344 Dr. A. Griinwald's Mathematical Spectral 



The group of lines thus harmonically related the author infers 

 to be due to a common component of A and B, and the ratio 

 of the wave-lengths to be dependent on the influence of the 

 other components. He had previously applied his method 

 to the analysis of the spectra of hydrogen and oxygen, and 

 concluded that hydrogen is composed of two primary elements, 

 a and b, and has the chemical formula ba± ; and that a is the 

 substance which, when uncombined, produces the " coronal 

 line " and some others in the solar atmosphere (hence called 

 " coronium "), while b is the substance which, when uncom- 

 bined, gives the lines ascribed to "helium" (D 3 &c). Oxygen 

 he thinks to be composed of a substance H7 combined with 

 another substance 0'; this substance 0' being a compound 

 with the formula & 4 5 ", where 0" is again a compound b 4 c 5 , 

 so that = U'b i (b i c 5 ) 5 . How he arrived at these particular 

 formulae he reserves for publication in a future more complete 

 memoir. The spectrum of O" will include a group of lines 

 due to b which will be harmonically related to a corresponding 

 group in the spectrum of hydrogen ; but inasmuch as b is 

 combined in the one case with c and in the other case with a, 

 and the proportions in which it is combined are also different 

 in the two cases, the wave-lengths of the group of lines are 

 not identical in the two spectra, but are only harmonically 

 related. Again, the wave-lengths of lines due to b in the 

 spectrum of 0" when it is free will be, not identical with, but 

 harmonically related to the corresponding lines in the spec- 

 trum of oxygen in which 0" occurs under the constraint of 

 combination with b and H'. 



The criteria by which the primary elements a, b, c may be 

 recognized are as follows : — 



I. If X be the wave-length of the group of rays produced 

 by a as it exists in hydrogen: 



(1) 19/30 X will be the wave-length of the corresponding 

 ray in the spectrum of water, due to a in the state in which it 

 exists in hydrogen in the state in which the latter occurs in 

 water-vapour ; and 



(2) 3/4 X& (3) 56/75 X will be the wave-lengths of two 

 other corresponding rays in the water-spectrum. 



II. If X be the wave-length of one of the group of rays due 

 to b in the state in which it occurs in hydrogen under the 

 influence of a: 



(1) 4/5 X will be the wave-length of the corresponding ray 

 in the water-spectrum due to b as it exists in hydrogen in the 

 state in which the latter occurs in water ; 



(2) 46/41 X will be the wave-length of the corresponding 

 ray of the oxygen-spectrum due to b as it exists in 0' in the 

 state in which the latter occurs in free oxygen ; and 



