Mr. R. Hargreaves on Wien's Law. 617 



The use of (1) with p = E/3v makes 



7^ ^dv ™ Ed\ 

 <?E + pdv=dE + -r— =6?E + -^- , 



or d'E + pdv d(E\) 10 /ei \ 

 -f— = \0= d ®> sa J 5 • • • (2) 



and if this is a true differential, then E\ and S are functions 

 of \0 or a, and a?= constant is the adiabatic relation. The 

 above is applicable to monochromatic radiation, or to 

 radiation within the range of an element d\. 



It is desirable to show the factor v explicitly in E, and for 

 that purpose we note that v/X z is constant or that vdX/X* is 

 constant ; i. <?., in presenting the part of energy attaching to 

 a range d\, we must count dX as susceptible of change in 

 the same proportion as X in connexion with change of 

 volume. Thus we are led to the forms 



™ vdX 6{oo) Q vdX N -j.1,^ !# cx\ 



For example, with Planck's law <f> = 1/(^—1), and then 



e c ' x 1 



ilog(^-l), 



T x(e° lx -l) c 



apart from a constant multiplier in each case. 



The above statement turns on two means expressed re- 

 spectively by _p=E/3r and A\/\ = Av/3i?, which are found 

 in very similar ways. The element of work is in fact 



£>Au=i t " — . w cos i dt . d$ cos i . sin i di 



Jsjo " 



Jsjo 



l[ 2w cos i Y dt cos idS^i • • ?• EAv 



■ vr — • o Esmidi=——-, . (4) 



V 2v dv v ' 



an exact counterpart of (1). Thus we have _pAu = EA\/\ 

 immediately without performing the integration ; and in 

 fact (2) is valid for radiation in two dimensions or in one. 

 It is essential to both arguments that energy-content should 

 in respect to all wave-lengths be uniform throughout the 

 volume. 



