﻿356 Prof. E. Rutherford on the Mass and Velocity of 



It is interesting to note that this formula for the determi- 



nation of does not involve l { or l 2 , and only involves the 



distance d to a subordinate extent. For example, in one 

 experiment where Z 3 = 10 cms., the value of d was only 1/15 D. 

 This is a great advantage, as the distance d is difficult to 

 measure with accuracy. 



While the distance l± is not involved in the final formula, 

 it must be remembered that the formula (2) only applies 

 when the a particle is deflected through a distance greater 

 than d in passing between the plates. If l { is made smaller, 

 the value of V must be made correspondingly greater before 

 the formula can be applied. 



It has been mentioned that the width of two deflected 

 traces obtained by reversal of the electric field decreases in 

 width with increase in strength of the electric field. The 

 reason of this can readily be shown from theoretical con- 

 siderations. For example, it is seen that the inside edge of 

 the deflected pencil (fig. 3 b) is produced by the a particles 

 whose paths touch at grazing incidence the plate AB at A 

 and also touch the plate CI). These conditions determine 

 the direction of the a particle in entering the electric field 

 at A. All a. particles passing through A which make a 

 greater angle with the plate AB than the above a particle 

 are stopped by the plate CD. As the width of the trace is 

 not required in the experiment, it has not been thought 

 necessary to include here the connexion between the width 

 of the deflected pencil and the strength of the electric field. 

 The calculations, though a little long, are not difficult. 



It is now necessary to consider how we are able to know 

 from the photographs obtained whether the formula (1) or (2) 

 is to be applied. The formula (1) holds provided the distance 

 of deflexion of the « particle is not greater than d. Suppose 

 that the a. particle is deflected through a distance d in passing 

 between the charged plates. The outside edge of the photo- 

 graphic impression, for example, on the right of the plate P 

 (fig. 3) is due to the u particles which start from the point C 

 parallel to the plate CD. With the same notation as before, 



d=\l 1 \ 



Following the same method of calculation as for case (2),. 

 it is seen that the value of D is given by 



r D=4Xl 1 l z +d. 



