Cause of the Structure of Spectra. 257 



same as for H, and /jl in the Li and Na Diffuse series is or 

 an integer as in the Balmer hydrogen series. Rydberg takes 

 Pickering's series with/* ='5 to be the Sharp series in hydrogen,, 

 whose formula is therefore 



n 1 1 



101)675"" (l+l) 2 (m-f *5) 2 ' 

 and therefore by Rydberg's law the Principal series for H 

 must be 



n 1 1 



109675"" (l + *5) 2 (m + 1) 2 ' 



With m = l this gives for the wave-length of the first line 

 common to both Sharp and Principal series the value 1687*88,. 

 almost identical with the 1688 found by Maury and Pickering 

 in certain star spectra for a line which exceeds in intensity all 

 the known hydrogen lines in the same spectra. In theoretical 

 spectrum analysis this discovery of the chief line in the 

 hydrogen spectrum is a worthy analogue to the great astro- 

 nomical achievement of the discovery of Neptune. 



As Rydberg points out, we should by analogy expect series 



? = x 1 an 



B (>i + /V)' 2 (^2 + ^.2)'^ " v J 



in which while m x has the fixed value 2, m 2 has ail possible 

 integral values, while m 1 is fixed at 3, m 2 has all integral 

 values, and so on, and vice versa. Corresponding to the 00 

 modes of vibration of a simple system we seem to have go 2 

 modes of vibration in spectra, as we should infer from our 

 idea that we have two things wdiose relative motion causes 

 radiation. For if our reference-vector like the disturbance- 

 vector rotates in opposite directions and rotates with the 

 angular velocities 1, 2, 3, ... n so that the projection of its 

 end gives a Fourier series of simple harmonic motions of 



periods 1, £. 1/n, then each possible motion of the dis- 



turbance-vectorcan be combined with a motion of the reference- 

 vector to give a relative motion of the type our analysis shows 

 to be the cause of the structure of spectra. If, instead of a 

 Fourier series with a general frequency n, we take our more 

 general series giving all possible undertones and overtones 

 with the general frequency >'+]>/s, and if we ascribe to both 

 the disturbance-vector and the reference-vector the go 3 modes 

 of vibration given by this, then there will be go 6 relative 

 motions connected with a spectrum. Thus our conception is 

 capable of explaining the great complexity of spectra. 

 If we compare (6) and (9) we have 



1 + wffc /_, 1 + P ti 

 m + p/jl 



(ori±A .... (12) 

 \ m + ufjbf 



