TABLE 322 

 SPECTRUM SERIES 



275 



In the spectra of many elements and compounds certain lines or groups of lines (doublets, triplets, etc.) occur in 

 orderly sequence, each series with definite order of intensity (generally decreasing with decreasing wave-length), pres- 

 sure effect, Zeeman effect, etc. Such series generally obey approximately a law of the form 



I - / _ N 

 = X (m + RP ' 



where v is the wave-number in vacuo (reciprocal of the wave-length X) generally expressed in waves per on; m is a 

 variable integer, each integer giving a line of the series; L is the wave number of the limit of the series (m = ); N, 

 the "Universal Series Constant"; and R is a function of m, or a constant in some simple cases. 



Balmer's formula (1885) results if L = N/n*, where n is another variable integer and R = o. Rydberg's formula 

 (1889) makes R a constant, and L is not known to be connected with N. Other formulae have been used with more 

 success. Mogendorff (1906) requires R = constant/^, while Ritz (1003) has R = constant/wt*. Often no simple 

 formula fits the case; either R must be a more complex function of m, or the shape of the formula is incorrect. 



Bohr's theory (see also Table 515) gives for Hydrogen 



If = {2ir*me*(M + m)}/MA, 



where e and m are the charge and mass of an electron, M the atomic weight, and h, Planck's constant. The best value 

 for N is 109678.7 international units (Curtis, Birge, Astrophys. J. 32, 1910). The theory has been elaborated by Som- 

 merfeld (Ann. der Phys. 1916), and the present indications are that N is a complex function varying somewhat from 

 element to element. 



Among the series (of singles, doublets, etc.), there is apt to be one more prominent, its lines easily reversible, called 

 the principal series, P(m). With certain relationships to this there may be two subordinate series, the first generally 

 diffuse, D(m), and another, S(m). Related to these there is at times another, the Bergmann series B(m). m is the 

 variable integer first used above and indicates the order of the line. 



The following laws are in general true among these series: (i) In the P(m) the components of the lines, if double, 

 triple, etc., are closer with increasing order; in the subordinate series the distance of the components (in vibration 

 number) remains constant. (2) Further, in two related D(m) and S(m), Av (vibration number difference) remains 

 the same. (3) The limits (L) of the subordinate series, D(m) and S(m), are the same. (4) Av of the subordinate series 

 is the same Av as for the first pair of the corresponding P(m). (5) The limits (L) of the components of the doublets 

 (triplets, etc.) of the P(m) are the same. (6) The difference between the vibration numbers of the end of the P(m) 

 and of the two corresponding subordinate series gives the vibration number of the first term of the P(m). The first 

 line of the S(m) coincides with the first line of the P(m) (Rydberg-Schuster law). 



ther inform i 



the following tables, based greatly upon L>unz's Die benengesetze der JLimenspeiura, IJiss., Tubingen, 1911, wmcn 

 has also appeared in book form, Hirzel, Leipzig. The following gives a schematic arrangement of the various series of 

 a family in accordance with some of the above laws: 



Let {m, a, a} = N/(m + a + a/m 2 ) 2 ; VP(m) = \m, p, IT); VD(m) = \m, d, d)' VS(m) = \m t s, ff) and 

 VB(m) = {m, b, /3); V originally referred to the variable part of the formula; when m takes a specific value, 

 it becomes a constant term, viz. FS(i). 



Then a single line system is represented as follows: 



P'(m) = FS'(i) - VP'(mY, Vfa) = FP'(i) - FZX(f); 



S'(m) = FP'(i) - VS'(mY, [B'(m) = VD'(i) - VB'(m)}. 



A system of double lines would be represented as follows: 



P\"(m) = VS"(i) VPi"(mY, Di"(m) = FP"(i) VD"(mY, 



P 2 "(m) = F5"(i) - VP 2 "(mY, D 2 "(m) = FP"(i) - VD"(mY, 



Si"(m) = FP!"(i) - VS"(mY, {Bi"(m) = FZ>"(i) - VB"(m)}; 



S 2 "(m} = FP 2 "(i) - VS"(mY, \B 2 "(m) = VD"(i) - F-B"(m)). 



And similarly for a series of triplets, etc. 



Series Spectra of the Elements. The ordinary spectrum of H contains 3 series of the same kind: one in the; Schu- 

 mann region, v = N(*/i 2 l /n?),n, 2, 3 . . .; one in the visible, v = N( l /2* V 2 ), n, 3, 4, 5- ', and one in the infra- 

 red, v = N^/Z? V 2 ), n,4,s,6. . .He has three systems of series, one " enhanced," including the Pickering series 

 formerly supposed to be due to H. The next two tables give some of the data for other elements. 



2,66 



1 



0.5>u 



0.3^ A 



1 



GUI 3|45 oo 



2| 3|4|5||oo 



21 3l4l5||oo| 



D(m) 



5000 10000 



20'000 



30t)00 



SEHIES SYSTEM or POTASSIUM. 



SMITHSONIAN TABLES. 



