Line-Spectra of the Chemical Elements. 335 



Between the principal and the sharp series there is also a 

 very close relation. For if we write the equation (1) in the 

 more symmetrical form 



■ g _ I L_ m 



± N -K + / , 1 ) 2 (m 2 + ^ 2 r * * ' K) 



it is found that this equation, without varying the constants a*i 

 and jj, 2 , will represent a principal series or a sharp series, ac- 

 cording as we assume the one or the other of the integers m 1 

 and ?n 2 to be variable ; to the number which is left unchanged 

 we must assign the value 1. 



To calculate with great approximation the spectrum of one 

 of the alkaline metals, we use only four constants (with Li 

 but three) , the common constant N not included. 



By the proposal of a system of notation for series and 

 lines, I have tried to show a way by which we can indicate 

 shortly the connexion of the different parts of a spectrum 

 with the whole system of vibrations, and which at the same 

 time allows the correspondence of the lines of different ele- 

 ments clearly to appear. A few examples will suffice to show 

 the arrangement and the use of this system. K [D 1? 4] 

 denotes the fourth line of the first diffuse series of the spec- 

 trum of potassium (\ = 5801) ; Mg [S 2 ] the (whole) second 

 sharp series of Mg (\= 5172-0, 333P8, 2938*5, 2778'7, 2695, 

 2646); Bb [P 12 , 2] the second doublet of the principal group 

 of Bb (\=4202 and 4216); the single lines are denoted bv 

 Bb [P„ 2] and Bb [P 2 , 2] respectively. 



4. The wave-lengths (and the wave-numbers) of corresponding 

 lines, as well as the values of the constants v, n , /jl of corre- 

 sponding series of different elements, are periodical functions of 

 the atomic weight. 



As an example, the wave-lengths of the second term (m = 2) 

 of the diffuse series may be taken together with the values of 

 v (with the triplets v x and v 2 ), which are given in smaller 

 figures in their respective places between the wave-lengths. 

 These values of v are means from the differences of the wave- 

 numbers of all doublets which have been employed in the 

 calculation. The components of the doublets are themselves 

 double ; the less refrangible of the secondary components is 

 the weaker, but corresponds to the constant difference, and is 

 consequently to be reckoned as the true component of the 

 doublet. 



