﻿316 ON EXTENDING A GEOGRAPHICAL SURVEY 



stration of the above formula lias been given by the 

 Astronomer Royal, and may be seen in the Phil. 

 Transactions for the year 1797, p. 450. 



Having, by this method, got the angles made 

 by the chords to very near the truth, the rest, M'itli 

 respect to distances, is evident. For the chord of 

 the measured arc (or base) may be had, since by 

 computing the lengths of arcs in any direction, on 

 the ellipsoid, the radius of curvature of that arc is 

 likewise had, and thence the chord. And that chord 

 forms the side of a plane triangle, from which, and 

 the corrected angles, all the data may be had for 

 proceeding upon each of the sides of the first plane 

 triangle. 



Now, to determine any portion of a degree on 

 the earth's surface in the meridian, two points may 

 be taken therein, and the direct distance between 

 them ascertained by the above method. Then, bv 

 taking tlie zenith distance of a known star, \vnen 

 passing the meridian, at each extremity of the dis- 

 tance, the celestial arc becomes known in degrees, 

 minutes, &c. from which the terrestrial arc between 

 the two objects is had in degrees, minutes, &c. 

 also : — and liaving determined the chord in fatlioms, 

 the -arc may likewise be determined in fathoms, 

 wliich being compared with the degrees, minutes, 

 &c. the value of a degree is thereby obtained in 

 fathoms, 



Th ];: length of a degree, at right angles to the 

 meridian, is also easily known by spherical compu- 

 tation, having the latitude of the point of intersection, 

 and the latitude of an*' object any where in a direc- 

 tion perpendicular to the meridian at that point. 

 Tor then the arc between tliese two points, and the 

 two celestial arcs or colatitudes, will form a right 

 angled triangle, two sides of which are given to find 

 the third, which is the arc in question. And this 

 will apply either to the sphere or spheroid. That 

 arc being known, in cjegrees and minutes, and the 



chord 



