﻿Emission and Absorption of Radiation. 513 



"synchronized" with the clock at 0' (see §4), we have 

 (from figs. 2, 3, and 4) : 



t' = i(rt + rt 2 ) (3) 



Finally, from the way in which the abscissa of A' has been 

 determined (see § 5), we have (from figs. 2 and 3) : 



a}'=*c{t'—rt ) (4) 



From these four equations, the required values of x' and 

 t' in terms of x and t are at once obtainable. Thus, solving 

 (1) for t and (2) for t 2 , and substituting in (3), we have 



*-l-(t;/ C )*V"?*7 



anl then substituting this value, together with the value of 

 t , in (4), we have 



1 — (v/c)" v 

 These are the required transformation equations (§ 13), for 

 a point A' on the axis O'X'. For a point A' not on the axis, 

 a similar chain of reasoning will give 



r 



y,= v/i-o/o 2 ^ 



as required, while the values of x' and y' remain as before. 



Thas all the transformation equations used in Theorem 1 

 are obtained by this entirely natural and elementary method. 



XLVII. The Emission and Absorption of Radiation in any 

 Material System and Complete Radiation. By S. B. 

 McLaren, AI.A., Assistant Lecturer in Mathematics in 

 the University of Birmingham *. 



Page 



§ 1. Results and Introduction 513 



§ 2. The Definition of Radiation , 516 



§ 3. The Modified Lagran»-ian Function 520 



§ 4. Expansion in Normal Functions 523 



§ 5. The Perturbations due to Radiation ...... 524 



§ 6. The Absorption of Radiation 527 



§ 7. The Emission and Complete Radiation .... 531 

 § 8. Absorption and Refraction of a ' Simple 



Harmonic Wave-Train 533 



§ 9. Radiation and Mechanics 53(5 



Conclusion 542 



§1. Results and Introduction. 



C COMPLETE or "black-body" radiation is the result of 

 J an equipoise in the radiation absorbed and that emitted 

 by a material system. \\\ this paper it is first shown how 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 23. No. 136. April 1912. 2 M 



