85 



be total darkness in a direction corresponding to a retardation 

 of (n+1)^. Let this direction correspond to the brightest part 

 of the image for the second sodium line ^2, so that (n+l)Zi=nl2, or 

 h~li='^. Under these conditions the two images are just "re- 

 solved." But lijli=_± for sodium lines, whence n=10C0. That 

 is a grating of 1000 lines will "resolve" the sodium lines in the 

 spectrum, or R=]000. In the second (where the common re- 

 tardation is two waves lengths) the resolving power is twice as 

 great, or 2n, and in the mth spectrum, xiii times as great. 

 The resolving power is therefore the product of the number 

 of lines in the grating by the order of the spectrum, that is, 

 R=wjw 



In order, therefore, to obtain high resolving power the grat- 

 ing must have a large number of rulings, and if possible a high 

 order of spectrum should be used. The rulings need not be ex- 

 ceedingly close together, but it is found practically sufficient if 

 there are from 500 to 1000 lines per millimeter. The earlier 

 gratings were relatively small and contained only a few thousand 

 lines. The best of these were ruled by Nobert, (1851). A very 

 great advance was made by Rutherford, of New York, who, 

 in 1868, ruled gratings two inches long, on speculum metal and 

 containing about 20,000 lines. These gratings exceeded in re- 

 solving power the best prism-trains in use at the time. The 

 next advance was made by Rowland, of the Johns Hopkins Uni- 

 versity, who succeeded in ruling gratings six inches long (by 

 two to three inches stroke) having about one hundred thousand 

 lines, and capable (theoretically, at least) of resolving in the 

 first spectrum, double lines whose distance apart was only one 

 one-hundredth as great as that of the sodium lines. Practically 

 this is about the limit of the power of the best Rowland grating 

 which I have examined. 

 The difference between the theoretical and the actual per- 



