2d 



566 Sir E. Rutherford and Mr. H. Robinson on Mass and 



radius of the tube (1/5 mm.). Now if we take as standard 

 deflexion that which would be experienced by a ray which 

 had just lost D cm. of its range in the tube, it is easy to calcu- 

 late the relative deflexion experienced by a ray issuing from 

 a point such as B. If R is the initial range in air of the 

 a ray, the ranges of the two sets of rays after emergence are 

 R— D and R— D sec (# + <£) respectively, and the ratio of 



their velocities consequently < -^ — ft -7^ rr > j as- 



^ J { R — D sec (0 + 4>) j 



suniing for simplicity Geiger's relation* between range and 



velocity. Now in the case of the electrostatic deviation, 



the deflexion is inversely proportional to the square of the 



velocity of the rays. Hence, if 2d Y is the double deflexion 



(with field reversed) obtained with a line source of a rays of 



range (R— D), the double deflexion 2d corresponding to 



points in the a-ray tube at angles ±0 with OSP will be 



where a is the radius of the a-ray tube, and consequently 

 ±a sin 9 the displacement from the central axis of the points 

 under consideration. l x and l 2 are the distances OS and SP 

 respectively. As a first approximation <f>, which is in any 

 case very small, may be regarded as a constant, and equal to 

 the mean value of the initial slope of the paths of the rays 

 which pass through the slit. The value of the above expres- 

 sion then depends only on #, and on examination is found to 

 reach a minimum for a certain value of #, which under the 

 conditions of our experiments was quite small — in typical 

 cases, 6 was about 11°. In this connexion, it is worthy of 

 note that the value of 6 making the deflexion a minimum is 



R — T) 

 almost directly proportional to — rr — . There is, therefore, 



within limits, a considerable advantage to be derived from 

 having this quantity as small as possible, i. e. by the use of a 

 fairly thick a-ray tube. 



The importance of this sort of " lens action ? of the a-ray 

 tube in concentrating a large proportion of its radiation 

 about a definite line of minimum deviation lies in the result 

 that the inside edges of the deflected beams are exceedingly 

 sharply defined, as will be readily seen from the photographs, 

 while the outer portions of the bands, which are produced by 

 rays of all velocities down to the smallest which can affect 

 the plate, " tail off " in a general blur, as would be expected. 

 This effect is more obvious in the actual photographs than 

 in the reproductions, which are made by printing lantern 

 * Geiger, Proc. Roy. Soc, A. lxxxiii. p. 505 (1910). 



