A RIGID BODY IN' ELLIPTIC SPACE. 
321 
Also 
C 0 C 11 
C 3 C 11 
C 9 C 11 
b c 
g h ‘ 
a c 
f Ti = ~ G '° C ^ 
a b 
7 9 
C 14 C 13 
y 
If we eliminate a, b, c, f g, h from the first three equations, by multiplication, 
the result takes the form 
C 6 C ]0 C 5 C 9“t _C l C 13 C 3 C 14— 
This equation among the constants does not hold in general; so we must suppose 
the parameters go, q, r, v, w of the theta-functions so connected as to make it satisfied. 
b c 
77 
them, we see that 
respectively, and comparing 
Again, multiplying the last three equations by 
7 
f 
a C 7 C 12 _ b c 5 e I2 _ c c n c u 
f 9 c 2 c n b c 9 c n 
Of these, the first equation is the same as the third of the first set. 
The second may be written 
-c 6 c 9 =—- Ca p 14 
Comparing this with the first of the other set we get 
C 6 C 10 C 5 C 9H~ C 1 C 13 C 2 C M~0 
which is the same as before, 
relation holds. 
They give us 
That is 
Similarly 
Hence the six equations are consistent if this one 
/ a\ 3 _ 6' n 2 c 5 c 14 b e 
\fj c 2 q 2 c 9 g li 
_ C 0 C h C U C 7 C 1 2 
C 2 C 7~ C 9 C 0 C U 
/ ® \ ~_ C 0 C 12 C 5 C 14 
\f I C 2 C 7 C 9 C 11 
C_ C 7 C 12 C 2 C I4 
C 0 C 9 C 5 C 11 
," = Wit 
C 0 C 2 C 11 C 14 
2 T 
MDCCCLXXXIV. 
