﻿On the Partition of Energy. 



823 



should be the same as that for electron impact. Results 

 of previous workers show wide disagreement in the value of 

 the minimum accelerating P.D. necessary for positive ions 

 to produce ionization. 



Two types of apparatus are described, the positive H-ions 

 being produced first by electron impact in hydrogen. The 

 peculiar difficulties of the experiment made it impossible to 

 test for ionization produced by positive ions accelerated 

 through less than 18 volts, and, as the ionizing current itself 

 depended upon three variable factors, it was more difficult 

 to obtain comparative observations. The results indicate 

 that positive H-ions produce ionization in hydrogen when 

 accelerated through P.D's. as low as 18 volts, and that they 

 are much less efficient in producing ionization than electrons 

 under similar conditions. 



In conclusion, I desire to thank Prof. Milner, F.R.S., who 

 proposed the problem, for his kindly interest and advice. 



Sheffield University, 

 July 31st, 1922/ 



LXXI. On the Partition of Energy. — Part II. Statistical 

 Principles and Thermodynamics. By C. G. Darwin, 

 F.R.S., Fellow and Lecturer of Christ's College, Cam- 



■ bridge, and R. H. Fowler, Fellow and Lecturer of 

 Trinity College, Cambridge *. 



§ 1. Introduction and Summary. 



IN a previous paper f we have -developed a method of 

 calculating the partition of energy in assemblies 

 containing simple types of quantized systems and free 

 molecules. In this method advantage is taken of the 

 multinomial theorem, which makes it possible to obtain 

 integrals expressing accurately the various average values 

 concerned in partition problems, and then the integrals 

 areeasilj- evaluated asymptotically. The " fluctuations " can 

 also be readily found, and from them it can be shown 

 that the possession of these mean values is a " normal " 

 property of the assembly in the sense used by Jeans J. 

 This method has the advantage of obtaining directly the 



* Communicated by the Authors, 

 t Phil. Mag. vol. xliv. p. 450 (1922). 



% Jeans, ' Dynami< al Theory of Gase?,' passim. Average and most 

 probable values are of course in practice the same. 



