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



§ 5. A comparison of t lie calculated mass-scale 

 with an actual photograph. 



The existing spectrograph was designed so that #=5*4 cm. 

 approximately and tan 20 — 0'168. The values actually 

 realized may be slightly different. ' The designed value of p 

 is less certain, but is about 2 - 3 cms. In order to compare a 

 calculated and observed mass-scale we have assumed the 

 above values for k and tan 20. Equation (2) now takes the 

 form 



D + 5'4 . 



=f(m[m ) > 



P 



w 



where the function / is exactly known. We do not kno 

 m directly or the exact value of p, and therefore m and p 

 may be regarded as disposable constants. In order to deter- 

 mine them, values of log 10 (D + 5*4) were tabulated for 

 observed values of D, for which the values of m are known, 

 and also values of log 10 f(m/m ) for selected values of m/m . 

 The difference of these logarithms, log 10 _p, should be constant 

 and m must and can be selected so as to obtain this 

 constancy. In the photograph analysed it happens that, 

 thus determined, m Q =l. The corresponding value of p was 

 2*388, in agreement with the designed value. 



Assuming the values of m and p, and the above values of 

 k and tan 20, values of D were calculated for a series of 

 values of m, and are shown by the continuous curve of fig. 2. 

 Observed values of D for the actual lines on the plate are 

 shown by circles. The agreement is excellent, in view of 

 the fact that the assumed values of k and tan 20 are not 

 reliable to the required degree of exactness. 



§ 6. A discussion of some recent criticisms. 



In this connexion some recent criticisms by Sir J. J. Thom- 

 son * call for comment. He there discusses the focussing- 

 effect of the electric and magnetic fields deflecting in 

 opposite directions, and assumes an ideal arrangement 

 practically identical with the existing instrument. He 

 points out that the emergent rays for each value of e/m must 

 have a caustic, but that when (as here) rays of constant 

 kinetic energy are selected only certain portions of the 

 caustic will be touched by the existing rays, and the photo- 

 graphic plate must be placed so that it passes through the 



* Proc. Roy. Soc. A, vol. xcix. p. 93 (19l4). 



