Cause of the Structure of Spectra. 247 



{AVied. Ann. xxv. 1885), expressing the wave-lengths of the 

 •chief lines in the hydrogen spectrum as terms of a simple 

 mathematical series, and Rydberg's relating to the identifi- 

 cation of similar series in the spectra of other elements, and 

 the existence of beautifully simple relations between the 

 series. Kayser and Runge, and Runge and Paschen, besides 

 contributing valuable experimental work, have also taken 

 part in the important work of identifying the series in com- 

 plicated spectra. But the great heartening to theoretical 

 spectroscopic students undoubtedly came from Balmer's 

 .discovery of his formula for hydrogen 



x =\;'-4- ro 



which, on giving m the integral values from 3 to 15, fur- 

 nishes the wave-lengths of the thirteen chief lines in the 

 hydrogen spectrum. Ames (Phil. Mag. [5] xxx. p. 18) 

 subjected this formula to a strict comparison with his experi- 

 mental measurements of the wave-lengths in the hydrogen 

 spectrum, using it in the form X=3647'20 m 2 /(m 8 — 4) for the 

 wave-length in vacuum, and found that from the longest 

 wave 6564*96 x 10~ 8 cm. to the shortest 3713*2, the greatest 

 discrepancy between experiment and formula was about 

 1 in 10 4 , and the average discrepancy about \ in 10\ 

 But in addition to this primary spectrum there is the 

 secondary one proved by Hasselberg to belong to hydrogen, 

 for which Ames gives the wave-lengths of 63 lines. 



An important fact concerning the relations of the two 

 spectra is that brought out by Trowbridge and Richards 

 (Phil. Mag. [51 xliii.) by means of their powerful electrical 

 appliances, namely, that the two spectra appear together in 

 the continuous discharge, but the primary alone in the oscil- 

 latory, as though in the latter the primary spectrum is 

 ■enhanced by a sort of resonance which causes the quenching 

 of the secondary. 



The simplest step in investigating theoretically the relation 

 between the two spectra is to inquire : — What values of m in 

 the formula for the primary spectrum would be required to 

 give the wave-lengths observed in the secondary spectrum ? 

 These are found by solving Balmer's equation for m, using 

 Ames's values of X reduced to vacuum, and also of \ , and 

 are given in the second row of the following table, where the 

 fourth row contains the numbers of the form r + l/s, or 

 -occasionally r+p/s, where r, s, and j> are integers, such as give 

 values nearlv equal to those of m. the same numbers beino- 



S2 



