Cause of the Structure of Spectra. 259 



term is 



l-fn+jn«, (14) 



where n is or a positive integer. Thus the law of v can be 

 written 



*/=«(! -|n + fn 2 )+/3, .... (15) 



where a and /3 are parameters characteristic of each natural 

 family ; for the Zn family « = 386'2, and /3 = 0; for the Na 

 family a=19'6, and /3=— 2. 



We can summarize the values of a and /3 in the following- 

 table, where v and v x denote whether the values belong to the 

 difference for a pair of lines v, or the first difference v x where 

 the Hues go in threes. 



Na stands for the Na family of metals, Cu for Cu, Ag, and 

 Au, while Ga stands for Ga, In, and Tl. 



Table II. 

 Na. Mg. Zn. Cu. Ga. 



a 19-6 31 386-2 325 633 



/3 -2 10 - 83 191 



The following numbers give a comparison of the values of 

 v 1 in the Mg series of metals as given by our formula and as 

 found by Kayser and Runge (Wied. Ann. xliii.) : — 



Mg. Ca. Sr. Ba. 



formula 41 103 382 878 



40-7 101-6 394 878 



A discrepancy, similar to that which occurs here with Sr, 

 occurs with Ag in the Cu family and In in the Ga family. 



An interesting case appears in the series discovered by 

 Runge and Paschen in the difficult spectra of 0, S, and Se, 

 where they find the following values of v: — 



3-7 2-08 



S 18-15 11-13 



Se 103-7 44-07 



Of these numbers four out of the six are the first four terms 

 of the series whose general term is 3' 7 (1 — 3>i/2 + 7n 2 /2), 

 which are 3*7, 11*1, 41*4, and 103*6, while 18'15 is nearly 

 five times 3" 7. 



Some values of v which do not come under this type of 

 formula are those for Vo in the Zn family, namely, 189'8, 

 542, and 1768, which can be expressed as 176 (1, 3, 10) + 12 

 where the series 1, 3, 10 takes the place of the normal 1, 3, 12. 

 For v 2 in the Mg series we have 15'2 (1, 3, 12, 24) +6*2 

 where 24 takes the place of the 28 proper to the normal series. 

 Again, in certain pairs of lines in Ca, Sr, and Ba we have 



