THE SPECTRUM OF HYDROGEN 



249 



development, etc. (to ensure the critical intensity being the 

 same for each), but in one case the intensity of the source is cut 

 down to a known fraction of its value in the other. Then the 

 first image will be narrower than the second, because the same 

 critical intensity must be reached at points nearer the central 

 maximum, when the whole source is weaker. The difference 

 in the width of the images is a known function of the half-width 

 of the line, and the dispersion of the spectroscope used. The 

 diagram will probably explain the method more clearly than a 

 longer description. 



The two curves represent the intensity distribution of the 

 light in the spectrum line ; the outer one is when the full 

 intensity of the source is used, and the inner one is when this 

 intensity has been cut down, e.g. by a screen, to the fraction 

 IJIq at all points. We have seen that a critical photographic 

 intensity exists. Let this be represented by the ordinate I,. 

 This intensity is reached at the points ab and cd respectively on 

 the two curves, and the plate is blackened between these points 

 only. The successive photographs will therefore present the 

 appearance of the blackened areas underneath the main diagram. 

 Owing to their sharp edges, the widths of the images can be 

 read very accurately under the micrometer, and so a method of 

 determining half-widths is provided in which the personal factor 

 is reduced to a minimum. Any spectroscope of sufficient dis- 

 persion and resolving power can be used. The interferometers 

 used in the other method are available, or the Lummer-Gehrcke 

 plate. Actually the instrument employed for the secondary 

 lines was a 3 5 -plate echelon spectroscope, which is peculiarly 

 convenient for the purpose. It can be set in two positions, in one 

 of which it gives two equally intense images of the line under 



