230 SCIENCE PROGRESS 



metre. The spectrum appears as a series of lines, getting 

 closer and closer together as the wave-length diminishes, and 

 containing no lines of wave-length less than 3646*13. The 

 figure 3646*1 3 is called the " limit " of the series. The intensity 

 of the lines falls off with decreasing wave-length, so that it 

 is not possible to observe many more than 30 of the infinite 

 number of lines that the formula suggests. It has been found 

 useful to modify Balmer's formula so as to obtain an expression 

 for the " wave-number " of the lines instead of their wave- 

 length. The wave-number {v) is the number of lines per 

 centimetre, and is obtained by dividing the wave-length 

 (in angstroms) into 10*, or by dividing the frequency by the 

 velocity of light in free ether. In these terms the formula 



becomes 1^=2 741 8 "75 1 ' There is no other spectrum 



containing quite so simple a series as this, but patient investiga- 

 tion has shown that the majority of line spectra are largely 

 built up by the superposition of a number of series of the same 

 general form. The essential characteristics of a spectrum 

 series seem to be that it has a maximum wave-number (its 

 limit), from which the various members of the series can be 

 calculated by subtraction of a variable quantity, sometimes 

 called the " term " ; that the lines converge uniformly to this 

 limit ; and that the intensity of the lines decreases as the limit 

 is approached — though this last quality appears to be not 

 without exception. In some spectra, each member of a series 

 consists of two, or even three lines, instead of one — ^which, 

 by an extension of our illustration, we might liken to musical 

 chords, giving us harmony as well as melody. There are 

 additional regularities attached to the separation of the com- 

 ponents of such doublets and triplets, but otherwise the series 

 they form have the same general features as the singlet series. 

 Attempts have been made to represent the wave-numbers of 

 spectral series, other than that of hydrogen, by a generalisation 

 of Balmer's formula, but they cannot be said to have been 

 completely successful. The lines are sometimes represented 

 approximately by adding a constant a to the variable m, and 

 still better representation is obtained by changing a into 



fj^ -\ , where //- and a are constant. The resulting formula, 



which seems, on the whole, to be the most satisfactory yet 



N 

 suggested, is then v == A — } ^. from which the lines 



{m + ti + -y 



are derived by inserting consecutive values of m. Here A 



N 



is the limit of the series, and 7 7- is the term. It is 



{m + H' + ^y 



