﻿Simplified Deduction of Planck's Formula. 297 



series spectrum of hydrogen consists only of lines which are 

 represented by the formula 



f=1097( 



\n x ~ n 2 z J 



and that the series spectrum of helium in addition to the 

 ordinary helium lines consists of all the lines which are 

 represented by the formula 



v=109750f T \- 2 ---\ > ). 



m em 



The author wishes to thank Sir Ernest Rutherford for 

 bringing the subject of the present investigation to his 

 notice and for valuable suo-oestions and encouragement 

 during the course of the research. 



The University of Manchester, 

 Dec. 1914. 



w 



XXXIII. Simplified Deduction of the Formula from the Theory 

 of Combinations ivJdch Planck uses as the Basis of his 

 Radiation Theory. By P. Ehrenfest and H. Kamerlingh 

 Oknes * . 



E refer to the expression 



(N _1 + F )i 

 p ~ P!(N-1)! ' v J 



which gives the number of ways in which N monochromatic 

 resonators R 1? R 2 , . . . Rn may be distributed over the various 

 degrees of energy, determined by the series of multiples 

 0, €, 2e . . . of the unit energy e, when the resonators to- 

 gether must each time contain the given multiple Pe. Two 

 methods of distribution will be called identical, and only 

 then, when the first resonator in the one distribution is at 

 the same grade of energy as the same resonator in the 

 second, and similarly the second, third, .... and the Nth 

 resonator are each at the same energy-grades in the two 

 distributions. 



Taking a special example, we shall introduce a symbol for 

 the distribution. Let N = 4, and P=7. One of the possible 

 distributions is the following : resonator Ri has reached the 



* Communicated bv the Authors. 



