﻿Deduction of Wieris Displacement Law. 921 



above, which is that followed in this paper, but they must be 

 present in some form or other. In the deductions I have 

 read, the treatment of the change of wave-length seems 

 somewhat difficult or obscure, and I have attempted to 

 simplify this part of the subject and make it easier to grasp. 

 The remainder of the demonstration contains little that is at all 

 novel, but is given for the sake of presenting a connected 

 whole, comprehensible to those who are not already familiar 

 with the subject. The treatment is elementary and relates 

 only to radiation in vacuo. 



2. Let ds be an infinitesimal plane element of surface at a 

 point within a fieid of radiation. A certain amount of 

 radiant energy passes through ds from the negative to the 

 positive side, in unit time, in various directions. Let us 

 consider only those directions comprised within a cone of the 

 infinitesimal solid angle dw described about the positive 

 normal to ds. The amount of energy of wave-lengths between 

 \ and \-\-d\, which passes through ds from the negative to 

 the positive side in one second, in directions close enough to 

 the normal to lie within the cone, may be expressed by 



R\d\ . ds . div. 



The quantity R^^ mav De called the strength of the radiation, 

 and H x the " radiant vector" at the given point, in the given 

 direction of the positive normal to ds, and for the wave- 

 length A. If the value of R^ is given for all values of \, for 

 all directions, and at every point within a given region, the 

 radiation within that region is, for our purposes, completely 

 specified, since questions of phase and state of polarization 

 will not enter into our reasoning. 



By speaking of " the energy of wave-lengths belween \ 

 and \ + d\" we make a somewhat violent though familiar 

 assumption, namely, that no matter what may be the nature 

 of the pulses which constitute radiation, since our spectral 

 apparatus enables us to analyse radiation into series of wave- 

 trains of assignable period, the radiation before analysis may 

 be treated as the sum of these wave-trains coexisting inde- 

 pendently. However obvious the truth of this assumption 

 may appear from a purely mathematical standpoint, it is well 

 to recognize that physically it is to be justified by the 

 agreement with experiment of conclusions drawn from it. 

 It is, in fact, thus justified and we shall make a rather full use 

 of this principle. 



3. Let us consider a closed evacuated shell, the walls of 

 which reflect perfectly but at least somewhat irregularly. 



