320 
ME. R. EUNKERLEY OX THE WHTRLIYG 
These experiments show tliat tTe method adopted in calculating the final resulting 
speed gives results approximating very closely to the observed speeds. When the 
overhanging portion is small, and both pulleys are near the bearings, the shaft is 
stiffened by tlie pulleys (Experiment 83, 93). In all other cases the resulting speed 
as calculated above is slightly below the actual speed. The formula consequently 
errs on the right side. 
Case XII. 
35. Shaft, lengtti /, resttno freely on a support at one end and fixed in 
DIRECTION AT THE OTHER, LOADED WfTH A PULLEY, WEIGHT W AND MOMENT OF 
INERTIA r, PLACED AT A DISTANC'D C, FROM THE SHOULDER END, AND C, FROAI THE 
FREE END. 
We have (§ 21, erpiation 2), taking the origin at the shoulder end A, 
y = " T" + ^ -T' + Cx + D 
from A- to the pulley, and 
y' = f *’ + T + G'x + D' 
from the pulley to B. 
When X = 0, 
whence 
y — 0, (Jyjlx = 0 ; 
D = 0 . . . 
( 1 ). 
When X — c, 
C = 0 
y = y\ dyjdx — dy'jdx ; 
1 (A - A') c, 
+ i (B - B') + (B - Cr) cq + (D - D') = 0 
_ A') 4-(B - B') cH-(C - C') = 0 . . . 
( 3 ) , 
(4) . 
whence 
