(154) 
The problem is to determine the position of A'B’C/ 
with respect to axes X,Y,2, fixed in space, where X,Y, 
is the ecliptic and X, is the descending node of the 
principal plane of the Earth, namely our former XY, on 
the ecliptic our present X6Y:. 
For the moment, I have no need to refer to X5Y52 
but fix my attention on the systems ABC and A’B/C’. 
If A’B/C’ are derived from ABC by three small rota- 
tions 6,, 0, 0; about A, B, C respectively, and if x, y, z 
are the coordinates of any point fixed with reference to 
ABC, whilst x + x, y + dy, z + Ôz are the coordinates 
of the same point when referred to A/B'C/, we have 
Ca — 6sy EEE 0,7, 
dy —= 017 — 0:%, 
02 = 0,7 — 6,y. 
First suppose that the fixed point lies at C'or [on a 
sphere of unit radius. We found above the rigorous 
expressions for the direction cosines of I the instanta- 
neous axis; on reducing these to an approximate form, 
we have to the first order of small quantities 
C— A C— A 
À nt, Yy= —Ssinxcos HR 2 = 
x —= Sin a sin 
But its coordinates referred to A’B’C! are 0, O0, 1. 
Therefore 
C— A 
dx = — sin & sin nl, 
C — A 
dy = Sin x cos nt, 97 = 0. 
