252 Prof. J. H. Jeans on Temperature-Radiation 



some numerical multiple of it {cf. §5 and § 29. infra). The 

 constant c is, on inspection of the formula, found to be of 

 the same physical dimensions as E 2 /K, where E is an electric 

 charge and K an inductive capacity. The only quantity of 

 these physical dimensions which can be constructed out of 

 quantities common to all matter is e 2 /K G , where e is the 

 charge of the electron, and K is the inductive capacity of 

 free aether. Thus we conclude that the c of Planck's formula 

 must be some numerical multiplier of g 3 /K *. 



28. Although the "steady state" is the same for all kinds 

 of matter which actually exist, yet it depends on the quantity 

 £, and so would be different for substances having different 

 values of <?, if such could exist f. 



Imagine for the moment matter for which e is very small — 

 matter for which we can say that 6 = 0. For such matter 

 the partition of energy in the aether in the steady state 

 is obtained by putting c = in Planck's formula. It is 

 therefore given by 



/(X, T) = 8tt^TX- 4 (35) 



This same formula of course gives also the partition of 

 energy for actual matter for large values of X. 



Planck's value of /(X, T) differs from this in that it falls 

 off in value as we come to small values of X. Let us examine 

 the physical significance of this. 



29. Planck's formula differs from formula (35) as soon as 



e 2 

 T , nflH becomes appreciable — i. c. as soon as X is so small 

 1\ R1X ri _ e2 



as to be comparable with ., Rr p . A physical interpretation 



of this last expression is readily found. 



The motion of two electrons, or the motion of an electron 

 and an atom (or molecule) can be regarded as the super- 

 position of two motions. There is first the motion of the 

 centre of gravity of the two bodies (which is unaffected by 

 a collision or encounter between them), and second, there is 

 the motion of the two bodies relative to their centre of 



* It can "be shown, from a consideration of physical dimensions (see 

 Proc. Roy. Soc. lxxvi. p. 545), that, subject to a certain assumption, the 

 *'• steady state " formula must be of the type 



/(*,T) 



K \ 5 * VK UTa/ ' 



Planck's formula determines the form of the function ©. 

 t See Phil. Mag. [6] xii. p. 57. 



