22 
MR. LUBBOCK’S RESEARCHES 
Cdr + (B — A)pqdt = 3 - M - ( '^ i — — x,y/At 
Bdq + {A- C)rpdt = 3 -—- C) z/x/d f 
^4dp + (C- B)yrd< = ^-^ ^y/z/dt 
Substituting for xj, y\, zj their values from equations, p. 20, upon the sup- 
position of 4 1 = 0, 
Cdr + (B — A)pqdt — 3 M ^ ~ ^ j { (y 1 cos 0 — s' sin 0) 2 — z' 2 } sin 2 ?> 
+ 2 x'( 2 /' cos 0 — s' sin 0) cos' 2 <p | 
Bdq + {A — C)rpdt = 3 —~— a — / «' <y sin 0 + z' cos 0) cos?) 
r i L 
+ ( y ' cos 0 — z' sin 0) ( y ' sin 0 + z' cos 0) sin <p j 
^ | (y'cos 0 — z' sin 0) (y'sin 0 + z'cos 0) cos <p 
— a:' ( y ' sin 0 + z' cos 0') sin p j> 
If 
Adp + (C — B)qrdt — 
3M 
r 
^ - | (t/' cos 0 — z' sin 0) (^' sin 0 + z' cos 0) | = 
| x ' s ‘ n ® + * f cos A) ^ = -P' 
Bd g + (.4 — C) rpd* = (^4 — C) d < {P'cos p + Psin 
A dp + (C — B) qr dt = (C — B) dt {P cos<p — P 1 sintp} 
P and P 1 may be developed according to sines and cosines of angles increasing 
proportionally to the time. Let h cos {it + e) be any term of P, sin {it + z) 
the corresponding term of P', 
Bd q + (A — C)rpdt — — ^ — d< < (k -f k') sin (<}> + it + e) + (k — k') sin (<p — it — a) i 
Adp + ( C — B) qrdt — d t < (k + k') cos (<p + it -j- s) + (k — k') cos (<p — it — a) !> 
The equations which were given p. 21, may still be considered as afford- 
