248 PROCEEDINGS OP THE AMERICAN ACADEMY. 



placement suffers a second discontinuity. Thus Ai gives 42,1 mm., Dg 

 o9.8 mm. The displacement of C4 is almost exactly that of Ci, and 

 very nearly that of group C, — 2790/x. The figures are 42.25 mm., 

 ■^2.25 mm., 42.21 mm. As stated before, the most obvious conclusion 

 from these data is that the lines A^ to C4 are not due to light of wave 

 lengths corresponding to the positions of the lines in the spectrum. They 

 seem to be reproductions of some part of the true spectrum. 



On the aluminum plate there are present six strong lines, — B^, Ci, D2, 

 E2, B3, C3, — with wave lengths from 2075 /x to 933 /x. There are faint 

 reproductions of these groups similar in arrangement to those observed 

 with magnesium. There is a background of fine, indistinct lines. On 

 allowing the groups to be displaced by the prism, we find group D2 less 

 displaced than group Ci, and group Bj less displaced than a real group 

 called I. 



We may now consider the false nature of the lines as established. 

 It remains to investigate the causes which produce this diffraction 

 phenomenon. 



It is perfectly evident that the phantoms are not due to a local varia- 

 tion in the rate of ruling, such as produce ghosts; for we have seen that 

 the fault is not local in the grating surface. Moreover, we know that a 

 ghost always occurs close to the line of which it is a reproduction. 



The phantoms are not due to a false source of light, since the dispersion 

 of the various reproductions is not the same as that of the real group. 

 We may discard the hypothesis that the mounting of the grating or the 

 position of the source of light has any effect. The lines occur with 

 various forms of mounting and with various positions of lens and source, 

 as will be seen later. We have to deal with a diffraction phenomenon, 

 with an inherent property of the diffraction grating itself. 



It seems probable that in developing the theory of the grating some 

 assumptions have been made which are not according to fact. It is in 

 the error of such assumptions that we find the solution of our problem. 



It is generally assumed in treating the grating that the lines of the 

 ruling are of equal width and are separated by equal spaces. In the very 

 nature of things, it is evident that this cannot be the case in view of 

 the very minute distances involved and the almost inconceivable rigidity 

 which would be necessary. These variations, slight in absolute amount, 

 may be a considerable fraction of the distance from line to line. It is 

 clear, moreover, on experimental as well as on theoretical ground, that 

 these variations are not local, but extend over the whole surface of the 

 grating. 



