rapidly moving Electrified Particles. 467 



to NqC is supposed to be uniformly distributed through the sphere 

 of radius h, then it is easy to prove that when ^j is small it is 

 given by the equation 



, e'' N.ir 

 ^ mv 4 



When the positive electricity is made up of definite units 6^ 

 the mean deflection due to these is given by the equation 



16 e^ 1 /2>N. 



where o- is the ratio of the volume occupied by the positive 

 electricity to the volume of the atom. 



The mean deflection Q due to both negative and positive 

 particles will be 



{e,^-^<^^f- or (^,^ + <^M 



according as we take the first or second hypothesis. 



The average deflection when passing through a thin plate 

 whose thickness is t is 's/Nirh^t . 6, and substituting the values 

 of 6, we find for this quantity 



e' 

 or — - 



mv 





"384 

 25 



Vi\^7r^ 



1^ (A) 



according as we suppose the positive electricity to be uniformly 

 distributed through the atom or done up into separate units. 



As these expressions contain no unknown factors beyond No, 

 the number of corpuscles in an atom, they indicate that ex- 

 periments on the scattering of light by very thin plates afford 

 a simple method of determining the number of corpuscles in the 

 atom. In making these experiments it is necessary to remember 

 that we have supposed the deflection small so that the length 

 of path was equal to the thickness of the plate, and secondly we 

 have supposed that the velocity remained unchanged ; as the 

 deflection varies rapidly with the velocity this condition is im- 

 portant, and it is the more so because the expressions for the 

 change in the velocity of the corpuscle produced by collision with 

 an atom are (see Discharge of Electricity tlwough Gases, 2nd 

 Edition, p. 378) much more complicated than those for the de- 

 flection, they involve other quantities besides the number of 

 corpuscles in the atom and thus are not suitable for measuring 

 that quantity. I am not aware of any experiments made quite 



