206 Scientifc Proceedings, Royal Dublin Society. 



assign to the lines their places in these series. The kind of for- 

 mula to be tried was suggested by Balmer's Law for the lines in 

 hydrogen, viz. : 



where k stands for the number 274*263. In this formula n be- 

 comes the oscillation-frequencies of the several hydrogen lines, 

 when for m we write in succession the positive integers 3, 4, 5, &c. 

 For the spectra of the other light monads, including sodium, 

 Rydberg made use of the form 



n = A + -. , (2) 



in which the quantities A, B, and h have to be determined for each 

 series. Kayser and Runge preferred the form 



7? C 



n = A + —^ + —^, (3) 



in which the three constants to be determined for each series are 

 A, B, and C. Either formula can be made to agree tolerably 

 with the observations, and sometimes in more than one way. 



In a Paper communicated last spring to the Eoyal Dublin 

 Society,^ the present author showed that each of the three series 

 in the spectrum of sodium is due to the motion of an electron — a 

 definite electric charge — within the molecules of sodium along an 

 orbit ; or at least to some event taking place within the molecules 

 which follows the same mathematical laws as are furnished by such 

 a motion of an electron. This motion may be resolved into its 

 elliptic partials by Fourier's Theorem, and it is shown that each of 

 these elliptic partials gives rise to a line in the spectrum, which 

 will become a double line if the partial is exposed to an apsidal 

 shift. It is also shown how the relative sizes, the forms, and other 

 information about the partials may be obtained from the observa- 

 tions ; and especially how the periodic time of each partial may be 

 deduced from the positions of the two constituents of the double 

 line to which it gives rise. It is found to be the periodic time 



1 Stoney on the cause of double lines in Spectra, Scientific Transactions of the Eoyal 

 Dublin Society, Vol. IV., p. 563. 



