( (^77 ) 



different kinds of electrons. The final result is therefore ^) 



^^ (^i"^ ^^1 ^ "x + V ^^'. ^. ''.+ •••) A to coVZ... . (24) 



§ 10. If now we divide (24) by (5), all quantities N', e, u and /, 



by which one metal differs from another, disappear. This is what 



might be expected according to Kirchhoff's law and the result 



an'T 



CO (In 



may be taken to express the emission by a perfectly I)lack l)ody 



under the circumstances we have supposed. It represents the amount 



of energy which, in the case of such a body, is transmitted per unit 



of time across an element to', in the rays whose frequency lies 



between n and ii ~\- (hi and ^vhose directions deviate infinitely little 



from the normal to the element, being contained within a solid angle 



to 4:7r^ 



— . Multiplving bv ;, we are led to the following expression for 



r^ * " ftoco 



the density of energy of which I have spoken in § 2 : 



2an'T 



dn (25) 



Taking for the group of rays those whose wave-lengths are included 



bet^veen X and k -\- dX, we get for the corresponding energy per 



unit volume 



16 staT 



dX (26) 



3 A* ^ ^ 



1) It is easy to Tree ourselves from the hypothesis that for all electrons of one 

 kind there is a single length of path / and a single molecular velocity u. Indeed, 

 the motion of an electron along one of the small straight lines /, which it describes 

 between the instants and 5, will furnish for the sum in (15) a quantity 



e cos nt . Hj: t, 



if u is the velocity for the particular line / we wish to consider, and t the time 

 required for the motion along it. 



Now, among all these rectilinear motions between two successive encounters, of 

 one kind of electrons, we may select those for which u and I have certain definite 

 values and we may begin by calculating the coelïicient dm and the emission, in so 

 far as they depend on the part of (15) which corresponds to these particular motions; 

 in doing so, we may use the method shown in §§ 7 — 0. The total emission 

 may be regarded as the sum of all the partial values (with different Vs and dif- 

 ferent u's) thus obtained, and a'ter all the expression (24) will still hold, provided 

 we understand by Z^, /o . . . certain mean lengths o ' path and by u^^ u.i , . . certain 

 mean molecular velocities. We need not however enter into these details, because 

 the conductivity and the coefficient of absorption liavc not been calculated with 

 a corresponding degree of accuracy. 



46- 



