312 
MR. S. DUNKERLEY ON THE WHIRLING 
Pulley II. 
Conditions. 
Calculated 
speed, neglect- 
Calculated 
speed, neg-lect- 
Resulting 
calculated 
spieed. 
Number of 
Experiment, 
Date. 
1 
in 
inches. 
c 
in 
inches. 
c' 
in 
inches. 
Ohserved 
speed. 
ing pulley and 
merely taking 
account of 
shaft (= Nj). 
ing shaft and 
merely taking 
account of 
pulley (= N 2 ). 
Percentage 
error. 
54 
1892. 
Nov. 4 
.32-00 
1-00 
31-00 
1L30 
1121 
10355 
1115 
4 1-3 
53 
32-00 
2-91 
29-10 
1046 
1121 
.3116 
1055 
- -8 
52 
32-00 
4-00 
28-00 
1007 
1121 
2389 
1013 
- -6 
51 
Nov. 3 
32-00 
5-33 
26 66 
942 
1121 
1808 
953 
- 1-1 
50 
32-00 
10-66 
21-.33 
803 
1121 
1122 
793 
+ 1-2 
49 
Nov. 2 
32-00 
16-00 
16-00 
769 
1121 
997 
745 
+ 3-1 
i 
It will be noticed that in no case does the error materially exceed 3 per cent, of 
the observed speed. From Experiments 48, 46, and 54 it would appear that with 
the pulley near the bearing the pulley stiffens the shaft. That is to say, the shaft 
would whirl at a lower speed without the pulley than with it. The resulting 
calculated speed given above (viz., NjN 2 /-v/(Ni“ + Ng^)) must, of necessity, be less 
than either or Ng. If, however, the resulting calculated speed be taken to be 
NiN 2 /\/(^i^ -p (xNg^), where a is some constant determined from the experiments, 
then when Ng is large compared to N;^, the resulting speed is and if a be less 
than unity this would be greater than N^. In this way all the calculated results 
could be made higher than those given above, so that in the experiments on Pulley I. 
(since the observed is greater than the calculated speed throughout) the observed 
and calculated results could be made to differ very slightly from one another. As, 
however, the errors in the experiments on Pulley II. are sometimes positive and 
sometimes negative, the resulting speed given by NiNg/y4(N^® + Ng^) is sufficiently 
near the actual speed for practical purposes. 
30. The following are the mean results of exj)eriments with both pulleys (I. and II.) 
on the shaft at the same time. It is shoivn in Case XVII., §§ 60, 61, that the only 
way to deal ivitli tivo or more 'pulleys is to consider each separately and. then obtain 
the resulting speed of whirl by a formida similar to that in §§ 28 or 62. The case oi 
the shaft only is considered in §§ 10, 11 ; whilst the calculated results for each of the 
pulleys (considered separately) are obtained from the preceding article. The resulting 
calculated speed is taken to be 
NiNgN3/v/(N,^Ng2 + Ng^NgS + 
where Nj, Ng, Ng are the speeds of whirl for the shaft, Pidley I. and Pidley II, 
takefb separately. The span in all the experiments was 2' 8". 
