(455 ) 
In this case y and x are both small quantities of the 
first order, and 6; is also small ; therefore 0,y in the first 
equation and — ;x in the second are of the second 
order and negligible. 
Hence the first two equations become 
ÔX —= — 02, 0y—= 0; 
these give 
C — A , C — A 
nt, 0, —= SIN & COS 
4 = sin æ sin nt. 
The value of 6; is not to be determined from this, 
save that it must be a small quantity of the first order. 
Secondly let the fixed point be P Iying on the circle 
CA on a sphere of unit radius. Its coordinates referred 
to ABC are 
x — COS À, y = 0, z = Sin À. 
Referred 10 A’ B’ C', its coordinates are 
x + 0X == COS (À + 0À), y + dy= 0, 
3 + 0x = sin (À + 0). 
Therefore : 
dx == — dÀ Sin À, dy = 0, dZ — dÀ COS À. 
Hence 
— DA Sin À == — 6, sin À, O0 = 6, sin À — 4, cos À, 
JA COS À — 4 COS À. 
Therefore 
D —0À,  65= à tan À. 
