346 Dr. W. F. G. Swann on the 



In virtue of the relations (3) the elimination of f,g, li from 

 the equations may be completed, for example 



G 2 



e l 9=9 + 4 ^t (o) 



Finally, on writing 



a 1} h u cj = e"* a, V, c ; /\, </ b /z x = e~i f\ #', A' ; 



our equations revert to the original type (1), the typical 

 equation becoming 



* d/i__d c i d^i (A 2\-i^ a i S/*i 0<7i , n 



o*i oyx dV ; o*i o^/i o*i 



The remainder of the argument then follows as given in 

 ' iftther and Matter ' (pages 174-177), the above being as 

 much as we need abstract for the purpose in hand. 



Now let us turn to the problem of the uniform rotation of 

 a cylinder, and let us choose coordinates 0, r, z. Let /, g, h, 

 a, b, c be the corresponding getherial displacement, and 

 magnetic vectors. Maxwell's equations may then be written 

 down in terms of #, r, z. It will only be necessary for our 

 purpose to write down one pair 



i o7 ~dc 'db n2\-i^ a O^ 1 0# 



If we transform to a system of coordinates 6', r\ z\ 



moving with the cylinder, so that ^ becomes A ©A 



Ot Ot uv 



co being the angular velocity, then in view of the fact that 



o/ do/ dA _ j Ba db oc 



