AND VIBRATION OF SHAFTS. 
341 
When X — 0, 
y' — 0, y" = 0, dy’jdx — dy"jdx. dxy’jdx^ = dJ^y"jdx ^; 
whence 
D' - 0 . 
. (0, 
D"- 0 . 
• (2), 
C' = C". 
. (3), 
B' = B". 
• ('I)- 
When 
Ob — 
y'" = 0, dY'Idx^ = 0 ; 
whence 
»/// g//' 
V ^ + D'" =0. 
• (S). 
A"7i + B'" = 0. 
■ (6). 
When 
X — — {1.2 4). 
/y = 0, d/yjdx^ = 0 ; 
whence 
-iA(4 + 4)^ + iB(4 + 4)^-C(4 + 4) + B=:o. . . 
• (7), 
~ A (4 + 4) A B = 0. 
. (8). 
When 
a? = 4> 
^ — U, y' —■ 0, dyjdx — dy'jdx, d^yjdx^ = dhj'jd^^ ; 
whence 
— bA 4^ "h iB4'' — C4 +0 = 0. 
• (9). 
- iA7.,3 + iB7,;^ - O'b + D' - 0. 
• (19). 
4(A - A') 42 _ (B - B') 4 + (C - O') = 0 . 
(11), 
-(A-A')4 + (B-B')=:0. 
■ (12). 
Again, 
, at the pulley E, when x — c^, 
y” - y"\ dy'ldx = dif'ldx, 
dhjdx — d.\xldx = — ^ly' (§ 7, equatiuii 5), 
L - II = - 
co^r dy"Id,x (§ 7, equation 6) ; 
