244 PROCEEDINGS OF THE AMERICAN ACADEMY. 



theory. Before leaving this first grating, which we will call No. 1, it 

 is important to note that although the groups in magnesium at 2790 fj., 

 1873 /x, and 924 /x, closely resemble each other, their wave lengths are 

 not exactly in the 1:2:3 ratio; 2 X 924 — 1848, which differs from 

 1873 by 25. 



It was proved that these phantom lines were not due to any local 

 variation in ruling by shielding all but a narrow strip of grating surface, 

 and then moving the screen so as to expose each strip in turn. In this 

 way a series of photographs were obtained, each from a different strip 

 of grating surface. They all showed the phantom lines with about 

 equal intensity. 



In addition to the grating with which the investigation was begun, 

 three others were examined. Two of these were of larger radius, — 

 21 ft. ; the other was similar in type to the first instrument. Of the 

 two large gratings, one showed the phantom lines distinctly. The 

 two strong groups formerly at 1873 /x and 924 /a were now found at 

 positions corresponding to 1728 /a and 1079 /a. The other large grat- 

 ing did not show the lines at all. The last small grating showed 

 the reproduction of group 2790 /x, at positions of about 1870 /x and 924 /x. 

 In addition, however, there were also numerous less distinct repro- 

 ductions scattered between these two positions. 



We may now sum up the facts arrived at in these few pages. Of 

 four concave diffraction gratings examined in this investigation, three 

 showed the phenomenon of phantom lines. These lines vary in 

 position with the grating by which they are produced, but the vari- 

 ation cannot be connected either with the variation of radius of curva- 

 ture of the grating or with the number of lines to the inch. The most 

 prominent of these phantom lines closely resemble some group in the 

 true spectrum. This repetition of a true group occurs most strongly 

 twice. The width of these phantom repetitions is proportional to their 

 apparent wave length. The wave lengths of the true group and its 

 pliantom repetitions bear no simple relation to one another. The 

 photographs obtained with gratings 1 and 4 show a very large number 

 of faint repetitions of a group or set of groups. These repetitions form 

 a sort of background to the main spectrum between 1800 /a and 900 /x. 



It may be safely said that a strong line in the spectrum is repeated a 

 great number of times, and that these phantoms are distributed appar- 

 ently at random. We have no reason to believe that this repetition is 

 confined to a certain proportion of the ultra-violet spectrum. Every line 

 in the spectrum is probably reproduced. These reproductions are con- 



