296 APPENDIX CALCULATION OF THE 



supplement of the inclination of P on the plane 

 a b c fy the angle B the inclination of P on T, and 

 the angle C the supplement of the inclination of T 

 on the plane a b cf. 



From this spherical triangle we deduce the side , 

 containing the required angle i b c, by the known 

 formula 



sin, i - R -t /-cos. \ (A+B+C). cos. \ (B-f C=A) 

 y sin. B. sin. C 



Fig. 328. 



and by applying the same formula to a second 

 spherical triangle, fig. 328, whose angle 

 C is similar to that of the preceding, 

 B is the inclination of M on T, 

 A the supplement of M on the plane a b c f\ 

 derived from actual measurement, or deduced from the 

 known inclination of P on the plane a b c /, and of P 

 on M, we may again obtain the sidec, which contains 

 the other required angle, i c b. 



Having thus determined the two plane angles, 

 i be, i c by the ratio of i b to i c is known from the 

 analogy between the sines of the angles of triangles, 

 and the sides subtending those angles, thus, 



i b : ic : : sin. \y i c b : sin. \/ i ' b c.* 

 Let us suppose i k : id:: m : n ; m and n being 

 any whole numbers whatever, and being already 

 known by means which will be pointed out in a later 

 part of this appendix. 



* This mark V ' s used to denote the word angle. 



