in Gases by the Motion of Negatively Charged Ions. 637 



ions, one positive and one negative. Let us consider the 

 effect of increasing the pressure and force in the same pro- 

 portion on the value of «, which we shall consider to be an 

 unknown function of p and X. When p is increased to zxp, 

 the total number of collisions per centimetre will be increased 

 in the ratio s, and all the free paths will be diminished in the 

 same ratio ; a force rxX acting along these shortened paths 

 will have the same effect as the force X acting on the longer 

 free paths. Hence the types of collision will not be altered, 

 and the only effect of increasing p and X will be to increase 

 the number of collisions per centimetre of any specified type 

 by the factor z. In particular, those types of impact which 

 produce new ions will be increased by the factor z. 



The connexion between the three variables «, p, and X 

 must therefore be such that when p and X are altered in the 

 same proportion, a similar alteration takes place in a. In 

 general, let a = <j>(X,p) ; therefore 



za. = $ (~X, zp) and z<f>(X, p) = <jy(zX, zp). 

 X 



Hence $ is of the form pf( — \ and 



r/(f) « 



This equation does not involve any assumption as to the 

 velocities of the ions before or after impact. If we take 

 the values of a for a fixed pressure and plot a curve having 



as coordinates — and -, its equation would be y=f(x), the 



same for all pressures. In fig. 1 we have marked the positions 

 of the points determining the curves for the various pressures 

 for the smaller values of the variables. The curves in fig. 2 

 are on a different scale and correspond to the larger values of 



X a 



— and -- Each point is numbered to indicate the experi- 

 ment in the tables from which the value of a was determined ; 

 the points bearing the same number belong to observations at 

 the same pressure. It is obvious that the curve through one 

 set of points goes through some of the other sets. It was 

 impossible to ^et points belonging to one set to cover the 

 whole range of the curves, as a discharge takes place in some 

 cases for rather small values of X. The curves overlap 

 sufficiently to justify us in regarding this coincidence as a 

 confirmation of the collision-theory. 



The point of contact of the tangent from the origin deter- 



