﻿920 Mr. E. Buckingham on the 



electrons in the atom. If it is regarded as holding, then 

 n = l almost exactly, but a is very much larger than seems 

 probable, a is also too large for helium, for which n = 2. 



The numbers obtained from absorption are applied to scat- 

 tering and give results in all cases in very good agreement 

 with experimental measurements. 



My thanks are due to Professor Rutherford for the interest 

 he has taken in this paper and for the advice with which he 

 has helped me. 



XCI. On the Deduction of W ten's Displacement Law. 



By E. Buckingham *. 



1. A LTHO UGrH Wien's displacement law T may be regarded 



jl\- as quite w T ell established by experiment, its great 

 importance seems to justify attempts to improve or simplify 

 the reasoning by which it may be deduced a priori as a 

 consequence of the general principles of thermodynamics 

 and the electromagnetic theory of radiation. Any such 

 deduction must, in substance, contain the following four 

 elements : — 



(a) The treatment, by Doppler's principle, of the change of 



wave-length produced when diffuse radiation is com- 

 pressed or expanded within a perfectly reflecting 

 shell, i. e. adiabatically. 



(b) The evaluation, by means of the principle of the 



conservation of energy, of the change of the volume 

 density of the radiant energy which occurs during 

 the adiabatic change of volume and accompanies the 

 change of 'wave-length. This step involves the use 

 of the value of the pressure of diffuse radiation on a 

 bounding surface, deduced from the electromagnetic 

 theory and confirmed by experiment. 



(c) The demonstration, by means of the second law of 



thermodynamics, that black radiation remains black 

 when its density and temperature are changed by 

 adiabatic change of volume. 



(d) The use of the Stefan-Boltzmann law to correlate the 



results obtained by the steps (a), (6), and (c), so that 

 the displacement law shall appear as a necessary 

 consequence of those results. 



These parts of the deduction need not be kept entirely 

 separate, nor do they necessarily occur in the order given 



* Communicated by the Author. 



