2 CATHODE RAYS LOSS OF ENERGY, ETC., 



R.S. TAS. 



matter, the velocity of tlie rays after traversing a distance 

 X is given by tlie relation 



vo* - ?;/ = ax (ii) 



and he has given the value of the constant a for the three 

 substances, aluminium, gold, and air. 



By a combination of this result with the result of my 

 experiments it is possible to determine the energy lost by 

 the cathode ?-ay foi- each ion made by it. 



The total number of ions made by a cathode ray in going 

 a distance x is given by 



X 



1 =. \ a dx (iii) 



• 



;Now a = -7,' and differentiating (ii) we get 



dx = dv 



a 



So that substituting in (iii) and inserting the proper limits 

 the relation becomes 



l=ri ^^'-dr -^l't'\^dv (iv) 



jV«av if E is thp energy of the ray we have 



dE 



IE = m,vdr or vdc 



in 



So that the relation (iv) becomes 



47. f^X 



/ = - — dE 



^ ^ E, 



= i^' {Eo - E^) 

 am 



Let us call the amount of energy lost by the ray for each 

 i©m produced Q. 



The. Q^^^S^^ (V) 



Since the expression for Q does not involve v we see that 

 the ray lomti ihe some anunirit of enerfjy per ion viade ivliat- 

 emr iU velocity may be. This result is one which might 

 almost have been assumed. In fact, Geiger in dealinij- with 

 tlie similar problem in the case of a rays has made such ai) 



