﻿ACROSS THE PENINSULA OF INDIA. S17 



chord having been previously determined in fathoms, 

 being a side of one of tliose plane triangles, formed 

 by tlie chords of the terrestrial arcs ; the length of 

 that Urc can also be determined in fathoms ; and, 

 therefore, a dcgrcj may be dctermiineil in fathoms, 

 having its middle point the point of intersection with 

 the meridian. 



Thus having obtained the length of a degree upon 

 the meridian, and its perpendicular, in any given la- 

 titude, they will serve as data for computing the lati- 

 tude and longitude of places near tliat parallel, and 

 near to that^ or a known meridian, by means of the 

 chord of a terrestrial arc, oblique to the meridian and 

 its perpendicular, and the chord of the meridional arc 

 intercepted by a great circle falling from the extre- 

 mity of tlie oblique chord, and cutting the meridian 

 at right angles. For it will be easy to find the mea-' 

 sure either of the part of the meridian, or the portion 

 of the circle at right angles thereto (even by using' 

 the observed angles ;) and if these be converted intd 

 degrees, minutes, &c. according to the length of i. 

 degree upon the respective circles, tJie forniGi' will 

 give the difference of latitude, and consequently, by 

 addition or subtraction, the real latitude ; the latter^ 

 with the co-latitude thus obtained, will enable us to 

 find the angle at the pole. In both these cj^ses the 

 truth may be obtained to within one-fourth, and ge- 

 nerally one-tenth of a second, (limiting the opera- 

 tions to a certain extent from a known parallel and 

 meridian ;) and that without having recourse to ob- 

 servation, or depending on any hypothesis of the 

 earth's figure. 



It will readily occur to the reader, that had thera'. 

 iio of the assumed diameters been what it really is, 

 and supposing the earth to be an exact ellipsoid, the 

 computed and measured degrees ought co come out 

 the same. But the reason for computing the length 

 of ellipsoidal arcs was only to gain the approximate 

 2 values 



