A RIGID BODY IN ELLIPTIC SPACE. 
319 
|/(-+f) =£/(*+« 
Hence, taking the first equation, 
•{ 
C 4 C 8' 
Q X Q ^12 
or 
d 
C ^ 8 dx \3, 
— C l C 13’^5'^9 C 6 C 10 r ^'2'^14 
3 „ 3, 
^5 
I — C 1 C 13 q Q C 6 C 10 q q 
^12 ^12 
14. 
12 
Performing the same operations on all the equations we arrive at the following six 
relations:— 
C ^ 8 dx [3, 
l — C l C 13 
d 
dx \3 
d 
CoCg — I 
* J dx \3i 
x- =c 1dl c 
'6"l0 
‘ C 9 C 11 
CaC 
9"12 
A 
dx V ^12 
d 13. 
C ^dx\3 
Cot ’ 9 dx\3, 
2 _ 
12 / 
3, 
d5 dg 
^12 d 12 
dp do 
14" 12 q q ‘ 
"12 "12 
3 2 3 9 
3 3 
"12 "12 
3 0 3 b 
l = C 0 C 5 Y q- 
^12 ^12 
d 0 3 U . 
= c o c,4 7T o +c 7 c. 
■CijC 7 
=C S c 
'0 "14 q q 
"12 "12 
3q 3 9 
12 
^12 d 12 
7" 9 
■ / 2"ll 
*^2 
d]4, 
^12 
3 W 
h. 
3 7 
3 12 
djV 
'k, 
d]2 
3 12 
3o 
3 ? 
3 12 
>9-] 2 
3 7 
^9 
$12 
3 U 
3 7 
dll 
d 12 
dl2 
57. If we take the mass of the body to be unity, and notice that 
A+F=B+G=C+H=1, 
the equations of motion of the body under no forces may be written 
A 
1_B —C Wl 6,30,6 ~~ 0,36,5 = ^ 
B 
+ ‘"1^6— () 
C 
YZX-B ^ + W 1 W 5“"2^4 = 0 
ai 4 +co 5 w 6 —OJ 2 &) 3 = 0 
W 5 + W -1 W 6 — oq&Jg = 0 
cug + ai^ —aii&j^O. 
1 —A 
B-C 
1 — B 
C-A 
1-C 
A-B 
A 
