138 MI CHELSON— RULING AND PERFORMANCE [April 22, 



where / is the total length of the ruled surface, A the wave-length of 

 the light, i the angle of incidence and Q the angle of diffraction, and 

 the maximum resolving power which a grating can have is that 

 corresponding to i and Q each equal to 90° which gives R = 2I/X ; 

 that is twice the number of light waves in the entire length of the 

 ruled surface. 



This shows that neither the closeness of the rulings nor the total 

 number determine this theoretical limit, and emphasizes the im- 

 portance of a large ruled space. 



This theoretical limit can be reached, however, only on the con- 

 dition of an extraordinary degree of accuracy in the spacing of the 

 lines. Several methods for securing this degree of accuracy have 

 been attempted but none has proved as effective as the screw. This 

 must be of uniform pitch throughout and the periodic errors must 

 be extremely small. 



For a short screw, for example one sufficient for a grating two 

 inches in length, the problem is not very difficult, but as the length 

 of the screw increases the difficulty increases in much more rapid 

 proportion. It was solved by Rowland in something over two 

 years. 



Since this time many problems have arisen which demand a 

 higher resolving power than even these gratings could furnish. 

 Among these is the resolution of doubles and groups of lines whose 

 complexity was unsuspected until revealed by the interferometer and 

 amply verified by subsequent observations by the echelon and other 

 methods. 



Others that may be mentioned in this connection are the study of 

 the distribution of intensities within the spectral " lines " ; their 

 broadening and displacement with temperature and pressure ; the 

 effect of magnetic and electric fields, and the measurement of mo- 

 tions in the line of sight, as revealed by corresponding displacement 

 of the spectral lines in consequence of the Doppler effect. 



All of these have been attacked with considerable success by 

 observations with the echelon, the interferometer and the plane- 

 parallel plate. These methods have a very high resolving power, 

 but labor under the serious disadvantage that adjacent succeeding 



