of Energy in the Spectra of Solids. 429 



(2) Proportional to a function of the energy of these 

 same atoms. In consequence of the relationship (4) and 



of the high value of - for all the radiations which we shall 



have to consider, this function may be reduced to a power 



*i 



(3) Finally, in the direct ratio of an unknown function of 

 the absolute temperature of the body. This function consti- 

 tutes a factor which ought to represent the mean reinforcement 

 or weakening produced in each primary wave by the whole of 

 the resultant vibrations* and by absorption in the radiating 

 body itself. We will denote this function hj f(0). 



Thus, then, denoting positive constants by A and p, we put 

 the intensity of the simple astherial undulation of the period t, 



lr=Av T Q,Jf(6) (7) 



Considering, as usual, the absolute temperature 6 as pro- 

 portional to the mean vis viva of an atom, we may replace the 



M, 

 constant k in formula (6) by -^- where M is independent of 6. 



Let us then introduce this expression (6) in equation (7). 

 Then putting, for the sake of brevity, 



a 256N . 



A-^ p 3 (Mm)? = B, 16 P mm=c: ... (8) 



we have \ r = m ^f(e)e~^r-^+^dr. . . . (9) 



Replacing here the variable r by the variable \=Vt, where 

 A, is the length of the aethereal wave, and V the velocity of 

 propagation of light. Thus denoting constant coefficients suit- 

 ably modified by B and c, we shall have 



I k dX, = Be~ § f{0)e~£*\-Vp + Vdk (10) 



This formula gives the intensity of a simple radiation of 

 wave-length X as a function of this length and of the absolute 

 temperature of the source. 



* According to the analysis of Helmholtz, resultant waves must be 

 produced in all cases where the square of the elongation is not to be 

 neglected. They explain, according to this author, the phenomena of 

 sound of Sorges and Tartini (combination tones). In the case which we 

 are considering they ought to form especially upon the surface of the 

 radiating body, the forces which retain the atoms in their positions of 

 equilibrium not being symmetrical in all directions. 



