18 SECTIONAL ADDRESSES. 



work of Liveing and Dewar and of Hartley, who appear, however, to have 

 made no very serious attempts to represent their results in any systematic 

 way. The first important step in this direction was the formulation by 

 Balmer in 1885 of the law of the line spectrum of hydrogen, in which the 

 four laboratory and ten stellar lines then known were represented by a 

 very simple formula involving a sequence of integers. The idea of a 

 ' series ' of spectrum lines which originated in this way was shortly after- 

 wards extended by Kayser and Runge, and by Rydberg, to the regularities 

 in other comparatively simple spectra, with results which are now generally 

 familiar. Three types of series — the so-called Principal, Sharp and Diffuse 

 series'- — were recognised, and while some of the series consisted of single 

 lines, others consisted of doublets or triplets.'"' 



The foundations for subsequent developments were firmly laid by the 

 classical work of Rydberg, in which the interrelationships of the different 

 series in the spectrum of a single element were clearly formulated. 

 Rydberg also suspected that other lines might be brought into the series 

 relationships, but it is to Ritz that we owe the first clear statement of the 

 ' combination principle ' and the emphasis which it gives to the significance 

 of spectroscopic ' terms ' as distinct from spectrum lines. 



In the representation of series spectra the wave-number of a line 

 always appears as the difference of two terms, and a series of lines appears 

 as a regular succession of differences between a limiting term and a 

 sequence of terms, the limit itself being a term of another sequence. Thus 

 the entire line spectrum of hydrogen, including the ultra-violet and infra- 

 red series, as well as the Balmer series, is represented by dift'erences between 

 terms of the form R/«^ where R is the Rydberg constant (=109,678 in 

 wave-number) and n takes successive integral values beginning with 1 

 and theoretically extending to infinity. Other spectra are more complex, 

 but lines in these also were found to be represented by dift'erences between 

 terms of the form R/(n*)^, where n* is not restricted to integral values and 

 has different values for the different sequences of terms included in a 

 spectrum ; ?i* increases, however, approximately by unity from one term 

 to the next in each sequence. 



Much of the early work on series regularities in spectra is summarised 

 in the now well-known symbolic representation of a series system, namely. 

 Principal series . . . . . . ..IS — wP, 



Sharp series . . . . . . . . 1 P, — wS 



Diffuse series . . . . ..IP, — »iD, 



Fundamental series .. .. 2D, — mF, 



where 1 S, for example, represents an individual term, and mS a sequence 

 of terms of S type. The S terms are always single, but the others are 

 complex in all but singlet systems ; so that i=l for singlets ; 1, 2 for 

 doublets ; and 1, 2, 3 for triplets (in the older numeration). A sequence 

 of terms may be represented by an approximate formula such as that 

 of Hicks, in the form R/[m-|-(j(. + a/m]'", where R is the Rydberg constant, 

 m a serial number, and [x and a constants (usually proper fractions) to be 

 determined from the observed Unes. The possible combinations of terms 



- The ' Fundamental Series ' was added later. 

 * See Fowler's ' Report on Series.' 



