AND VIBRATION OF SHAFTS. 
307 
Therefore 
D = 0. 
B = 0. 
When 
X = I, y' = 0, (P'y'jdx- = 0 ; 
therefore 
f + f «^ + CT + D'=0 .... 
A7 + B' = 0. 
At the pulley, when x = c, 
y = y\ dyjdx = dy'jdx ; 
therefore 
+ + (C - C')c +(D - D') = 0 
+ (B - B')c +(C - C') = 0 .... 
Again, when x — c, 
dhjdx — dRjdx = — (o^y.Wlg (§ 7, equation (5)), 
and 
L — R = — (JY dyjdx (§ 7, equation (6)) ; 
whence 
and 
(A - A')c + (B _ B') = - + Be + C) 
The elimination of the seven ratios 
A : B : C : D : A' : B' : C': D' 
from the equations marked leads to the equation 
in which 
a = WojY^'EI, k = ^{gVjy^f) (see § 23, p. 305). 
2 R 2 
( 1 ), 
( 2 ). 
(3) , 
(4) . 
(7) , 
( 8 ) . 
[A], 
