Chap. VIII.

GEOMETRY.

811

means of a scale : the opening of the angle,1174 degrees, could be set out at Q, andthe distance O S made 67 yards, and O Von the line T 64; then by the scale Pthe distance from V to S will be found112 yards, which will be that also from Mto L.

To find the length of a building, as fromT to L, select two stations, as Y and P,and plant two piquets : at the first takethe angle PYL, which will be found tobe one of 30°, and measure the distancebetween the two piquets, which is here45 yards: then from the piquet P, con-struct the triangle YPL, which is also oneof 30°.

Then set out a scale, and draw bd equalto Y P, and the angles bdy, answering toY PL, and kbh equal to LYT ; the wholemay then be measured, and in this casethe distance from i to k will be found 102yards, which is the length of the buildingTI,

Fig 968.

Fig. 969.

Maps may be laid down by means ofthe demicircle, and all the towns at A, 13, C,

I), E, F, G, II, be accurately measured, andput at their proper distances from eachother. First place the instrument at II,and a piquet at N; after having takenall the angles, move the instrument to N,and make a similar observation: measurethe distance from II to N, which here is200 yards, and then lay down the severalangles as observed accurately upon paper, and the lines at their intersection will give thepositions of the towns.

This system was practised inFrance as early as the seven-teenth century, when a baseline was measured from thetown stationed at N and L,and all the others shown onthe map accurately laid downfrom drawing a series of anglestaken at the two stations.

Picard, in 1670, called theattention of the moderns to themeasurement of a degree ofthe meridian, and his observ-ations were confined to a linestretching between the parallelsof Malvoisine and Amiens : thiswas succeeded by the very ac-curate observations and thetrigonometrical survey madeby Delambre and Mechain ; theterrestrial arch it embraced ex-tended over nearly 10 degrees,and it was almost exactlybisected in the parallel of 45 Fig. 971.

degrees: these observations, made during the gTeat revolution, led to a more exact methodof measuring, and to the adoption of the trigonometrical system of surveying. After thelabours of Delambre and Mechain , Biot and Arago carried a train of triangles southwardas far as Tormentcra, which is a small island near Ivica, in the Mediterranean.

It must always be borne in mind, that the magnitude of the angles of the connectingtriangles are affected by the earth’s curvature, and these must undergo a correction corre-spondent with it before the length of the unknown sides can be accurately obtained; for weknow that triangles drawn on the surface of the globe cannot be regarded as plane, neithercan horizontal angles at one station be considered as in the same plane with those at

Fig. 970.