Uniform Rotation of a Circular Cylinder. 347 



the above equations give 



i7r dt' = ^'~ r 57 ^ " (4,rC } S? " 57 -^ 57 liTO 1 ) 



corresponding equations of course holding for 



a.? 9/t a ft a^ 



3*" a*" a*' a*'- 



When we reached this stage in the case o£ uniform 

 rectilinear motion (see equations 2), we were able to put 



the terms on which ^—7 operated together, and similarly for 



the terms on which ^— , and - — -, operated. Considering 

 ox oz 



the corresponding case in our present problem, however, we 

 see that we cannot for instance put ^—7 — r'^— ,(\ntvq) in the 



I -fry/ £,. V 



~dc 

 form ^— , unless we know a as a function of the variables ; 

 Or J 



and similarly for the other equations it would be necessary 

 to know /and h, a, b, and c, as functions of the variables in 

 order to accomplish this, i. e., it would be necessary to know 

 the strengths, distributions, and motions of the electrons in 

 the system. Again, even supposing that these were known 

 so that we could put our equations in the form corresponding 

 to set (4), a, b', c, /', g' 1i\ being, however, functions of 

 r, 0, 2, t, which involve the strengths, distribution, and 

 motions of the electrons in the system, we should, neverthe- 

 less, be unable in general to perform the step indicated by 

 (5) in such a way as to obtain for example g in the form 



g^Ag' + Bc', 



where A and B are constants. A and B would have to be 

 functions of the variables depending on the conditions 

 peculiar to the particular system we were studying. If A 

 and B cease to be constants, of course the whole endeavour 

 to perform the step analogous to that performed in (6) 

 breaks down, and the equations cannot in general revert to 

 the type for the fixed system of coordinates. It may be 

 remarked that even in the case of uniform rectilinear motion 



2 A 2 



