Velocity of Swiftly Moving Electrified Particles. 599 



higher atomic weight, the assumptions used in the calcula- 

 tions are satisfied to a still smaller degree than for aluminium, 

 and accurate agreement with the measurements cannot be 

 obtained, although the theory offers an approximate expla- 

 nation of the way in which the stopping power of an element 

 and the shape of the velocity curve vary with increasing 

 atomic weight. 



In section 2 we considered the probability variation in the 

 ranges of the single particles of an initially homogeneous 

 beam of a rays. Denoting the mean value of the ranges by 

 R , we get from (12) and (13") for the probability that the 

 range R has a value between R 'l + s) and R (l + s-f-ds) 



W(«)«fr= K= e W ds, .... (21) 



where 



2u 2P t ,T /<rr\- :j rr 



(22) 



This expression is much simplified if we use an approxi- 

 mate formula for clT/d.v. Putting #=0T r , we get 



) \di) di -^-2 Li -;s;-2TA,/,7 ' 



Introducing this in (22) we get * 



l__3r-2 T dl 



p 2 ~ r- 2 V d.r 



(23) 



* Note added in proof. For r=|, this expression is equivalent to the 

 expression deduced by L. Flamm (loc. cit. formula (25)) for the variation 

 in the ranges of a particles due to collisions -with the electrons. This 

 author has considered also the collisions with the central nuclei and 

 concluded that, although the effect of these collisions on the mean value 

 of the rate of decrease of velocity of the a particles is very small com- 

 pared with that due to the collisions with the electrons, their effect on 

 the variation in the ranges is not negligible but will be given by an ex- 

 pression of the type (21) for a value of p of the same order of magnitude 

 as that given by (23). From considerations analogous with those applied 

 in section 2 in the case of /3 rays it appears, however, that the collisions 

 between the a particles and the nuclei will produce a variation in the 

 ranges of a type different from (21). In these collisions only very few of 

 the particles suffer a considerable diminution of their ranges, while the 

 greater part of the particles suffer diminutions which are very small 

 even compared with the average differences in the ranges produced by 

 the collisions with the electrons. It seems therefore that the effect of the 

 collisions with the nuclei may be neglected in a comparison with the 

 measurements. 



