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



and retaining only the lowest powers of <£, 



[V +L(1 -#4fl„)}' 



p- ■ L „ 



W{y+L(i-<ft/4fl } 3 



L(S'+*L) 



We observe that this radius of curvature can be kept 

 reasonably large by making b' fairly large compared with L. 

 For example, if // = 2L, <f> = 4:d , the radius required is^ 4 # 2 L. 

 Even when O = ^ as in the present apparatus, this is ^L, 

 and if =^ it is JfL, which is by no means unmanageably 

 small. It is therefore possible that the focussing can be 

 improved by this means, although it is not so likely to be 

 possible to improve the position of the plate. The reason 

 why this improvement is possible without the use of an 

 unreasonably small radius of curvature on the trailing edge 

 of the field is that, by making V large, we can scatter the 

 rays of different velocity well before they impinge on the 

 leading edge of the field. Thus the necessary difference of 

 path length can be achieved on paths which are not too 

 close together — that is, by a trailing edge of reasonable 

 curvature. 



In actual practice the curvature would be applied to the 

 leading edge, since this arrangement possesses all the advan- 

 tages, from a structural point of view. In the region of 

 <£ = 4# , where the paths are symmetrical about the magnetic 

 field, it is theoretically immaterial to which edge the curva- 

 ture is applied. 



§ 10. Considerations of tlie dimensions of the apparatus. 



In designing physical instruments of precision, it is of 

 importance to study the absolute scale of dimensions likely 

 to yield the best, results. Now, pressures being equal, the 

 shorter the path of the beam of positive rays between the 

 cathode and the photographic plate the less likely it is to 

 lose intensity and sharp outline through collisions. Also 

 the smaller the area of the plate affected by a beam of given 

 intensity the easier will be its detection and the more 

 accurate its measurement, for we are very far at present 

 from the limits of accuracy of the measurement of position 

 on the plate determined by the fineness of the grain of the 

 emulsion. Hence both these considerations point to an 

 instrument of the smallest practicable dimensions. 



