TOLMAN. — ELECTROMOTIVE FORCE PRODUCED IN SOLUTIONS. 121 



speed there was a certain amount of vibration of the steadying cords. 

 In general, however, it was found possible to raise the speed at which 

 this vibration took place by moving the supports W, X, Y, and Z nearer 

 to the shaft, and there 

 is no doubt that the 

 apparatus could be ar- 

 ranged to go to still 

 higher speeds. As will 

 be seen later, for other - 

 reasons, the actual 

 measurements had to 

 be made at speeds of 



5000 revolutions or : 



less. 



The fact to be special- 

 ly noticed with regard 

 to this " spinning-top 

 method" is that it per- 

 mits the driving at a 

 very high speed of a 

 rotator which has not 

 been specially adjusted 

 for either " stationary " 

 or " running " balance. 

 The method was adopted after considerable experimenting with a 

 rotator driven on a shaft with fixed bearings. Although this rotator 

 had been put into " stationary " balance, it caused so great a vibration 

 that one of the bearings gave way at a speed under 2000 revolutions 

 per minute, wrecking a machine upon which a considerable amount of 

 labor had been expended. 



The mathematical theory of a symmetrical top rotating with one 

 fixed point and acted upon by gravity alone has been completely 

 developed. It' has further been shown by H. Lamb ^^ that, in the 

 case of a rotating top hanging below its fixed point, as in this appara- 

 tus, the effect of viscous forces in the Hooke joint is to produce a 

 gradually increasing precessional motion which would finally raise 

 the axis of the top horizontal. This is the precessional motion 

 which was prevented by the steadying device described above. It 

 must be noticed in general, in designing rotating apparatus of this 

 kind, that the actual motion may differ considerably firom that pre- 



FiGURE 3. The Steadying Cords. 



" H. Lamb, Proc. Roy. Soc, 80, A 168 (1908). 



