AND VTERATTON OF SHAFTS. 
337 
When X = 0, 
^ = 0, dyjdx = 0 ; 
whence 
D=0.(1), 
C = 0 ..(2). 
When X = Cj, 
y — y', dyjdx = dy'jdx ; 
whence 
i(A-A')ci5 + i(B-BV,2 + (C-C')ci + (D-D')=0 . . (3), 
HA-A')o.» + (B-B')ci + (C-C') = 0. (4). 
When X = I, 
y' = 0, dy'jdx = 0, 
whence 
i A' + IB' + C7 + D' = 0.(5), 
iA'/2 +B7+C' = 0. (6). 
When X = c (at the pulley), 
dVijdx — dV\,jdx = — to^y.WIg (§ 7, equation 5), 
and 
L — B = — (jj^V dyjdx (§ 7, equation G), 
whence we obtain, putting as before (§ 23, p. 305) 
a = Wa)~/pEI, yS = oj^I'/EI, and yS = aid, where k = j'^)} 
A — A' = — a A ^ B + CC] + D j.(7), 
(A-A')ci+(B-B')= -y8[iAci2 + Bc, + C] .... (8). 
The elimination of the seven ratios 
A ; B : C : D : A : B' : C' : D' 
from the eight equations marked leads to 
+ a — /wcic^(ci3 + c.^)] -P—Q . . . [A], 
a quadratic in which is symmetrical with respect to c,, Cj. 
MDCCCXCIV.—A 2 X 
