324 
MR. R. S. HEATH ON THE DYNAMICS OF A RIGID BODY. 
Hence, performing the same operations as before 
d [V 
C ° Cs tfcc IV 
J $3 
C ° Clo dr d u 
_ $7 $ 4 , ^9 'ffio 
— C 8 C 11 q Q + C 5 C 6 £ ^ 
^12 ^12 ^12 ^12 
$7 $g $o $13 
= C 4 C llq“~ Q C l C 14(f“ IT - 
^"12 ''''12 ^12 2 
cl /$ 0 
Whence the coefficient of x in — 7^' 
C 8 C 11 C 7 C 4 ~t C 5 C 6 C 9 Go 
C 0 C 3 C 12 2 
d /$ \ 
and the coefficient of x in — (~ I 
d x \$i3/ 
_ C 4 C n C 7 C8 G C 14 C 2 C 13 
C 0 C 15 C 12“ 
Hence 
Now 
C 5 C 9 C 6 C 10"^ C 1 C 14 C 2 C 13 
= c 0 c 13 2 X coefficient of x in { c 3 £(^)- c i 5 £(^ 
= 2c 0 c 13 3 X coefficient of x 2 in 
i 0 /tA 2 d 
^15 = C 15~ yK/ dp' Cl5 ~^~ ' * ' 
n /7r\ 3 d 
■^3 =c 3 ?- x (^y dp' Cs ’ * ’ 
&n- c i z- 2 x { k ) d /±*+ • • • 
in Mr. Forsyth’s notation ; therefore 
c 3^]5 c ir/b; — h x 
_i ^tz\*L d 3 , d ^ r 
K/ [ lo dp' 3 clp' 
and finally 
( 77-\ 2 f dc z dcj 5 
C 6 C 10 C 5 C 9 “b C l C 13 C 2 C 14 — C 0 C I2T^ J j C lo"^y C 3 d p' 
Hence, if this vanishes, we have 
dCn (l f/1 - . / ■. 
C ^J V =c ^’ smce P = ]o SP > 
that is, — is independent of p. 
0 = 
