LYMAN. — FALSE SPECTRA FROM THE ROWLAND GRATING. 249 



It appears, then, that the departure from equal spacing assumed in the 

 theory of the concave grating is not the random departure which is next 

 in theoretical simplicity, but a more or less systematic departure which 

 has emphasized disproportionately certain of the subordinate maxima 

 called for in the conventional theory. If the position of the false maxima 

 occurred in the ratio 1:2:3, or in any other simple ratio, the phenomena 

 would invite an analytic discussion. As an experimental fact, however, 

 our lines are not harmoniously placed with respect to the slit, nor are 

 they arranged according to any discoverable system. Moreover, they are 

 different in character and position when obtained by different gratings 

 ruled by the same engine. It seems most likely that the phantom lines 

 are due to a number of superposed first spectra of varying dispersions ; 

 and that these false spectra owe their existence in some manner to the 

 variation in width and separation of the grating lines. Under these con- 

 ditions, an analytic discussion seems less profitable than the presentation 

 of the experimental data. 



In order to substantiate the statements just made, it becomes the 

 next object of the investigation to observe carefully the relative posi- 

 tions of the phantom lines, not only in one, but in several different 

 gratings. 



We must observe, in looking over the tables already given, that al- 

 though several groups bear a strong resemblance to each other, and though 

 the apparent wave lengths of these groups are nearly in one, two, three 

 ratio, this ratio is never exact. 



In aluminum, the line C 3 seems to resemble the line C 1? but 

 2 x 933 = 1866, not 1890. The group B 3 resembles B x , but 2B 3 = 

 2046, not 2075. There certainly is no exact 1, 2, 3 relation, although 

 lines corresponding roughly to 3C 3 and 3B 3 in wave length may be found 

 for aluminum. The difference between 2046 and 2075 = 29 Angstrom 

 units cannot possibly be due to the error of observation. It is perfectly 

 safe to say that the measurements of wave lengths in the table are correct 

 to 1 Angstrom unit. 



Before examining another grating, there are one or two more points 

 which need attention. A concave grating produces two spectra of the 

 first order, which in this form of mounting lie on each side of the slit. 

 The spectrum on the left had been investigated ; it was now necessary 

 to observe the spectrum on the right of the slit. The grating was there- 

 fore turned upside down, by which process the spectrum formerly on the 

 right of the slit now fell upon the left. Photographs taken showed the 

 lines A x , C u A 4 , C 4 , etc., in magnesium as clearly as before. The grat- 



