44 Mr. S. B. McLaren on the 



for it denies the possibility of rigid bodies anywhere. I am 

 prepared, therefore, to accept Einstein's atomism for matter 

 but not for radiation. The hypothesis that radiation is a 

 continuous wave motion appears to me indispensable. It 

 penetrates and simplifies the complexity of observed fact so 

 profoundly that a rival version seems almost impossible. 



The methods of this paper are at once more simple and 

 more general than those given in Phil. Mag. July 1911 and 

 April 1912. I assume the ordinary undulatory theory of 

 light, but I do not assume the formulae of classical dynamics. 

 The laws of motion of matter are not deduced from the 

 principle of least action, they need not even be laws of 

 continuous motion at all. A mathematical theory of emission 

 and absorption complete radiation and refraction, in fact of 

 the whole process of interaction between radiation and material 

 systems, can be reached without these restrictions. But some 

 at least of the variables specifying the state of matter must 

 have a continuous range ; that is required by conservation 

 of energy and the continuous theory of radiation. 



§ 2. Statistical Theory. 



The material system is exposed to radiation in a space 

 bounded by walls which prevent its escape. For any wave- 

 length 27r^7i I suppose that there exists a differential 

 equation of the form 



1 d 2 



it . 2 +«k=i ei) 



(ra— 1, 2, ... go ) 



Here c is the velocity of light, and <j> m is defined by the 

 material state at the time t. The variables a„„ &c, fix the 

 state of the field of radiation. By increasing the space 

 enclosed a OT can be made simple harmonic for as many 

 periods as we please. 



« Hl =(a»i) COS (CK m t — CKmt^)+l — j^J (c/C m )~ l Sm (CK m t — CKmto). 



. . . . (2) 



(a B .)o and I : " l ) denote values at time t . (2) holds so 



long as t — 1 is sufficiently small. 



Where Lorentz's electromagnetic theory is assumed I 

 have shown (Phil. Mag. April 1912) how «,„ and cf> in are to 

 be determined. The variables defining the state of the 

 material system I denote by # l9 x 2 , &c, .v n . These have all 



