352 Prof. 0. V. Raman and Mr. Ashutosh Dey on 



whether this intrinsic field is to be treated as altogether a 

 true magnetic field, or if it is in part due to other than mag- 

 netic forces which are in operation and which, playing the 

 part of magnetic forces, have been evaluated in terms of a 

 magnetic field. 



In conclusion, the ferromagnetic equation does not claim 

 to be a complete statement of the complex facts of magnetism, 

 but rather is to be regarded as a limiting law to which ferro- 

 magnetic substances tend to conform when the molecular 

 magnets are free to move under thermal agitation with no 

 other constraints than the external field and the intrinsic 

 field, just as the paramagnetic equation is a limiting law to 

 which paramagnetic substances tend to conform when the 

 molecular magnets are free to move under thermal agitation 

 with no other constraints than the externally applied field. 



XXXIII. On Discontinuous Wave-Motion.— -Part III. 

 By 0. V. Raman, M.A., and Ashutosh Dey *. 



[Plate VIII. J 



IN a previous communication under the same title pub- 

 lished in this Journal (Phil. Mag. Jan. 1916), it has been 

 shown that by imposing a linear distribution of initial velo- 

 cities with a discontinuity at one end upon a stretched string 

 in its position of equilibrium, free oscillations may be 

 obtained of identically the same type as the principal mode 

 of vibration of a bowed string. The experiment furnishes a 

 striking confirmation of the analytical theory of the motion 

 of bowed strings. In the present paper it will be shown 

 that some of the more complicated types of vibration of a 

 bowed string may also be investigated by similar methods. 

 Figs. 1 and 2 (Plate VIII.) reproduce a few typical records 

 from amongst those secured in the course of this work. 



From the mechanical theory, it appears that the most 

 general form of vibration of a bowed string obtained by 

 applying the bow at a point not coinciding with any node 

 of importance approaches in the limit a t} r pe defined by one, 

 two, three, or more equal discontinuous changes of velocity 

 travelling over it. But when the limiting conditions are 

 not attained, the mode of vibration may still to a close 

 approximation be defined by a finite number of such discon- 

 tinuous changes of velocity, these no longer being all equal 

 to one another or of ihe same sign. In the present paper we 



* Communicated by the Authors. 



