32G 
MR. S. DUNKERLEY ON THE WHIRLING 
When X = — 
whence 
When X — Jo, 
whence 
y z= 0, d~yjdx^ = 0 ; 
_ 4-+ D == 0.(5), 
—• -|-B — 0.(6). 
y" = 0, d^y”jdx^ = 0 ; 
iA'7,3 + ib'7/ + 0"l, + D'' = 0 ...... . (7), 
A% + B" = 0.(8). 
At the jmlley (D) we have, when x = c^, 
y' = y", dy' jdx = dy" jdx, 
dh/dx — d^jdx = — (jj'^y'.W/g (§ 7, equation 5), 
L — B, = — dy’jdx (§ 7, equation 6); 
whence 
i(A'- A") + MB'- B'Vi^ + (C'- C") c, + (D'- D") = 0 . . (9), 
MA'-A")c,^ + (B'-B'>, + (C'-C'') = 0 .... (10), 
A'-A"= -a(iAV + iBV + CM + B') .... (11), 
(A'- A") Cl H-(B'- B") = - ^ (lAV + B'cq + C') . . . (12), 
where, as in § 23, p. 305, 
a = WwV^EI, ^ = co^iyEI and /3 = aP, where k = ^(gl'/W). 
The elimination of the eleven ratios A : B : C ; D : A': B': C': D': A" : B" : C" : 1)" 
from the twelve equations marked leads to 
-y(«i+4)=o.[A], 
a quadratic in co^ which is not symmetrical with respect to cq, % 
If in equation [A] we put = co, it reduces to 
[CiV4 - (ci' + cqS)] - // = 0, 
