270 Lord Rayleigh's Investigations in Optics, 



of the present section was solved in the Philosophical Maga- 

 zine for March 1874. I there showed that if n denote the 

 number of lines on a grating and m the order of the spectrum 

 observed, a double lino of wave-lengths X and X + 8X will be 

 just resolved (according to the standard of resolution defined 

 in the previous section), provided 



X mn> ^ ; 



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

 n. When the ruling is very close, m is always small (not 

 exceeding 3 or 4) ; and even when a considerable number of 

 spectra are formed, the use of an order higher than the third 

 or fourth is often inconvenient in consequence of the over- 

 lapping. But if the difficulty of ruling a grating may be 

 measured by the total number of lines (n), it would seem 

 that the intervals ought not to be so small as to preclude the 

 convenient use of at least the third and fourth spectra. 



In the case of the soda- double line the difference of wave- 

 lengths is a very little more than yoVo > so that, according to 

 (1), about 1000 lines are necessary for resolution in the first 

 spectrum. By experiment I found 1130*. 



" Since a grating resolves in proportion to the total number 

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

 depends on different principles in the case of gratings and 

 prisms ; but the distinction is not fundamental. The limit to 

 definition arises in both cases from the impossibility of repre- 

 senting a line of light otherwise than by a band of finite though 

 narrow width, the width in both cases depending on the hori- 

 zontal aperture (for a given X). If a grating and a prism 

 have the same horizontal aperture and dispersion, they will 

 have equal resolving-powers on the spectrum." 



At the time the above paragraph was written, I was under 

 the impression that the dispersion in a prismatic instrument 

 depended on so many variable elements that no simple theory 

 of its resolving-power was to be expected. Last autumn, 

 while engaged upon some experiments with prisms, I was 

 much struck with the inferiority of their spectra in comparison 

 with those which I was in the habit of obtaining from gratings, 

 and was led to calculate the resolving-power. I then found that 

 the theory of the resolving-power of prisms is almost as simple 

 as that of gratings. 



* In my former paper this number is given as 1200. On reference to 

 my notebook, I find that I then took the full width of the grating as an 

 English inch. The 3000 lines cover a Paris inch, whence the above cor- 

 rection. From the nature of the case, however, the experiment does not 

 admit of much accuracv.. 



