Theory of Radiation. 243 



When x is very large, then (Gray and Matthews, BessePs 

 Functions, p. 6Sj 



and we see tliat for short wave-lengths 



"1 4 ' 8<g 



E A varies as ~ 5 e A " .dX. 



X 



For these wave-lengths Lord Rayleigh/s formula makes 



and Planck's 



_ 1? 

 E v varv as — e kd . d\. 



•j 4-95 <g 



E A vary as r-g e Ad . dA,. 



A. 



Thus for both long and short waves the variation of E A 

 with temperature and wave-length indicated by the preceding- 

 theory is very much the same as that given by Planck's 

 theory ; from Aldis's Tables the values of E A given by 

 equation (2) can easily be calculated when X and 6 are given. 



From the equation 



27rh= y . X m 6 



we find, putting «=l-42xl()- lG ; X m . = 2940 x 10" 4 , that 



/< = 5'3xl0- 28 . 



But h = ^y/ fjbin. If we suppose the repulsive force due to 

 an electric doublet of moment M, //, = 2M<?, and we have 

 approximately 



2Mem = 10-'°\ 



or ]VL? 2 = 2-5xlO- 37 ; 



taking e = 4x 10" 10 , then M = P5 x 10" 18 . 



The distance between the charges in the doublet would thus 

 be 4XlO~ 9 cm. 



The existence of these doublets has a very important 

 bearing on the theory of the distribution of energy in light- 

 waves. There are many phenomena which can be inter- 

 preted as indicating that the energy in radiation is made up 

 of definite units, and that these units are indivisible, the 

 energy in each unit of light of frequency n being h'nftir where 

 Ifi is a constant introduced by Planck, having the value 

 6*55 x 10~ 27 erg. sec. As an example of a phenomenon which 

 suggests this division of the energy of light into definite 

 units, we may quote the very interesting experiments made 



