348 Dr. A. Griinwald's Mathematical Spectral 



wave-length there are may mostly be ascribed to errors of 

 observation ; though they may be in some part due to slight, 

 merely physical differences of condensation of the chemically 

 condensed gas b as it exists in water-vapour on the one hand, 

 and in magnesium on the other. 



That these magnesium-lines, which are also water-lines, 

 really belong to the group of lines due to b as it exists in 

 hydrogen in water the author thinks to be proved ; because 

 when their wave-lengths are multiplied by 5/4, they satisfy 

 the criteria II. so far that if X" = 5/4X, 23/32 x 46/41 X" and 

 21/32 x 70/59 X" respectively are groups of wave-lengths which 

 agree well with observed wave-lengths in the water-spectrum. 

 46/41 X" and 70/59 X" should also be the wave-lengths of 

 oxygen-lines ; but of these only a few agree with the wave- 

 lengths of observed lines. The absence of the greater part 

 of the lines of these groups from the observed oxygen-spectrum 

 and of the group with wave-length X" from the hydrogen- 

 spectrum, the author ascribes to the weakness of the lines 

 under ordinary circumstances ; and he expects that oxygen 

 and hydrogen will yet, under some different conditions, be 

 made to emit them with sensible intensity. His theory, then, 

 is that magnesium is a compound containing : — 



(1) Helium, without condensation or dilatation, which in 

 magnesium emits only the rays of group I. ; all its other rays, 

 including D 3 , being weakened by the influence of the other 

 components. 



(2) The primary element c, in the same state in which it 

 occurs in oxygen and carbon, giving the rays of group II. 



(3) The primary element b in that state in which it occurs 

 in free hydrogen, giving the rays of group III. 



(4) The primary element b, but in the chemically more 

 condensed state in which it occurs in the hydrogen of water- 

 vapour, giving, under the influence of the other components, 

 the rays of the partial group IV. with more or less intensity. 



Applying the same method to carbon, he finds ll : 1 1 

 rays of the elementary line-spectrum of that substance form 

 five groups. The first consists of the rays for which X is 

 6583-0, 6577-5, 5694-1, 5660-9, 5646-5, 5638-6, and 5150*5. 

 In this group X, when multiplied by 3/5, satisfies very com- 

 pletely the criteria II. for b as it occurs in hydrogen, so far 

 as the calculated wave-lengths of rays of water are concerned; 

 but only one of the corresponding rays of hydrogen, and none 

 of those of oxygen, have been recorded as occurring in the 

 spectra of these substances. Nevertheless several of these 

 rays have been observed by Liveing in the oxyhydrogen- 



