466 Professor Thomson, Oii the Scattering of 



or whether it is supposed to be divided into equal units, each 

 occupying a finite volume probably much greater than the volume 

 occupied by a corpuscle. 



We shall calculate the deflections due to the negative and 

 positive charges separately. Let us take that due to the cor- 

 puscles first. We can show easily by the theory of forces varying 

 inversely as the square of the distance that when the moving 

 particle is travelling so rapidly that its deflection is small, this 

 deflection is equal to 



2f_ 1 

 mV^ x' 



when V is the velocity of the particle, e its charge, m its mass, 

 and X the perpendicular let fall from the corpuscle on the direction 

 of motion of the particle. Thus the mean value of the deflection 

 pi'oduced by the corpuscles which are within a distance a of the 

 line of motion of the particle, supposing the corpuscle uniformly 

 distributed is 



4e- 1 



mV- a 



Now if the length of the path of the particle in the atom is I, 

 the number of collisions between the particle and the corpuscles 

 within a distance a from its path is, when the corpuscles are 

 uniformly distributed, niraH, when n is the number of corpuscles 

 per unit volume of the atom ; hence by the theory of probability 

 the average value of the total deflection of the corpuscle when 

 passing through the atom is 



4e2 1 



mv^ a 



_ 4e2 



~ — n Nmrl, 

 mv- ' 



Now if b is the radius of the atom, the mean value of \/l is 

 I '\/2b. Hence 6-^ the mean deflection of the particle due to the 

 corpuscles in the atom is given by the equation 



01 = -^ -^ V?i7r6 

 5 mv^ ^ 



16_e^l /3N, 

 5 mv'^ 6 V 2 ' 



where Nq is the number of corpuscles in the atom. 



Let us now take the case of the positive electricity, let ^i be 

 the average deflection when the positive electricity amounting 



