Uniform Rotation of a Circular Cylinder, 3-15 



Suppose our system is moving parallel to the axis of x 

 with velocity v. Let /, g, h bo the setherial displacement 

 vectors, a, b, c the magnetic induction vectors, and C the 

 velocity o£ light. The electromagnetic equations when 

 referred to a system of axes at rest in the aether are of the 

 form 



, of__oe ob / w p2W<^__dA S g 



ot Bj/ oz ot oy qz 



.,, . ., ,. r 'dg B/i 3& ck° 



with similar equations for ^-- , ^-, ^— , ^~ 



qc ot ot ot° 



When we transform to axes x r , y\ z moving with the 

 system so that 



x\y\ z'=(x-vt,y, z) t'=t, 



we obtain, in view of the fact that -7- becomes -y-. — v -r-p 



at at ax 



(of t eg , oh n , ~da ob , Be A \ 

 a set of equations of which a typical pair are 



±*f -0° O^irvg) /]^w Jfl - M 4-^UttC 2 / 



ot oy oy v y 3*' 3/ -by' 



~db ^(A-rrvh) "dg 



a 



— sr> + 





M«) 



Now it will be seen that the terms on which ^ 7 operates 

 may be grouped together, a similar remark applving 

 respectively to the terms on which ^-j and ~ f operate in 



X QZ 



the other equations. On writing 



a', h\ c' — (a, b + 4.7rvh, c — iirvg) . . . ^ 

 » t 7/ ( j. vc -, rb \ r(3) 



our equations take the typical form 

 P/«X Jl%. S. 6. Vol. 21. No. 123. Mrrc-7< 1911. 2 A 



