p= 



588 Dr. N. Bohr on the Decrease of 



Now similarly denoting the probability that AT has a 

 value between AT and AT + dT by W(T)dT, we get by help 

 of a fundamental theorem in the theory of probability, 



(aT-a T) 2 

 W(AT)dT=(27rPA#)-ie~ 2P ** d? 9 . . (8) 

 where PA.= S^- (Q r A,) 2 = S A r QA 



On the above assumptions this can simply be written 



PA^=JQ^A. 



Introducing in this expression the values for Q and dA 

 given by (1) and (3), and integrating for every kind of 

 electron fromp = to p=p v we get 



47re 4 E 4 N^/l 1 \ 



Assuming, as in the former section, that p v is large compared 

 with a, we get, neglecting the last term under the X and 

 introducing in the first the value of a from (2), 



r- (M + m) 2 - N " W 



It will be noticed that this expression is very simple. It 

 depends only on the total number of electrons in unit volume, 

 but neither on the velocity of the sc or j3 particle nor on the 

 interatomic forces. 



From (8) and (9) we can simply deduce the probability 

 distribution of the thickness of the layers of matter through 

 which particles of given initial velocity will penetrate before 

 they have lose all their energy. Putting AT = A T(1 + s), 

 we get for the probability that s has a value between s and 

 (s + ds), 



W(s)ds=A/£-e-i™ 2 ds, .... (10) 

 where (A T) 2 <j> . 



m -"pa^t = p oi ' • • • • i 11 ) 



AT 

 <f> being the mean value of - A — . 



^ ° Aa? 



If we now suppose that the straggling of the rays is small 

 — this assumption is already indirectly involved in the 

 assumptions used in the deduction of (8) — the formula (10) 



