202 Mr. WHEWELL on the Angle made by two Planes, se. 
But manifestly, in this case, the equations .are 
4 & 
a = ———.,, and y= - : 
cos. LZ cos. Yz 
for the two lines respectively. Hence 
1 1 
a= ———__, b=0, d= 0, = — ——_., 
COS. VS ‘ cos. Ys 
and putting these values in cos. y, 
cos, ry 
1-1-1 + ———4*_ 
Cos. @Z COS. Y% 
V (acest) V (oe t1-2) | 
COS. LY — COS. L% COS. YS 
ore sin. vz sin. y% ’ 
cos. 7 = 
Now if a sphere be described about the origin, the co-ordinate 
planes will cut it, making a triangle, of which the sides are 
measured by the ‘angles xy, «2, yz, and the angle opposite to 
xy is ». Hence, the above is the expression for the cosine of the 
angle of a spherical triangle in terms of the sides. ‘ 4 
el 
