456 
PEOEESSOE CAYLEY ON THE BICIECULAE QIJAETIC. 
and thence 
dS =Mv-l l dv i —^ 2 dv. 2 -{-^ 3 dv 3 , 
eZSj =}>dv -f- % l dv l + % 2 dv. 2 — \dv 3 , 
dS 2 = %dv — S 1 <?u 1 + \dv. 2 — d 3 c?y 3 , 
dS 3 =ldv — l 1 dv i — o. 2 dv 2 — \dv 3 , 
■which are the correct signs in regard to the particular figure. 
Reduction of j ^ ^ ^ to Elliptic Integrals. — Art. No. 29. 
29. The expression in question is 
\/ (cos to V/+ fl — a) 2 + (sin w \Zff + Q—[ 3) 2 - y 2 
r 
cos 2 « , sin 2 «) 
T+F+i+sj 
