322 Prof. F. L. 0. Wadsworth on the Resolving Poiver of 



require only J the time for ruling, and hence in general 

 would be only J- as difficult to make as the first one. The 

 question of the relative brightness of the spectra in the two 

 gratings would be, as already stated, almost entirely a question 

 of the selection of a ruling-point. 



Let us now consider the resolving power of a spectroscope 

 for wide slits (width s) and monochromatic radiations. The 

 formula ordinarily given for this is 



^=^Tx r (6) 



This is based on the assumption that for distinct resolution 

 of wide lines, the angular distance between the contiguous 

 edges of the two lines must be equal to the resolving power 

 of the aperture through which they are viewed. According to 

 this assumption the angular distance between the centres of 

 the two lines of width s, which would be just resolved, would 

 have to be 



where yjr is the angular magnitude of the aperture b as viewed 



from the line s,f is the distance of the line itself from the 



lens, and /' the focal length of the observing telescope. But 



I have recently found that it can be shown, both by theory 



and by experiment, that this assumption is incorrect, and 



that the resolving power of an instrument for wide lines is 



considerably greater than is indicated by the above expression. 



As this point has apparently escaped notice heretofore it may 



be considered a little in detail. 



The diffraction-pattern due to a line of width 6-, or angular 



s 

 width cr=j, is found by integrating the effect due to each 



linear element over the whole width of the line. In the case 

 of a rectangular aperture the diffraction-pattern due to each 

 linear element is represented, as is well-known, by the equation 



• 2^ JL 



sin— <z> 

 tx 



^m <8) 



<j) being the angular distance from tie centre of the diffrac- 

 tion-image. The intensity at any point 7 due to the effect of 



