﻿24: Mr, C. V. Raman on Motion in a 



series. This fact may be explained in the following general 

 manner. 



We may assume, to begin with, that the independent 

 driving is less powerful than that required to overcome re- 

 sistances, so that the wheel is a little behind the correct 

 phases. In the case of the integral series, one or two or 

 more teeth pass for every intermittence of the current, the 

 wheel being in the same relative position, whatever this may 

 be, to the electromagnet, at each phase of maximum magne- 

 tization of the latter. This is not, however, the case with 

 the fractional speeds. It is only at every alternate phase of 

 maximum magnetization that the wheel assumes the same 

 position (whatever this may be) relative to the electromagnet. 

 At the intermediate phases, it is displaced through a distance 

 approximately equal to half the interval between the teeth. 

 Whereas with the integral series, every phase of maximum 

 magnetization assists the rotation, in the fractional series the 

 wheel is alternately assisted and retarded by the successive 

 phases of maximum magnetization, and it is the net effect of 

 assistance that w r e perceive, this being of course comparatively 

 small. 



As the synchronous, half-synchronous, and double-s}^n- 

 chronous speeds can all be readily maintained without inde- 

 pendent driving, they can be very effectively exhibited as 

 lecture experiments by lantern projection in the following 

 way. The synchronous motor (which is quite small and 

 light when the stroboscopic disk is removed) is placed on 

 the horizontal stage of the lantern and the rim of the wheel 

 is focussed on the screen. In front of the projection prism, 

 where the image of the source of light is formed, is placed 

 the fork-interrupter with the necessary device for intermittent 

 illumination fitted to its prongs. When these are set into 

 vibration and the synchronous motor is set in rotation, the 

 " pattern " corresponding to the maintained speed becomes 

 visible on the screen, and the effect of reversing the direction 

 of rotation can also be demonstrated. 



We now proceed to discuss the mathematical theory of 

 the maintenance of uniform rotation in each of these cases. 

 The first step is obviously to show that with the assumed 

 velocity of rotation, the attractive forces acting on the disk 

 communicate sufficient energy to it to balance the loss due 

 to frictional forces. Taking the line joining the poles as the 

 axis of a;, the position of the wheel at any instant may be 

 defined by the angle 6 which a diameter of the wheel passing 

 through a given pair of teeth makes with the axis of reference. 

 Tf n is the number of teeth in the wheel, the couple acting 



