﻿Periodic Field of Force. 2T 



a periodic function of the time, and the function F(t) which 

 expresses its value at any instant may be expanded in the 

 following form 



F(t)±at2,b sin [(rp 1 ±sp 2 )t + E'], 



where pij2ir and p^ftir are the frequencies of the two 

 interrupters, and r, s are any two positive integers. Using 

 the same notation as before, we find that in any complete 

 number of revolutions, a finite amount of energy proportional 

 to the time is communicated to the wheel only in any one- 

 of the followino- sets of cases : 



nd=(rp~ i ±sp 2 )t, 

 or 2 n = (rp x ± sp 2 )f, 



or ?)n6 = {rp l ±sp 2 )t, 



and so on. 



The cases actually observed in which rotation is maintained 

 fall within the first two of the sets given above. 



Summary and Conclusions. 



The vibrations of a dynamical system maintained by a 

 periodic field of force have been investigated experimentally 

 and theoretically, and it is shown that they form a new class 

 of resonance-vibrations, in which the frequency of the main- 

 tained motion is any sub-multiple of the frequency of the 

 exciting force. The possible speeds of synchronous rotation 

 of a motor of the attracted-iron type under simple and double 

 excitation are also investigated. The experiments and ob- 

 servations described in the present paper were carried out 

 in the Physical Laboratory of the Indian Association for the 

 Cultivation of Science, Calcutta, where further work on 

 the dynamics of vibration is now in progress. One very 

 interesting case which has been worked out is that of the 

 Combinational vibrations of a system maintained by subject- 

 ing it simultaneously to two simple harmonic forces varying 

 its spring. This is experimentally realized by attaching a 

 stretched string at its two extremities to the prongs of two 

 tuning-forks of different periods, the directions of motion of 

 which are parallel to the string. If M and X are the 

 frequencies of the forks, it is found that the string is set 

 into vigorous transverse oscillation if its tension is so 

 adjusted that the natural frequency is nearly equal to 

 -MM/» + N>*), where m and?/ are integers. Further details 

 of this investigation will be published in due course. 



