,'1 + Ic 



vhere I- 



2SG Mr. C. D. Child on Ionization in the 



of collisions between electrons and molecules is much greater 

 than that between electrons and positive ions. As a result 



jj-r will be sufficiently small, so that the higher powers of 



this fraction may be neglected. When this is true, 



log ( 1 + -. jj- J is approximately equal to yy-^ , and equation (G) 



may be written 



x=^{io g (i^)--}, 



k is also very small as will be shown below, so that 

 l°g(— tt~) i s l ar S e compared with ~^, and we may write 

 this equation as follows, 



. H( ^'> . . . 



If k is a constant, this is a linear equation between X and 

 £, and also between X and p, where %> is the pressure, if the 

 temperature is constant, since the pressure is then propor- 

 tional to the density. This is of the form X = A/?-{-B. On 

 the other hand, if k is not a constant, this is not the equation 

 of a straight line. Measurements have been made of X and 

 p by Herz *, Graham t, Wiedemann and Schmidt J, Heuse§, 

 H. A. Wilson ||, and Matthies IF, and the data in each case 

 when plotted give a curve of the form X = Ap + B. We 

 are therefore justified in assuming that k is a constant. 



When we consider the relation between the electric force 

 and the current, we find that the data do not agree with the 

 equation, if we consider Y 1 to be a constant. In the equation, 

 X increases when m increases, and m increases when the 

 current increases. The increase to be expected is indeed 

 small, but in reality there is a slight decrease when the 

 current increases. There is but little doubt that this lack 

 of agreement is due to the fact that Y x is not constant, but 

 decreases slightly as the current increases. Since c varies as 

 V 1? the expression for X decreases when V x decreases. 



* Wied. Ann. liv. p. 263 (1895). 

 7 Wied. Ann. lxiv. p. 58 (1898). 

 t Wied. Ann. lxvi. p. 320 (1898). 

 § Ann. d. Phys. v. p. 681 (1901). 

 || Phil. Mag. [5] xlix. p. 505 (1900). 

 H Ann. d. Phys. xviii. p. 473 (1905). 



