18

CALCULATIONS TO ASCERTAIN THE TRACT 26.

These sections are very numerous, and were made in all di-rections from the primitive points before-mentioned,andmanyof them extended to great distances, indeed far beyond thebounds of the plan here annexed, so as to include the nearesthills and valleysof the surrounding country. They were mostlymade in vertical planes, in the manner described in the articleof the Phil. Trans. before referred to, excepting some few,which are level sections, in planes parallel to the horizon, andsome indeed irregular, being neither vertical nor horizontal.To compute the relative altitude of each point in these sec-tions, it is evident, requires the resolution of two differenttriangles, viz. a horizontal triangle, by which its place in theplan is ascertained, and a vertical triangle, of which one sideis the elevation or depression of the point. Of these sections,there are above 70, containing near 1000 points, whose placesin the plan and relative altitudes have been computed: so thatthe number of triangles, whose numeral resolutions have beenperformed in the course of this business, amounts to severalthousands.

Before the abstract of the computation of the sections, wemay here set down at large the calculation of one of them, toshow the manner in which they have been computed, in thereadiest and easiest way which occurred, preserving at thesame time the proper degree of accuracy. I shall for this

purpose select the third section, as not containing so manypoles as some of the others. This sec-tion commences at s, and is carried upthe hill in a vertical plane, making anangle of 105° with the line rs. The di-rection of this plane is here representedby the line s ppp, making with Rs the an-gle RS p = 105°. The points ppp &c,mark the places of the poles, whose an-gles of elevation or depression weretaken at s, with a proper instrument, and they are written inthe second column of the table in this example. At it wereobserved the several horizontal angles, which lines supposed

R s

From - ISO* 1Take Z 105

Leaves / r+ Zj>=75