442 DR. CHARLES H. LEES ON THE EFFECT OF TEMPERATURE ON THE 



Hence we have the more general solution 



1 1 , mr,r 

 r, = --4cos- 



Ip( 



where Ao.-.A^ are arbitrary constants. 

 But at r = a, v n = V for all values of x. 

 Therefore 



A - - 



and 



c 7 H, nirx 

 ,._V=^cos^ r 



fnirc\ v fmrr\ *+\W) 



)S 



which satisfies equations (1), (2), and (3), and corresponds to a source of strength 

 H B cos ^^ situated c from the axis of the cylinder. 



If the source is of intensity = SHcos ^-, the temperature = v = Sv V. 



H I n 



In the apparatus used the source had a constant intensity H from x 17 to 

 x = + 1/, and the temperature was = V at x = 1. 



The intensity may therefore be represented by the Fourier series 



dt 



n ^ x u rr 1 P'TJ nirf 

 SH.cos p where H B = j I H cos ^-. 



2H 

 nir 



2H 



HIT 



2n7rl 

 a-s-f 



