A RIGID BODY IN ELLIPTIC SPACE. 
323 
The last two equations are given by Mr. Forsyth in equations (212), (219) of his 
Memoir. Differentiate these equations with regard to x and then put cc=0, y— 0, 
£=0, p = 0 ; they give us 
Hence 
Hence 
C 0 C 12 ■ 
C 6 C 10“b C 3 C 15 ' 
> C 5 C 9 + C 4 C 8 ■ 
1 C 2 C 14 : 
C 0 C 12 • 
C 5 C 9 “h C 3 C 15 ■ 
1 C 6 C 10~h C 4 C 8 ■ 
, c x c l2t 
C 0 C 12 • 
1 C 2 C 14“b C 3 C 15 • 
1 C 1 C 13 C 4 C 8 • 
C 6 C 10 : 
C 0 C 12 • 
C l C 13"b C 3 C 15 
• C 2 C 14 C 4 C 8 ' 
■ c 5 c 9 
C 4 C 8( C 2 C 14 C 1 C 13) — ( C 0 C 12“f" C 3 C 15)( C 6 C 10 
C 4i C 8( C 6 C 10 —C 5 C 9 )— ( C 0 C 12 C 3 C 15)( C 2 C 14 
2^j 2 — 2, 
°4 °8 — Oto. o 
0 v 12 
2^ 
J 2> u 15 
or 
C ^ — r* 2^ 2 I ^ 2 n 2 
°0 °12 —°4 °8 T°3 °15 
But we have also 
C 4 C 8 ( C 2 C 14“i“ C l (i 13) ~ ( C 0 C 12 C 3 C 15)( C 6 C 10H" C 5 C 9) 
Multiplying this by the first of the other two equations we get 
If therefore 
we have also 
whence 
i.e., 
p 2 2 . /-» 2x* 2 — 2x» 2 ___ p 2p 2 
°2 °14 °1 °13 —°6 °10 °5 °9 • 
^ 2 p 2p 2p 2 p %p 2p 2p 2 
°2 °14 °13 — °6 °10 °5 °9 
2 1 _ 2 ^ 2 — /-> 2 2 [ ^ 2 ^» 2 
°2 °14 T °1 °13 —°6 °10 °9 
Qp 2 — x» 2 p 2 
°6 c '10 —°2 c 14 
x» 2y^ 2 — p 2p 2 
°5 °9 —°1 °13 
C 6 C 10— i C 2 C 14 
C 5 C 9 = =Fc lCl3 
Addition. 
(Added March 4, 1884.) 
The relation between the constants may be put into another form. We have 
C 0 C 3 (®I5® 12 ®12® 15} = ^ { ^8^11^4+ ^5^6 'V^lo) 
C 0 C 15 { ®3 ® 12 ®12® 3 ) = ^ {f^il^d-s ^i^i4,d- 2 d- 13 } 
2 t 2 
