520 Dr. F. W. Aston and Mr. R. H. Fowler on 



§ 7. The resolving power. 



Equation (2) enables us to discuss accurately the resolving 

 power of the apparatus, but we begin with some preliminary 

 considerations. In fig. 1 we denote ZO and OF by b and a 

 respectively, and the centre of the slit system by S, where 

 SZ = c. We consider the spread of an otherwise homo- 

 geneous beam of rays which pass through the slits at slightly 

 different angles distributed over a range ha.. This spread 

 arises of course from the width w of the slits and we have 



8* = 2w/T, (5) 



where T is the distance between them. The beam may be 

 taken as diverging from 8. We are not here concerned 

 with the focussing for different velocities, which may be 

 assumed perfect. 



The total path of the rays is of length SZ -{- ZO + OF or 

 a + b + c very nearly, and therefore the linear spread of the 

 beam at F is (a-\-b-rc)8a at right angles to OF. This can 

 be converted when desired into an expression for the width 

 of the image on the plate. At the moment we regard it as 

 equivalent to a spread in <f> equal to (a + b4-c)hct/a. 



Now the instrument will resolve beams of different masses 

 if the change in </> for change of mass is greater than the 

 geometrical spread, and the greater </> for a given mass and 

 given spread the greater the resolving power. Thus we 

 may take 



(pa 

 (a-r b + c)Sa 



as a rough measure of the resolving power of the instrument. 

 Now the relation between a and b is (loc. cit.) 



&/a=(<jf>-20)/20, 



and we find on eliminating the variable a that the resolving 

 power is measured by 



* 



H£+i(4-»)} 



<«) 



It is our object to make (6) as large as possible. To do this 

 we can keep Sa and c/b as small as possible, but there are 

 strict limits to what can be done in this direction. The only 

 other method is to increase <£ without increasing the denomi- 

 nator, which can only be done by making <£ and 6 both 



