2 __ 



5 



242 Dr. 0. W. Richardson on the Rate of 



in which, as before, e has the values -p * and - p ,V 



corresponding respectively to the pressures at which 



a = 4:7reRi and a = 47r<?R 2 . 



Note. — The idea of adjusting the pressure so as to 

 render the equation of conduction of electricity between 

 parallel plates more manageable occurred independently to 

 Mr. G. W. Walker and myself. It was used by Mr. Walker 

 to complete the integration in the case when R 1 =R 2 - It was 

 shown by him (Phil. Mag. Nov. 1904) that this may be done 



if -r^-rr — 2, i, 1-, i, and he selected 2 as the simplest. 



I pointed out to him in a letter that according to Langevin's 



theory, e= -x — r, must be a fraction, and that therefore the 

 J bireil 



value 2 was physically impossible. 



He replies that he had not observed the limitation im- 

 posed by Langevin's theory, and suggests that I should lay 



emphasis on the point that while the value - — ^ =2 is 



possible if a. be constant and R vary inversely as the pres- 

 sure according to McClung's and Rutherford's results, yet 



according to Langevin - — - can never be greater than 

 unity. 



There is thus a serious difference to be explained. 



XXX. The Rate of Recombination of Ions in Gases. 

 By 0. W. Richardson *. 



11HE following is an attempt to explain the variation of 

 the rate of recombination of ions formed in gases with 

 the pressure of the gas. The basis of the method is a theorem 

 due to Langevin f, which may be stated as follows : — If we 

 describe around each negative ion a sphere whose radius is 

 arbitrary, except that it must be large compared with the 

 mean free path of an ion and small compared with the 

 average distance between two ions — both of which couditions 

 are capable of being satisfied in the case of ionization pro- 

 duced by Rontgen rays and radium radiation, in gases at 

 moderate pressures — then the number of positive ions which 



* Communicated by the Author. 



t Theses de PUniversiti de Paris, A. 431, p. 103 (Gauthier Villars). 



