Rate of Recombination of Ions in Oases. 



151 



between them, then the formulae given by Maxwell* enable us 

 to obtain the law of force between an ion and a molecule from the 

 variation, with the velocity of the ion, of the number of collisions 

 made by an ion in travelling through a centimetre of gas. These 

 formulae show that the number of deflections of path through an 

 angle 6 is unchanged, provided 



K(M 1 + M 2 )\ 



remains constant : where b is the smallest perpendicular distance 

 between the original straight paths of the particles whose masses 

 are M x and M 2 , V is their relative velocity, and K is the magnitude, 

 when the particles are unit distance apart, of the force, which 

 varies inversely as the nth power of the distance between them. 

 If we keep the law of force and the mass of the particles constant, 

 we find that the number of deflections through a given angle is 



2 



unaltered provided bV n ~ x remains constant. We see therefore 

 that the number of collisions per centimetre is proportional, 



4 



ceteris paribus, to V n ~ 1 ; so that if we determine the way in 

 which the number of collisions varies with the velocity we can at 

 once obtain the value of n, which determines the law of force. 

 The following numbers indicate the way in which the number of 

 collisions made in passing through a centimetre varies with the 

 velocity for different laws of force, on the hypothesis that the 

 particles can be regarded purely as centres of repulsive force, 

 whose magnitude varies as the — ?ith power of the distance 

 between them. 



In conclusion, I wish to acknowledge my indebtedness to 

 Professor J. J. Thomson for valuable suggestions. 



NOTE [added April 20, 1903]. 



In the application of the formulae deduced in the preceding 

 paper to the calculation of the coefficient of recombination of ions 



* Scientific Papers, n. 36. 



