the Spectrum of Sodium. 505 



of fju for the various parts of the spectrum shall have been 

 made. 



Method of Analysis. 



The spectrum of sodium, so far as it has been explored, 

 consists of 14 pairs of lines, and of 8 others which have not 

 jet been seen to be double. Professor Rydberg and Pro- 

 fessors Kayser and Runge independently discovered that all 

 the observed lines — with one remarkable exception — lie in 

 three definite series, somewhat similar to that which Dr. 

 Huggins had found in the Spectrum of Hydrogen ; and they 

 have worked out empirical formulee which assign to the lines 

 their places in these series. The kind of formula to be tried 

 was suggested by Banner's Law for the lines in hydrogen, 



viz. 



"-K 1 -?) (1) 



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

 becomes 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 + 7 — —rr 2 , (2) 



(m + h) 2, v J 



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

 for each series. Kayser and Runge preferred the form 



n = A+^ 2 + —±, (3) 



mr m 1 v ' 



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 year to the Royal 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 



* Stoney, "On the Cause of Double Lines in Spectra," Scientific 

 Transactions of the Royal Dublin Society, vol. iv. p. 5b'3. 



