Theory of the p Striated Discharge. 983 



hardly defensible, and wholly so if the collisions between the 

 ions and the molecules are elastic, when the ion retains after 

 collision any energy it may have acquired before. 



I shall suppose that the energy co possessed by an electron 

 at as is represented by the relation 



= p e-^-^X d£, 



Jl, 



where X^ is the electric force at f, f { the value of % at the 

 place where the electron was generated. This equation 

 expresses the condition that if the electron acquires an 

 amount of energy Sco at any place, the chance of its retaining 

 this energy after passing through a distance x is e~ Ax . 



We must proceed to find the probability of an electron 

 i ravelling a distance x without being absorbed. The ab- 

 sorption of the electron arises in two ways : — (1) By the 

 adherence of the electron to a molecule of the gas through 

 which it is passing ; this gives rise to a negatively charged 

 molecule. The magnitude of this absorption is proportional 

 to the density of the gas through which the electrons are 

 passing. (2) By the combination of an electron and a 

 positively-charged molecule, resulting in the formation of 

 a neutral molecule. The magnitude of this absorption is 

 proportional top the density of the positive electrons. Thus, 

 if a stream of electrons is travelling through the gas, and if 

 I be the number which pass through unit area in unit time, 



where p is the density of the gas and a and ft are constants ; 

 thus, if I is the intensity of the stream at #=0, I the 

 intensity at x will be given by 



I = I e Jo 



(ap + j3p)dx 



Hence, if q% be the number of ions produced per unit time 

 per unit volume at a place where the x co-ordinate is equal 

 to f, the ionization in the region d£ will cause 



e J£ qt:d% 



electrons to pass in unit time through unit area at a.\ Hence 



(*x -\ X (ap+Pp)d.r 

 .0 



