﻿Dioxide and Hydrogen at Different Temperatures. 749 



a definite limiting velocity, then the ions in a gas at any 

 instant may be divided into two groups, in one of which only 

 can recombination take place. It* the temperature is altered, 

 the number of ions in one group is increased and in the 

 other is diminished. At a high temperature practically all 

 the ions would have velocities greater than the limiting 

 velocity and the coefficient of recombination, as well as its 

 change with temperature, would be small. At a low tempe- 

 rature practically all the ions would have a velocity less than 

 the limiting velocity, and the coefficient would be lar.o-e. 

 The values of a plotted against temperature would thus 

 give a compound curve of the same character as the experi- 

 mental curve. 



Langevin's theoretical expression for a, namely 



a = 4we(X- 1 + A' 2 ), 



is also suggestive. In this expression ki + k 2 is trie sum of 

 the mobilities and e is the ratio of the number of collisions 

 that result in recombination to the total number of collisions 

 between ions of opposite signs. The value of e depends upon 

 the lower of the two groups mentioned above. 



By integrating Maxwell's expression for the distribution 

 of molecular velocities between the limits zero and some 

 limiting velocity, and dividing this by the same integral 

 taken between the limits zero and infinity, we obtain the ratio 

 of the number of ions having velocities less than the limiting 

 velocity to the total number. If in the above integral the 

 most probable velocity corresponding to different tempe- 

 ratures be used, we get the values of this ratio at these 

 different temperatures. Substituting the square of the 

 ratios thus obtained for e in Langevin's expression, and con- 

 sidering the mobilities constant, we obtain a curve for the 

 variation of ex. with temperature that is similar to the experi- 

 mental curve at the higher temperatures, but is too steep 

 at the lower temperatures. Kovarik * has shown, however, 

 that at constant gas density the mobilities diminish at the 

 lower temperatures. This brings about a closer agreement. 



It gives me great pleasure to acknowledge my indebtedness 

 to Prof. Sir J. J. Thomson and Prof. John Zelenv in con- 

 nexion with this research. 



Physical Laboratory, 

 University of Minnesota. 

 Sept. 20, 1910. 



* Kovarik, Phys. Pev. vol. xxx. p. 415 (1910). 



