314 
MR. S. DUNKERLEY ON THE WHIRLING 
and from B to C 
When 
whence 
= y cc® + ^02^ + O'x + D'. 
rr = 0, y=o, y =0,. 
dyjdx = dif'jdx, d^yjdx^ = d^^if jdx^ ; 
D = 0 
D' = 0. 
c = cr . . . . 
B = B' . . . . 
At A, where x — ~ 1, 
y = 0, d~i/jdx^ = 0, 
therefore 
- # + ? l- - c« + D = 0 
U 
- AZ + B = 0 . . . 
When X — c (at the pulley) 
and 
whence 
and 
d\jldx — dYildx — — os^y. Wig (§ 7, ecpiation (5)), 
L — B = w^I' dyjdx (§ 7, equation (6)) ; 
(1), 
(2), 
( 3 ) , 
(4) . 
( 5 ) , 
( 6 ) . 
( 7 ) , ■ 
( 8 ) . 
The elimination of the seven ratios— 
A : B : C : D : A' : B' : C' : D' 
from these eight equations leads to 
a = and h = (see § 23, p. 30,5). 
in which 
