200 Lord Rayleigh on the Manufacture and 



jection of A B on B Q is {mn + l)\. Suppose now that X + 8\ 

 is the wave-length for which B Q gives the principal maximum, 

 then 



(mn + l)\=mn(\ + BX) ; 

 whence 



X mn 



which shows that the resolving-power varies directly as m and n. 

 It is not possible to say precisely under what circumstances a 

 double line would appear to be resolved — something no doubt 

 would depend on the intensity of the light — but it seems pro- 

 bable that there would be no distinct resolution when the two 

 images are separated by only half the width of the central band 



of either. If this be so, we may take — kt- as the least number 



of grooves capable of resolving in the mth spectrum a double 

 line whose wave-lengths are \ and X + 6X In the case of the 



£\ 1 



soda-lines — is about ; and therefore to resolve them in 



A, JLuUU 



the first spectrum would require 1000 grooves, in the second 

 spectrum 500, and so on. It is evident that if the ruling be 

 perfectly accurate and the illumination sufficient, the work may 

 be accomplished with comparatively few lines by using a spec- 

 trum of elevated order. 



The result of an attempt to determine experimentally the 

 number of lines necessary to resolve D in the solar spectrum 

 may here be recorded. The 3000-to-the-inch Nobert was used, 

 its horizontal aperture being limited by the jaws of an adjustable 

 slit. From the width of the slit found to be necessary the 

 number of lines in operation was calculated. 



In the first spectrum 1200 lines were required, in the second 

 630, and in the third 375. These numbers should be in the 

 ratio 6:3:2; but the last, which presents the greatest deviation, 

 was difficult of exact measurement. 



The number of lines necessary in the first spectrum is very 

 much what might have been expected. The effect of a limitation 

 of the aperture of the grating by a slit whose length is horizontal, 

 is, of course, quite different. As the slit is narrowed, the image 

 of a point would be dilated in a vertical direction ; but this is of 

 no moment when the subject of observation is itself a uniform 

 vertical line. As was mentioned in the first part, the definition 

 is often materially improved. 



Since a grating resolves in proportion to the total number of 

 its grooves, it might be supposed that the defining-power de- 

 pends on different principles in the case of gratings and prisms; 



