37] ON THE ROTATION OF A SOLID BODY ROUND A FIXED POINT. 
249 
whence 
and therefore 
Next, to find 
{observing 
where 
(a, /cot) 
by equations (29), 
that is 
Also 
whence 
or putting v = v 0 , 
and therefore also 
{(h, e)} = — 2, 
(h, e) = — 2 (52). 
(a, 8), (b, 8), (c, 8), (h, 8), 
S = 2tan -i‘g--k[ (h + % du , 
2k J vV 
= 8' + 8" suppose, 
(a, 8) = (a, 8') +(a, 8")» 
, ^ k , , , ,, d8' 
(a, 8) = — (a, /cot) + (a, k) , 
/c 2 ot 2 + 4>k 2 = 4 (il 2 + & 3 ) = 4kv] 
= —(a, /cot), 
KV 
= i { ( 1 + A 2 ) (kv + 2Aot) — ( Aw 4- ot) /cA 
+ (\/x — v) (kv + 2/¿ot) — ( Xv + w) K/JL 
+ (v\ + fi) (kw + 2vu ) — (— v + Aw) kv } 
= | k (u + Aot) = Ap — vBq + (¿Cr + Ail = \ (a + Ap) k (53), 
(33), and (10) ; 
( a > &) = ^ J (* + A P)- 
(a, 8") = - k ^ (a, v) + (a, b) ^ + &c. 
= -1 k (hCr - cBq) + Fv - Fv 0t 
(a, 8) = ^ {a + Ap- (bCr - cBq)} + Fv - Fv 0 , 
(a, 8)=A {a + ^ o _^+^ ( bGr 0 -c% 0 )} (54), 
(b, 8) = A {b + Bq 0 - (cAp 0 - aGr 0 )}, 
(c, 8) = A (c + Cr 0 - h t.^ (aBq a - bAp 0 )}. 
ZVq v 0 
C. 
32