Analysis of Magnesium and Carbon. 345 



(2a) 23/32 x 46/41 X will be that of the corresponding ray 

 of the water- spectrum due to b as it exists in 0' in the state 

 in which the latter occurs in the combined oxygen of water ; 



(3) 70/59 X will be a wave-length of a ray of the oxygen- 

 spectrum due to b as it exists in 0" in the state in which the 

 latter occurs in 0' in free oxygen ; and 



(3a) 21/32 x 70/59 X will be the wave-length of the corre- 

 sponding ray of the water-spectrum due to b as it exists in 

 0" as the latter exists in 0' in the combined oxygen of water. 



III. If X be the wave-length of a line in the oxygen- 

 spectrum due to c as it exists in 0" as the latter exists in 0' 

 in free oxygen : 



(1) 3/5 X will be the wave-length of the corresponding ray 

 of the water-spectrum due to c as it exists in 0" in 0' in the 

 combined oxygen of water (chief criterion) ; 



(2) 5/8 X will be the wave-length of another line of the 

 group in the same spectrum due to 0", which group includes 

 other rays besides those referred to in the last preceding 

 paragraph. 



IV. If X be a wave-length of free helium, that is of helium 

 in the state in which it occurs along with coronium uncom- 

 bined, when hydrogen is dissociated at high temperature and 

 diminished pressure, and its volume thereby increased in the 

 ratio 3/2: 



2/3 X will be the wave-length of the corresponding ray of 

 the hydrogen- spectrum due to b as it is chemically combined 

 in hydrogen; and X' = 2/3X will satisfy the criteria above 

 given under II., so that 4/5 X', 23/32 x 46/41 X', and 

 21/32 x 70/59 X' will be the wave-lengths of three lines of 

 the water-spectrum, and 46/41 X' and 70/59 X' those of two 

 lines of the oxygen-spectrum. 



Y. On the other hand, if X be the wave-length of a ray of 

 free "coronium," 2/3X(=X') will be the corresponding 

 wave-length in the group of lines of hydrogen due to the 

 combined " coronium," and will satisfy the criteria above 

 given under I.; so that 19/30 X', 3/4 X', and 56/75 X' will be 

 very nearly the wave-lengths of three lines of the water- 

 spectrum. 



VI. The wave-lengths of all the lines of the elementary 

 line-spectra of hydrogen and oxygen, when multiplied by 2/3 

 (the factor of condensation of the gases in the formation of 

 water-vapour), become wave-lengths of corresponding lines 

 in the spectrum of water. 



Applying his analysis to magnesium, the author finds that 

 the lines of the magnesium-spectrum fall into four groups. Of 

 these the first consists of the lines for which X = 5710, 5529, 

 5527, 5183, 5172, 4481, 4456, which he ascribes to helium (or b 



