﻿Sli ON EXTENDING A GEOGRAPHICAL SURVEr 



served angles. The difference of lonj^itude of any 

 two points might be as easily had ; for, knov/ing 

 th,e arc between them (which would always corre- 

 spond with a celestial arc,) and the co-latitndes of 

 the two places, the angle at the pole, or difference 

 of longitude, might be found. 



But since the earth is not a sphere, but an oblate 

 spheroid, anfl diliering considerably from a sphere, 

 it becomes necessary to determine the length of a 

 degree on the meridian, and a degree at right angles 

 to that meridian, making the point of intersection 

 of the meridian and its perpendicular the middle 

 point of each degree. Now, in determining the 

 measure of those degrees, if the first measurement, 

 or base line, cannot be had in the meridian, two 

 other objects must be chosen therein, and their 

 distance computed trigonometrically, and then com- 

 pared with the celestial arc. But here the operations, 

 for obtaining this distance, will be attended with 

 some trouble, on account of its being necessary to 

 calculate the chords of the arcs, and the difficulty 

 of determining- the ano-les made bv these chords to a 

 jiullicient degree of accuracy. For here we are 

 obliged to assume data, and proceed by an approxi- 

 mating method. And, 1st, we must either suppose 

 the earth to be a splicrc, and by taking the three 

 angles made by the intersections of three great circles 

 of that sphere, find the sides in degrees and minutes : 

 then take double the sines of half the arcs, or the 

 chords, and there will be had the thiee sides of a 

 plane triangle, defined in parts of the radius. With 

 these three sides determine the three angles, and 

 these are the angles for calculating the direct dis- 

 tances. Hence, by knowing the base in /athoihs, 

 the chord subtending that base (or arc) may also be 

 had in fathoms, by computing trom the radius ot 

 the assumed sphere, which we must suppose to be of 

 some given njagnitude. Tlien having the length ot 

 the chord in fatho;ns, and tlic angles corrected as 



above, 



