﻿18 Mr. C V. Raman on Motion in a 



intermediate between those of the series are maintained. 

 In obtaining the 1st case, in which the oscillations of the 

 wheel and the fork are in unison, it is generally found 

 necessary to increase the '* spring " of the wheel by passing 

 u steady direct current through the electromagnet of the 

 motor from a cell connected in parallel, in addition to 

 the intermittent current flowing in the same direction from 

 the interrupter circuit. 



Tt is found that the Lissajous figures for the 1st, 3rd, and 

 5th cases are distinctly asymmetrical in character, the 3rd 

 being markedly so. The 2nd, 4th, and 6th types are quite 

 symmetrical. 1 his, it will be remembered, was what was 

 anticipated above, and in fact the 1st, 3rd, and 5th types 

 differ rather markedly in their behaviour from the 2nd, 4th, 

 and 6th types. These latter are maintained with the greatest 

 ease, while the former, particularly the 5th, are not altogether 

 so readily maintained. In fact it is found advantageous, in 

 order to maintain the 5th type steadily, to load the wheel 

 somewhat unsymmetrically and to put it a little out of level, 

 in order to allow the oscillations to take place about an axis 

 slightly displaced from the line joining the poles of the 

 electromagnet. 



It is noticed also that the lower frequencies of vibration 

 have much larger amplitudes. This, I would attribute princi- 

 pally to the greatly reduced damping at the lower frequencies 

 owing to the slower motion, the larger masses, and the weaker 

 magnetic fields employed. 



We are now in a position to consider the mathematical 

 theory of this class of maintained vibrations. To test the 

 correctness of my theoretical work, I have prepared a series 

 of photographs of the simultaneous vibration-curves of the 

 fork and of the armature-wheel, which are reproduced as 

 figs. 1 to 6, PL II. These curves were obtained by the 

 usual method of recording the vibrations optically on a 

 moving photographic plate, it being so arranged that the 

 directions of movement of the two representative spots of 

 light on the plate lie in the same straight line. The upper 

 curve in each case shows the maintained vibration of the 

 armature-wheel. The lower represents that of the fork- 

 interrupter. The frequency of the former, it will be seen, 

 is } or ^ or I or J or ] or -^xthat of the latter. The 

 precise features of the vibration-curve noticed in each case 

 will be referred to below, in connexion with the mathematical 

 discussion. 



The equation of motion of a system with one degree of 

 freedom moving in a periodic field of force, and subject also 



