96 EULER'S EQUATIONS OF MOTION, 
2. To determine the component changes of the body’s moment of 
momentum. 
At time ¢ the components of the moment of momentum are Aw, 
Bw,, Cw, in the directions of the principal axes, where A, B, C denote 
the principal moments of inertia. At time ¢+6¢ the components are 
A (wv, + san, &e., in the directions OA’, OB’, OC’. Employing the 
figure in a new sense, the former components may be represented 
by OA, OB, OC, and the latter by OA’, OB’, OC’. The changes 
of the moment of momentum in time 6 are therefore 4A’, BB’, 
CC’. Resolving these changes into their components parallel to 
the axes at time ¢ we get, as in the former case, (observing that 
Di eh ah 18 are now the displacements in time 6¢ of the point F 
(doy +A + dt, 0, o), &e.), the following as the resultant changes 
of the whl of momentum in time dt : 
(A was ~ Bow, + Cw.) ot along OA; 
(Ao,o, + B a — Cw,w,) 6¢ along OB ; 
(- Aw,o, + Bo.w, + C os) ot along OC. 
The changes per unit time are therefore A ) WW, We., 
in the directions OA, OB, OC, respectively. 
November 21st, 1878: 
