AND VIBRATION OF SHAFTS. 
349 
When X = 0, 
y=0, y' = 0, 
dyjdx = dy jdx, d^yjdx^ = dry'jdx^ ; 
whence 
D = 0.. (1); 
0.(2), 
C = C'.(3), 
B = B'.(4). 
When X — — 
y =z 0, dryjdxr — 0 ; 
whence 
— ¥ -^4^ “h 2 B — C4 + I) = 0.(5), 
— A/j ^B^O .(6). 
When X — 4? 
" /A "f r\ 
y ^0, y =0, 
dy"jdx — dy'"jdx, d^y'jdx" = d~y'"jdx^ ; 
whence 
iA"4^^ + 4B"4^ + C% + D" = 0.(7), 
i A"7,^ + 4 B"7,^ + 0'"l, + D"' ==0 .(8), 
i (A" - A'") 4^ + (B" - B'") I, + (C” - C'") = 0 .... (9), 
(A" - A"') 4 + (B" - B'") = 0.(10). 
When X = li 4) 
y"' = 0, d''y'"jdx^ ~ 0 ; 
whence 
iA'"(4 + i,f + i B'"(4 + 4)^ + + 4) + u" = 0 . . (11), 
A'"(4 + 4) + B'"=0 .(12). 
Again, at the pulley E, when x =■ c^, 
y' = y", dy' jdx = dy" jdx, 
dLjdx — dEjjdx = oy^y' (§ 7, equation 5), 
L — R = — oj^r dy'jdx (§ 7, equation 6) ; 
