(487) 
Having obtained these results, we are in a position 
to introduce the axes Xo Yo Zo-: 
Let us suppose that the position of ABC is defined 
with reference to the ecliptic by the Eulerian angles 
0, ©, L. The same figure will serve again with 8,0, 
occupying the positions of 65, 0, Lo respectively. X, Y,, 
which replaces XY, will be the ecliptie, and X, is the 
first point of Aries. The angle 0 being the obliquity of 
the ecliptic will no longer be small as was 0,. 
If 0+00, w+0v, d+0V are the Eulerian angles 
defining A’ B’ C’ with respect to X,, Y,, Lo, We require to 
find 0, do, 04. 
They may be determined at once by exactly the same 
method as that by which the geometrical equations are 
obtained connecting the rates of change of the Eulerian 
angles with the angular velocities p, q, r. We have 
merely to replace velocities by displacements and thus 
obtain 
dB — — 0, cos ? + 8, Sin », 
- sin 009 — — 0, sin ? — 4 cosy, 
dp + COS 60) — D. 
We have also the geometrical equations 
de 
RD int, 
. dy 
sin Ar = — p SIN p—.4q COS +, 
