74 
ANALYTICAL RESE AECHES CONNECTED WITH 
L 114 
the first equation divides by (V£3(£ 4- jp), and the result is 
(f ■+ O + 8(v + 20?) - (Va (? + D -/(«i + 20?)} = 0. 
Also, by an easy transformation, the second equation becomes 
- KS (f + 0 -/(, + 20?)}’ + 46cf ((? + 0 + 0 (1» + 20?) - (1 + 0») ?) = 0, 
or putting 
£ + £ +0(77 + 20f) = @, 
^ (VS (? + ?)-/(<; +20?)) =<t>, 
f 
the equations become 
hence eliminating <i>, 
or observing that 
© - 2\<ï> = 0, 
<J)2 + 4 q/ {©-(1 + 0 2 ) ^} = 0; 
1 + ov (i + 0 s ) s 
1 + =j-, (Vs©+jf) <v©a+©) < vas + ?§), 
and reducing, we obtain 
,,, h">-> V(VS© -Jf) VS©',. 
(vas®+jf) (V©a+©) (Vas+?§) 
also © = 2X,<Ï> gives 
4> = 
\ 2 J30T 
iT© 
Suppose 
then substituting 
■JWm+№) (Vaaa+w vs© ' 
VS© + JF = a, VS© — JF = a,, aa, - Ka, 
v©a+ffi=0. v©a - ©i=/s„ /3/3,=irt, 
v as+= 7, vas — — 7,, 77,=kc, 
= 0, 
V/3,7, 
® - p- (a + «,) (l - 7 ^=) ¥ = 0, 
P/7/ \ Va + a/