Discontinuity in the Phenomena of Radiation lb 



though what it is forms a matter rather of speculation than of 

 sure knowledge at present. But I will come to that in a moment. 

 To proceed. With this set of symbols, two of them absolute 

 universal constants, two of them standing for measures of definite 

 physical properties, let us calculate the number : 



3hnl2aT 

 where h stands for Planck's constant. 



Call this calculated number r. This number r has, of course, 

 a definite value for each point P on the frequency axis, so long as 

 we are considering a definite pair of curves corresponding to a 

 definite temperature. 



Now, Planck has pointed out that the ratio AP to CP is 

 equal to the sum of the series 



1 + r/2 + 7--/6 + 7-V24 + 7'-Vl 20 + etc. ad iniin. 

 That is not the most elegant way of putting this ratio. 

 Those of you who have some knowledge of mathematical functions 

 will recognize this series as 



(e'--l)/r 

 Where e is Naperian base of logarithms. 



Of course the ratio varies as we pass along the corve, for r 

 is a different number at different parts of the curve. 



This is a new principle of partition. It has been discovered 

 that its a]:iplicability is not confined to partition of energy in the 

 ether alone. Indeed it is its application to the distribution of 

 heat energy among the types of vibration of solid bodies that has 

 constituted one of its triumphs, and first brought it seriously 

 into consideration. 



To slate it once more — when apportioning vibrational energy 

 among the degrees of freedom of any substance, ethereal or 

 material, at a definite temperature, one first of all estimates the 

 amount to be assigned to each narrow frequency range by 

 the equipartition principle and then divides the result by the 

 expression. ^ 



(e''-l)/r 

 where r is the frequency temperature number calculated as above. 



