346 Dr. A. Grunwald's Mathematical Spectral 



as it occurs in hydrogen) existing as a component of magnesium 

 without condensation. The proof is that 2/3 X, which may be 

 written X', satisfies the criteria above given for such lines ; 

 that is to say, 4/5 X' is the wave-length of a line of the water- 

 spectrum, as are also 25/32 x 46/41 X' and 21/32 x 70/59 X'. 

 In fact, of the 21 numbers calculated from these formulae, 

 15 agree, within a fraction of a unit of Angstrom's scale, 

 with the wave-lengths of lines of the water-spectrum observed 

 by Liveing and Dewar. The remaining 6 lines the author 

 thinks must have escaped observation merely through their 

 feebleness, because the wave-length of each of them is the 

 half of the wave-length of a corresponding line in the com- 

 pound line-spectrum of hydrogen ; and he has elsewhere 

 shown that, in general, the half of the wave-length of a line 

 in the last-named spectrum is the wave-length of a line of the 

 water-spectruni. 



X' ought to satisfy also the criteria IV., but no line of 

 wave-length X' has as yet been observed in the spectrum of 

 hydrogen ; while of 46/41 X' only 4135-5, and of 70/59 X' only 

 4371*7, are the wave-lengths of observed lines of oxygen. 



The magnesium-lines 5529, 4481, and 4456 coincide, 

 within the limits of errors of observation, with lines of the 

 compound line-spectrum of hydrogen. 



The second group of magnesium-lines consists of those for 

 which X = 



5167 



4481 



3894 



4808 



4456 



3892 



4705 



4351-2 



3730 



4703 



4350 



3334 



4587 



4165 



3330 



4586 



4057-3 



3329-1 



4570 



3896 



3327 



This group the author ascribes to the primary element c in 

 the same state in which it occurs in oxygen ; and it satisfies 

 the criteria III., for in most cases 3/5 X and 5/8 X are found 

 to agree, within a unit of Angstrom's scale, with the wave- 

 lengths of lines of the water-spectrum observed by Liveing 

 and Dewar, and in most of the few remaining cases they are 

 the halves of the wave-lengths of lines in the compound line- 

 spectrum of hydrogen. The author gives a list of 43 lines of 

 the oxygen-spectrum which belong to c in free oxygen ; but 

 of these only 4705, 4588, and 4455 are identical, or nearly so, 

 with lines in the second group of magnesium-lines. In ex- 

 planation of this, he says that when an element c occurs in 

 different substances (as, for example, in oxygen, in magnesium, 



