300 
MR. S. DUNKERLEY OR THE WHIRLING 
whence, when x = c, since R = 0, we get 
A \ sinh me + cosh me 1 -f- I cosh me + sinh me 
mhjYA 
m^gYA. 
, r^ \ ■ . 1 T. f . 
+ h \ Sin me + cos me> — D i cos me - tyw sin me ^ = 0 
' J [ vA'g^l 
(i). 
Again, from ecj[nation (6), p. 287, we have 
wherefore, when x =■ e, 
R — L = oj^T dyjdx ; 
A I 
OT/ 
W'-i 
cosh me + sinh me 1 - 4- B I sinh me 4- ^ - cosh me 
viiA J L 
2T' T r ^T/ 
1 . I r-x . W i 
— C -j cos me + sin me [> — D | sin me — 
?aEI 
cos me ^ = 0 
(2). 
Again, when x = 0, 
whence 
?/ = 0, dyjdx = 0 ; 
A + C= 0 . . 
B+ D = 0 
( 3 ), 
(-!)• 
The elimination of A : B : C : D from the four marked equations leads to 
1 I . Wa)T'\ , . [<AV Wo."- 
cosh me \ cos me 1 H-ttyr. + --yY4 
' ' iiAgWl^J \??iEI ndg^l 
+ sinh me cos me 
. wR'l . r. Wa)H' 
-»rVEI 
mYi I i ^ f 
= 0 
[A]. 
If we assume the pulley to be removed, that is, if we put 
in equation [A], we obtain 
w = 0, r = 0, 
cosh me cos me -{-1=0, 
the same as that obtained in Case I., p. 288. 
The equation [A] can only be solved by assuming some relation between the 
coefheients; in other words, we cannot obtain a general solution which could be 
readily applied in any actual case. 
