356 
MR. S. DURKERLET ON THE WHIRLING 
When X — c^, 
ij — y\ dyidx = dy' jdx, 
dljjdx — d^jdx — — . oi^y (§ 7, equation (o)), 
L — E, = — dyjdx (§ 7, equation (6)); 
whence, 
+ (C - C') c, + (D - D') = 0 . . . (3), 
A - A' 
c^3 + (B - B') c, + {C - C') = 0 
A - A' _ - '*^1’ (a ^ + B ^ + Cci + Dj 
(A - A-)c, + (B - B') = - (A c."- + Bci + C 
Similarly, when x = c^, we have 
A' -A" o , B' ~ B" 
—6“^^ +-T“ 
c/ + (C' - C") C3 + (D' - D‘") = 0 
A' - A" 
c/ + (B' - B") cq + (C' - C") = 0 
A' - A" = 
(A' - A'O c, + (B' - B") = 
/ A I TD' I ri‘ 
Ei' YW+Bc, + C 
(4), 
( 6 ). 
(7) , 
(8) > 
(9), 
( 10 ). 
Again, when x = I, 
whence 
2 / 3 " = 0 , dy'jdx- = 0 , 
\// -I)// 
6' + W + B" = 0 
tll)> 
Putting 
= W.cYEI, 
“2 — 
A'7+B" = 0 ... . (12). 
— oj^I^/EI and = “liiqy where l\ = -v/(f/Ii/W^), 
ySg = oj^Io/EI and /B., = where /.q = 
