96 PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



It appears that, whatever the kinetic configuration may be which is the source of 

 the vibrations, the light periods depend on the difference of frequency of two systems, 

 each with distinguishing train of frequencies. This train, or sequence, we have 

 denoted in the foregoing by putting the letter V before the letter representing the 

 series. In what succeeds we will refer to them as the P-sequence, S -sequence, and 

 so on. We recognise four typical sequences, the P, S, D, and the new F type. The 

 evidence adduced in the preceding goes to show that the F type is the fundamental 



c 



or primitive type. The P is formed from it by adding sbll -- j, where b, c are 



\ ?H/ 



constants, or atomic volume term x (1 m~ l x. '195 ?), the D by deducting the same 

 term or the atomic volume term, with some as yet unknown law for the term in a./m. 

 The S term is found roughly by deducting a constant from the /x, of P. The theory 

 will fall in, as we shall see, with the Li, H, and He spectra also. Regarded from this 

 point of view, we may look upon P as standing for positive, D for difference, and S 

 for semi. 



Lithium. 



It is now time to take up the discussion of the spectra of lithium in the light of 

 the knowledge gained from the consideration of the other alkali metals. The spectra 

 of Li have been arranged like the others in three typical series, called the P, S, and 

 D series. Taking these letters at present to stand for the arrangement hitherto 

 accepted, and using the first three lines of each to calculate the constants, there 

 result the following formulae : 



P. . n =-- 43482'20M8-N/{m + "951609+ (318) + wr 1 x ['007365 (262)]} 2 

 S. . i = 28579'44 -54-N/{>i + '602191+ (389)-r 1 x[-013039 + (735)]} 2 

 D. . n = 28579-994-52-N/{m+l-000845 



The first glance shows at once that the lines ascribed to the P series follow a 

 D type, and those of the D look like a P type. Also the values of the constants are 

 very different from what we should be led to expect from the relationships discovered 

 amongst the other elements. We should all the more expect to find these relations 

 to hold, since Li falls in so closely with the analogous relationships for the atomic 

 volume. In the above formulas 



D of P( co ) = 1-588172+ (21) D of P(l) = 1-958974+ (23) 



D S( oo) = 1-958993+ (13) D S (l) = T589152 (354) 



D D(oo) = 1-958980 + (115) D D(l) = 1'995451(2183) 



It follows at once extremely closely that the laws (D), (F) hold, viz., 



