Theory of Radiation. 241 



where A and B arc arbitrary constants, and 



K.-(-iyi.a.5.(fc-i)^f" a "^»V . 



Jo cosh (j> 



Tables for K and K 1? and I and I : are given by- 

 Mr. W. S. Aldis, Proceedings of the Royal Society, vol. lxiv. 

 p. 203. 



I n (#) becomes infinite when x is infinite, while K n (V) 

 vanishes in that case. 



We see that the solution of (1) is 



w=AI 1 (a?)+BK 1 (a?). 



Sine* u and therefore w vanish when x is infinite, A = 0, and 



we have 



u = XW = BtfK^tf), 



where 



_ 1 ( °° cos f.?;sinh(f>) . , 



Ki = — - 1 , , , — - dd>. 



x ' cosh" cf> 



Since when x = 0, 



2 



and -^ f x def) 



t,= C(i4' 



'0 



we see that _ 2 



c- 



hence a C +co cwqtdt 



\ mv / 



- 2u \/^ ?Kl ( ? \/^)- 



As -|rai> 2 is the kinetic energy of a corpuscle, we have if 

 the corpuscles are in thermal equilibrium with the body 



±mv 2 = ot0, 



where 6 is the absolute temperature of the body, and 



a =i-42xl0- 18 , 



hence, if h = h\/ pm, we have 



*--»(3)*@)' 



* See Gray and Matthews, Bessel's Functions, p. 67. 

 Phil Mag. S. 6. Vol. 20. No. 115. July 1910. R 



