On the Forcing of Oscillations. 115 



normally from its end faces — an assumption far from being- 

 realized in our actual experiments. Hence the importance 

 of this term must be reduced, when applied to the case usually 

 subject to experiments. 



Thus far, the agreement between theory and experiment is 

 in general to be considered as fairly good, if we consider the 

 difficulties encountered in measuring the minute strains 

 caused by magnetization, and also the considerable dependence 

 of the magnetization upon the order of magnetizing and 

 ■straining. Since the theories, which are based upon quite 

 different considerations, all agree with one another in the first 

 important term, it may be concluded that for the first ap- 

 proximation, they are all verified by the present experiments. 

 It seems, however, impossible to decide experimentally 

 the correctness of the terms of second importance for ferro- 

 magnetic substances, in which the hysteresis effect appears 

 in no inconsiderable amount. 



In conclusion, we wish to express our best thanks to Dr. 

 S. Sano for useful suggestions in working out the theoretical 

 part of the present investigation. 



Y. On the Forcing of Oscillations by Disturbances of Different 

 Frequencies. By Andrew Stephenson *. 



1. HHHE simple oscillation of a system may be influenced 

 JL in two distinct ways : either by a force which is a 

 function of the time alone, or b} r a force which is a function 

 of both the time and the configuration of the system. In the 

 former case resonance occurs only when the period of the 

 force is equal to the free period of the system ; in the latter 

 the effect of the disturbance is cumulative when the ratio of 

 its period to that of the system has any value within a certain 

 range in the vicinity of \r, where r is any integer f, the 

 intensity being maximum when r=l. We now enquire as 

 to the effect of the two different types in joint action. Will 

 the two together under any circumstances produce and con- 

 tinually intensify an oscillation when each acting separately 

 would have no appreciable result ? 



* Communicated by the Author. 



t "Ona class of forced oscillations," Quarterly Journal of Pure and 

 Applied Mathematics, no. 148 (1906). The case of double frequency, 

 r=l, was examined by Lord Eayleigh, " On the maintenance of vibrations 

 by forces of double frequency, and on the propagation of waves through 

 a medium endowed with periodic structure," Phil. Mag. vol. xxiv, (1887). 



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