( 401 ) 



Physics. — '^On the radiation of heat in a system of bodies having 

 a uniform temperature" . By Prof. H. A. Lorentz. 



(Communicated in Uie meetings of September and October 1905). 



§ 1. A system of bodies surrounded by a perfectly black enclosure 

 which is kept at a definite temperature, or by perfectly reflecting 

 walls, will, in a longer or a shorter time, attain a state of equi- 

 librium, in which each body loses as much heat by radiation as 

 it gains by absorption, the intervening transparent media being the 

 seat of an energy of radiation, whose amount per unit of volume 

 is wholly determinate for every wave-length. The object of the 

 following considerations is to examine somewhat more closely this 

 state of things and to assign to each element of volume its part in 

 the emission and the absorption. Of course, the most satisfactory 

 way of doing this would be to develop a complete theory of the 

 motions of electrons to which the phenomena may in all probability 

 be ascribed. Unfortunately howe\'er, it seems very difficult to go as 

 far as that. I have therefore thought it advisable to take another 

 course, based on the conception of certain periodic electromotive 

 forces acting in the elements of volume of ponderable bodies and 

 producing the radiation that is emitted by these elements. If, without 

 speaking of electrons, or even of molecules, we suppose such forces 

 to exist in a matter continuously distributed in space, and if we 

 suppose the emissivity of a black body to be known as a function 

 of the temperature and the wave-length, we shall be able to calculate 

 the intensity that must be assigned to the electromotive forces in 

 question. The result will be a knowledge, not of the real mechanism 

 of radiation, but of an imaginary one by which the same effects 

 could be produced. 



§ 2. For the sake of generality we shall consider a system of 

 aeolotropic bodies. As to the notations used in our equations and 

 the units in which the eleclromagnclic (luantilics are expressed, 

 these will be the same that I have used in my articles in the 

 Mathematical Encycloj>edia. We may therefore start from the following 

 general relations between the electric force ^, the current ^, the 

 magnetic force S^ and tiie magnetic induction 03 



rotS^ = ~^, (1) 



c 



1 . 

 rot^ = 5S (2) 







