dp 
-2 
Bp, 
dq 
-2 s dr 
8( i> 17 
dv bGr — cBq dv bCi— cBq ly dv bGr — cBq 
Br, 
dv hCr — c Bq 
or the equation to be verified is simply 
V j'bC%'- cB = 2 {bpq (A-B)- crp (0 -4)}; 
which follows immediately from the three equations just given for the determination of 
dp dq dr , 
dv’ dv’ dv 
From these values also 
Next, to calculate (h, e), 
(k, e) =0 (49). 
(h, e)={(h, «)}+(/., a) | + b)^+(A, c)^; 
but the three last terms being evidently such as to vanish for v=v 0 , we may neglect 
them, and consider (h, e) as the value which {(h, e)} assumes for this value of v. 
{(h, e)} = 2p {(Ap, e)} + 2q {(Bq, e)} + 2r {(Cr, e)}, 
{(Ap, e)} = - ^ (Ap, v), 
(Ap, v)— ^ [ ( 1 + X 2 ) {(1 + k) mot + Xot 2 } — (Xu + ot) [u + X (1 + k) ot' 
+ (Xp + v) {(1 + k) mot + pvs 2 ] — (Xv — w) [v + p (1 + tc) ot} 
+ (vX — p) {(1 + k) WUJ + fOT 2 ] — ( V + Xw) [w + V (1 + k) ot}] 
= {(1 + k) отг¿ + A.KOT 2 — X (1 + k') ot 2 — X (u 2 + v 2 + w 2 ) — otw} — (a, v) 
= \ (bCr — cBq), (50)>