( 410 ) 



l"'iS=la'|S', 



_ -^A'P' = d'hP, (28) 



a theorem similar to the former. 



§ 8. The absorption of rays being measured by the amount of 

 heat developed, the expression (24), in which (£ is the real current, 

 will be often used in what follows. It may be replaced by 



ic = {S . ^), 

 if we write % for the vector [a] (5, so that 



%, = «„ a^ + a,, dy + «13 e., etc (29) 



Now, by a well known theorem, the axes of coordinates may 

 always be chosen in such a way that the coefficients «j,, «jj, «ji in 

 these equations become zero. Denoting the remaining coefTicients by 

 «J, «J, «3, we have for the relation between g and 6 



S':i- = «1 ^a» % = «2 d?/^ 5- = «, dzy 



and for the development of heat 



w = a, d,' + a, (Ï/ 4- «3 dJ (30) 



The directions we must give to the axes in order to obtain these 

 simplifications, may properly be called the pnncipaJ directions; in 

 general, they will not be the same for different frequencies. This is 

 due to the fact that the coefficients in (29) depend on the value of ??. 



It is also to be noticed that by this choice of the axes of coor- 

 dinates, the coetTicients ^^^, ^J,,, |?3,, and />,._;, p.^^, p^^ will not, in 

 general, be made to become zero. 



In the case of an isotropic body we may take as principal direc- 

 tions any three directions perpendicular to each other. 



§ 9. Thus far we ha\e only j)repared ourselves for our main 

 problem. In the next paragraphs we shall first consider the absorption 

 by a very thin plate surrounded by aether on both sides, and receiving 

 in the normal direction a beam of rays. Combining the result with 

 the ratio between the emissivity and the coefficient of absorption of 

 a body, we shall be able to determine the amount of energy, radiated 

 by the plate in a normal direction, and our next object will be to 

 calculate the intensity we must ascribe to electromotive forces acting 

 in the plate (^ 1), in oriler to account for that radiation. This will 

 lead us to a general hypothesis concerning the electromotive forces 

 acting in the elements of volume of a ponderable body and we shall 

 conclude by showing that, if these electromotive forces were applied, 

 the condition required for the equilibrium of radiation would ahvays 

 be fulfilled. 



