On a Supposed Proof of a TJieorem in Wave- Mot ion. 459 



where A is a directed quantity and is obviously determined 

 by the definite integral given on p. 283, being related to F 

 in the same way as A 1 is to F l5 &c. 



Dr. Stoney in fact admits as much as this, but he then goes 

 on to say on p. 371 that "on a close scrutiny we find that 

 although this furnishes an apparent solution, in the form of 

 forced vibrations, or rather a group of such solutions, the 

 group unfortunately does not include the solution which 

 would be selected by nature under any conceivable circum- 

 stances. The analysis furnishes undulations which could not 

 propagate themselves through an}' medium. The motions 

 which it furnishes are the non-natural motions of a mere 

 forced kinematical resolution, of no use in physics. That 

 this is so can be made plain by taking a very simple 

 example . . . ;" and he then takes an example and discusses 

 it in a manner which shows clearly that his letter was written 

 under some misunderstanding as to my interpretation of the 

 expansion. What I state is, that when the disturbance which 

 exists throughout any given region is specified, then a system 

 of plane waves can be determined which will produce the same 

 disturbance at every point of that given region. Now in his 

 example Dr. Stoney takes the given region of space to be a 

 circular disk having its plane perpendicular to the axis of z, 

 and he specifies the disturbance throughout the disk to be 



so that in this case the specified disturbance throughout the 

 given region is already in the form of plane waves, and thesa 

 can be resolved into simple harmonic components when the 

 form of the function / is given ; and nothing more remains 

 to be done. As to what happens outside the disk, this is quite 

 another question and belongs to the class of problems dealt 

 with by Sir G. G. Stokes in his classical paper on the 

 Dynamical Theory of Diffraction. 



So far there has been no necessity whatever for considering 

 the nature of the medium or the manner in which it pro- 

 pagates waves, plane or curved, or even whether it propagates 

 waves at all. We simply ask for the disturbance, and this 

 being given we can determine the equivalent simple harmonic 

 plane-wave system. 



But if the given disturbance happens to be the actual dis- 

 turbance existing in some medium capable of propagating 

 plane waves unaltered, then the specification of this dis- 

 turbance will involve the properties of the medium. The 

 equivalent plane-wave system will represent the actual dis- 

 turbance, and these waves will be propagated through the 

 medium and will continue to represent the disturbance. 



