[ 514 ] 



LIX. Some Problems of the Mass-Spectrograpli. 

 By F. W. Aston, I).Sc.,F.R.S., and R. H. Fowler, M.A.* 



§ 1. Introduction. 



IN the account of the principle of the Mass-spectrograph 

 which appeared in this journal t, and in subsequent 

 papers describing the constructional details and the results 

 obtained by its means J, attention was called to certain 

 points, e.g. the linearity of the mass-scale and the possibility 

 of improved focussing, which at that time had not been fully 

 investigated. The following paper contains a mathematical 

 analysis of these points and suggests the directions in which 

 development is most likely to take place. It also supplies 

 an answer to a criticism recently expressed as to the efficacy 

 of the apparatus for the analysis of positive rays. 



§ 2. The distribution of the mass-spectrum over 

 the photographic plate. 



An inspection of actual photographs shows that the various 

 lines of the mass-spectrum are distributed along the plate 

 in such a way that the distance of any image from the 

 fiducial spot is very nearly a linear function of the mass m. 

 It was suggested § that the unexpected linearity might be 

 due to some special feature in the geometry of the apparatus. 

 We have now worked out the distribution exactly, and can 

 account for the linear mass-scale. We can also show that 

 the actual observed positions of the lines agree closely over 

 the whole scale with the positions calculated on simple 

 assumptions. This is satisfactory in that it shows that 

 the paths are not seriously distorted by stray fields. 



In fig. 1, let be the centre of the magnetic field, assumed 

 uniform and circular, of radius d. Let Z be the virtual 

 focus from which the rays diverge after passing the electric 

 field, and F their focus on the plate which lies along ZF. 

 Let R be the radius of the circular path (centre C) of rays 

 of mass m in the magnetic field, and let p be the length of 

 ON, the perpendicular from on ZF. The angle <f> is the 



angle at C and FZO = 2#. The angles 6 and (f> are the 

 angles through which the rays are bent by the electric and 



* Communicated by the Authors. 



t Phil. Mag. ser. 6, vol. xxxviii. p. 707 (1919). 



% Ibid. vol. xxxix. pp. 449, 611 ; vol. xl. p. 628 j vol. xlii. pp. 140, 436. 



§ Ibid. vol. xxxix. p. 454. 



