metres in length; of these one is in Majorca, another in Minorcai, and a third in Iviga. The last base just measured in the province of Bar- celona has a length of :'2lS3'5381 metres according to the first measurement, and 24836383 according to the second. The total number of base lines measured in Europe up to the present time is about eighty, ﬁfteen of which do not exceed in length 2500 metres, or about a mile and a half, and two—one in France, the other in Bavaria—exceed 19,000 metres. The question has been frequently discussed whether or not the advantage of a long base is sufficiently great to warrant the expenditure of time that it requires, or wl1etl1er as nmch precision is not obtainable in the end by careful triangulation from a short base. But the answer cannot be given generally ; it must depend on the circum- stances of each particular case. It. is necessary that the altitude above the level of the sea of every part of a base line be ascertained by spirit levelling, in order that the measured length may be reduced to what it would have been had the measurement been made on the surface of the sea, produced in imagination. Thus if 1 be the length of a measuring bar, It its height at any given position in the measurement, 1' the radius of the earth, then the length radially projected on to the level of the sea is l—I£ I. In the Salisbury Plain base line the reduction to the level of the sea is — 0'6294 feet. In working away from a base li11e ab, stations c, (I, e, f are carefully selected so as to obtain from well-shaped tri- angles gradually increasing sides. J- Before, however, ﬁnally leaving the base line it is usual to verify it by triangulation thus: during the measurement two or more points, as p, q (fig. 1), are marked in the base in positions such that the lengths of the different segments of the line are known; then, taking suitable external stations, as It, Is, the angles of the triangles blip, 7)/tr], It/Id‘, /rr/rt are measured. From these angles can be com- puted the ratios of the seg- ments, which must agree, if all operations are correctly per- formed, with the ratios resulting from the measures. Leaving the 0 base line, the sides increase up Fi'o'- 1- to ten, thirty, or ﬁfty miles, occasionally, but seldom, reach- ing a hundred miles. The triangulation points may either (3 tions, such as church towers; or they may be objects specially constructed in stone or wood on mountain tops or other prominent ground. In every case it is necessary that the precise centre of the station be marked by some permanent mark. In India no expense is spared in making permanent the principal trigonometrical stat.ions—costl_v towers in masonry being erected. It is essential that every trigonometrical station shall present a fine object for ob- servation from surrounding stations. Ilo-rizontul A 71 gles. In placing the theodolite over a station to be observed from, the first point to be attended to is that it shall rest upon a perfectly solid foundation. The method of obtain- ing this desideratum must depend entirely on the nature of the ground; the instrument must if possible be supported on rock, or if that be impossible a solid foundation must be obtained by digging. When the thcodolite is required to be raised above the surface of the ground in order to command particular points, it is necessary to build two scaf- folds,—the outer one to carry the observatory, the inner one to carry the instrument,—and these two ediﬁces must have no point of contact. Many cases of high scaffolding have occurred on the English Ordnance Survey, as for instance at Thaxted Church, where the tower, 80 feet high, is sur- mounted by a spire of 90 feet. The scaffold for the ob- servatory was carried from the base to the top of the spire ; that for the instrument was raised from a point of the spire 140 feet above the ground, havingits bearing upon timbers passing through the spire at that height. Thus the instr11— ment, at a height of 178 feet above the ground, was insulated, and not affected by the action of the wind on the observatory. At every station it is necessary to examine and correct the adjustments of the theodolite, which are these :—the line of collimation of the telescope nmst be perpendicular to its axis of rotation; this axis perpendicular to the vertical axis of the instrument ; and the latter perpendicular to the plane of the horizon. The micrometer microscopes must also measure correct quantities on the divided circle or circles. The method of observing is this. Let A, B, 3. . . . be the stations to be observed taken in order of azimuth ; the telescope is first directed to A and the cross-hairs of the telescope made to bisect the object presented by A, then the microscopes or verniers of the horizontal circle (also of the vertical circle if necessary) are read and recorded. The telescope is then turned to B, which is observed in the same manner; then C and the other stations. Coming round by continuous motion to A, it is again observed, and the agree- ment of this second reading with the ﬁrst is some test of the stability of the instrument. In taking this round of angles——or “ are,” as it is called on the Ordnance Survey—— it is desirable that the interval of time between the first and second observations of Ashould be as small as maybe consistent with due care. Before taking the next arc the horizontal circle is moved through 20° or 30°; thus a dif- ferent set of divisions of the circle is used in each are, which‘ tends to eliminate the errors of division. It is very desirable that all arcs at a station should contain one pointin common, to which all angular measure- ments are thus referred,—the observations on each are com- mencing and ending with this point, which is on the Ord- nance Survey called the “ referring object.” It is usual for this purpose to select, from among the points which have to be observed, that one which affords the best object for precise observation. For mountain tops a “referring ob- ject ” is constructed of two rectangular plates of metal in the same vertical plane, their edges parallel and placed at such a distance apart_tl1at the light of the sky seen through