some Problems of the Mass-Spectrograph. 521 



large together. It is important to note that larger resolving 

 power can only be obtained by increase of: cj> if 6 is increased 

 as well. 



These arguments are too rough to give an exact value for 

 the resolving power of the actual apparatus. This we can 

 obtain by considering linear displacements along the plate. 

 The width of the image on the plate is 



(a-\-b + c)Sacosec (<j) — 26). 



Consider the region near cj) = 4z0, a = b in the actual appa- 

 ratus, where a + b + c = 26 cm. and T= 10 cm. Thus Su = w/6 

 and the width of the image (in cm.) is 31'4w. 



By direct calculation with formula (2), with p — 2*388 cm., 

 we tind that there is an interval of 0*797 cm. between the 

 corresponding parts of the images for m/m = 34, 36. This 

 corresponds to an interval of 0*139 cm. for a. change of 

 1 per cent, in m. The actual width of the slits used was 

 about 1/25 mm., so that the theoretical width of the image 

 in this region is 0126 cm. This agrees very well with the 

 actual image widths, showing that there was little (if any) 

 increase in width due to inexact focussing, and further 

 that theoretically the apparatus should be able to resolve 

 lines corresponding to masses differing by just less than 

 1 per cent. In actual practice a slightly greater resolving 

 power was obtained, probably by using the ends of the images 

 which correspond to a narrower part of the slits. 



These considerations show that the theory and practice of 

 this form of mass-spectrograph are in very satisfactory 

 agreement, and present no anomalous and disturbing dis- 

 cordances. 



§ 8. Possible improvements in focussing and in the 

 position of the photographic plate. 



The focussing achieved by the existing apparatus is only 

 "first order focussing"; it is not exact, but the rays all 

 touch a caustic and the plate is placed to pass through the 

 points of contact of the rays actually existing. Asa result, 

 many of the rays must have a very oblique impact on the 

 plate, which is unsatisfactory for a variety of reasons and 

 should be avoided if possible. It is natural therefore to try 

 so to modify the apparatus that both the focussing and the 

 position of the plate may be improved. The only feature 

 which is really at our disposal is the shape of the magnetic 

 field. It ought to be possible so to modify the shape that 



