360 
ON THE WHIRLING AND VIBRATION OF SHAFTS. 
under discussion, is neglected. The resulting whirling speed may then be obtained by 
an empirical formula of the form given in the preceding article. The speed thus 
obtained will be less than the actual speed of whirl (see § 46, p. 334). A nearer 
approximation to the actual speed might be obtained by considering only those pulleys 
which lie near the centres, or between the centres of the side spans and the bearings of 
the middle span (see § 45, p. 334), neglecting the effect of those pulleys which lie 
beyond the centres of the side sj^ans. In doing so, however, there is a danger of the 
calculated speed exceeding the actual, whilst, by taking all the pulleys on the two 
sides into account, the calculated speed will be less than the actual speed (see 
§ 46, p. 334). 
[The above method of solution and the consideration of only three adjacent spans, 
is based on the results arrived at in §§ 54, 58, pp. 347, 353. It has been verified, not 
only by experiments made with the experimental apparatus, but also by experiments 
made on actual cases of shafting carrying heavy pulleys.] 
In the case of a continuous shaft of equal spans which are all similarly loaded, each 
span whirls independently of the rest, and the problem, therefore, reduces to the case 
of a shaft loaded in a given manner and merely resting on a bearing at each end—tbe 
distance between the bearings being the same as between those of the continuous 
shaft. 
