318 
MR. S. DUNKERLP]Y (JN^ THE WHIRLING 
resulting speed—viz., when and NiN 2 /\/(N 2 ^ + «N^®) 
when Nj > —holds, to a sufficient degree of approximation, whatever be the ratio 
of the overhanging portion to the span, or whatever be the size of the pulley. 
Moreover, as in § 29, p. 311, when the pulley is near the bearing the shaft is stiffened 
by the pulley, and the lighter the pulley the further the distance which it might be 
from the bearing before this stiffening action ceases. (Compare § 29, Experiments 48, 
46, 54, and present article Experiments 63, 64, 62.) 
34. The following are the mean results of experiments with both pulleys, T. and II., 
on the shaft. It is shown in Case XVII., 59-62, pp. 76-80, that the only way 
to deal with two or more pulleys is to consider each separately and obtain the 
resulting whirling speed from a formula of the type 
N,N2N3/v/(N,^N/ + N22N32 -f N3^Np), 
where N^, N^, N 3 are the separate speeds of whirl due to the several causes on the 
assumption that each cause is neglected except the one under consideration. In the 
present series of experiments Pulley I. was kept at the end of the overhanging 
portion, whilst Pulley II. was placed in different positions between the bearings, the 
distance between the bearings being also altered. The notation used in the following 
results will be understood from the diagram. 
Fig. 15. 
- Z -—-^ 
c —.j.-r -Y"-- 
' ' I 
To get the resulting calculated speed, the resulting speed for the shaft (N^), and 
for Pulley I. (Ng) is obtained, as explained in the preceding article. Let this be 
called N 3 . The whirling speed for Pulley II. alone is obtained from equation A., 
§ 26, p. 308. Let this be N 4 ,. Then the resulting speed for both the pulleys and the 
shaft combined is taken to be 
N3N4 
v/ (N/ + N/) 
or 
