384 Mr DAVIES on the Equations of Loci 



4 



From this formula, expressions for all the great circles, segments, and 

 spherical angles that enter into the figure, will be presently derived. 



XXXIX. 



The several other parts of the figure may be obtained by the simple ap- 

 plication of NAPIER'S rules to the right-angled triangles that constitute 

 the system of mutually dependent quantities. The manner of obtaining 

 them is so obvious, that I shall omit all indication of it here, and merely 

 tabulate the results for the purpose of reference in future inquiries. 



1st, Equatoreal or Geographical Co-ordinates. 



Let PE, EK be the axes of co-ordinates, that is, the meridian and equa- 

 tor of reference. Then, MK being the tangent at M to a spherical curve, 

 and MW the normal, if we put ET = 0, 5 and TM = < we shall obtain 

 TABI.B I. 



