502 HENRY A. ROWLAND 



all the terms of the series except the first vanish. In the case where the 

 slit and focus are on the circle of radius %p, as in the automatic arrange- 

 ment described above, we have A = and the second and third terms of 

 the series disappear, and we can write since we have 



TO r 



t = cos fJL and - cos v , 

 P P 



n db / . \/i i sin >j. tan // + sin v tan * 3 \ 



2 = cos d (sin ,u + sin > ) 1 J - r+ &c. . 



ds \ sm fj + sm > / 



But in the automatic arrangement we also have v = 0, and so the 

 formula becomes 



2 -j- = cos d (sin /; + sin K O ) { 1 J tan ^ ^ ! + &c. }. 



6t5 



To find the greatest departure from theoretical perfection, d must 

 refer to the edge of the grating. In the gratings which I am now mak- 

 ing, p is about 260 inches and the width of the grating about 5-4 inches. 



Hence d = - approximately and the series becomes 



Hence the greatest departure from the theoretical ruling, even when 

 ta.nfji ( f=2, is 1 in 1,000,000. Now the distance apart of the compon- 

 ents of the 1474 line is somewhat nearly one forty-thousandth of the 

 wave-length and I scarcely suppose that any line has been divided by 

 the best spectroscope in the world whose components are less than one- 

 third of this distance apart. Hence we see that the departure of the 

 ruling from theoretical perfection is of little consequence until we are 

 able to divide lines twenty times as fine as the 1474 line. Even in that 

 case, since the error of ruling varies as 3 s , the greater portion of the 

 grating would be ruled correctly. 



The question now comes up as to whether there is any limit to the 

 resolving power of a spectroscope. This evidently depends upon the 

 magnifying power and the apparent width of the lines. The magnify- 

 ing power can be varied at pleasure and so we have only to consider the 

 width of the lines of the spectrum. The width of the lines evidently 

 depends, in a perfect grating, upon three circumstances, the width of 

 the slit, the number of lines in the grating and the true physical width 

 of the line. The width of the slit can be varied at pleasure, the number 

 of lines on the grating can be made very great (160,000 in one of mine), 

 and hence we are only limited by the true physical width of the lines. 



