AND VIBEATION OF SHAFTS 
311 
bearing to the centre of the span, the limits between which whirling is possible 
approximate more closely to each other. 
28. Experimental Results. 
The results, as given by equation [A.], page 308, merely take account of the effect 
of one pulley, the effect of the shaft and of all other pulleys which it carries being 
neglected. Jf Ng he the separate speeds of whirl of the shaft and p)ulley, on the 
assumption that the effect of one is neglected ivhen that of the other is under con¬ 
sideration, then it is shown in § 62, page 357, that the resulting speed, of ivhirl due to 
both causes combined may be taken to be of the form 
N,Ng/y(N,2 + N/). 
If the resulting speed given by this formula does not sufficiently approximate to the 
observed speed, then, by the introduction, in the terms of the denominator, of constant 
multipliers {which are determined by experiment), it will he shoivn, as occasion arises, 
that the speed given by the formula may be made to sufficiently approximate to the 
actual speed in all cases. Generally, however, the resulting speed given by the formula. 
NiNg/v/(N,=^ + 
will be found to give results sufficiently accurate for practical puiposes. 
29. The following are the mean results of experiments made with pulleys I, and II. 
(see Chapter I., § 6, page 285) in different positions. The shaft, witliout the pulley, 
has been investigated in §§ 10, 11 ; whilst the calculated speeds for the pulleys alone 
have been obtained from equation [A.J, page 308. The resulting calculated speed is 
taken to be NiN 2 /v'^(Ni^ + where No are the separate speeds of whirl of the 
shaft and pulley. In all cases the distances c, c are measured from the centre of the 
bearings to the centre of the pulley. 
Pulley I, 
Conditions. 
Calculated 
speed, neglect¬ 
ing pulley and 
merely taking 
account of 
shaft (= Ni). 
Calculated 
speed, neslect- 
Besultiwj 
calculated 
S])eed. 
Number of 
Experiment. 
Date. 
1 
in 
inches. 
c 
in 
inches. 
o' 
in 
inches. 
Observed, 
sjieed. 
ing shafc and 
merely taking 
account of 
pulley ( = Nj). 
Percentage 
error. 
48 
1892. 
Oct. 26 
32-00 
1-00 
31-00 
1150 
1121 
13537 
1117 
+ 2-9 
46 
32-00 
2-91 
29-10 
1123 
1121 
4621 
1089 
+ 3-0 
47 
32-00 
4-00 
28-00 
1101 
1121 
3563 
1069 
+ 2-9 
4.5 
32-00 
5-.33 
26-66 
1044 
1121 
2705 
1036 
+ -8 
44 
?) 
32-00 
10-66 
21-33 
952 
1121 
1683 
933 
+ 2-0 
43 
Oct. 24 
32-00 
16-00 
16-00 
921 
1121 
1495 
897 
+ 2-6 
