6i OUTLINES OF NATURAL PHILOSOPHY. 



tioned, all the methods of finding the longitude 

 may be reduced. 



68. If the latitudes of any two places are gi- 

 ven, and also their difference of longitude, their 

 distance may be found by spherical trigonome- 

 try. 



a. If the earth is considered as a sphere, then, in the 

 spherical triangle contained by the arches joining 

 the two places with one another, and with the pole, 

 two sides are given, viz. the distances from the pole, 

 or the complements of latitude, and the angle at 

 the pole, or the difference of longitude ; and there- 

 fore the 3d side may be found by the 2d case of 

 oblique-angled spherical triangles. This side is the 

 distance of the places expressed in degrees, &c. ; 

 and may be turned into miles, by multiplying by 

 69.04-4, the mean length of a degree, ( 60. b.) 



If the angles at the base or the azimuths are also re- 

 quired, it will be best to resolve the triangle by 

 NAPIER'S Formula. See Elem. of Geomet. Edin. 

 1810, p. 378. See also WOODHOUSE'S Trigono- 

 metry 9 p. 126* 







b. But if the spheroidal figure is to be taken into ac- 

 count, the calculation becomes more complex. For 

 as, on this supposition, the directions of the plum- 

 mets AD, BF, (fig. 6.) at the two places, if their 

 latitudes are different, do not meet the axis in the 

 same point $ these three lines do not contain a solid 



3 angle, 



