THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 553 
Still more convenient for computation are the following transformations, in which », 
and A,, the wave-frequency and wave-length of the xth line of the spectrum, are 
introduced : 
1 mi 1 y a 1 1 ds ; 
Vov, \vo—v,/ a, (m+pyP—(e@+pe* ve—v, (m+pyP—-wtePet 8 
(5) 
1 ( de) 1 1 1 as 
aie eS: a Gal eae we Gee eee te 
The advantage of using these two formule lies in the fact that we may choose for 
y, or X, the wave-frequency or wave-length of any observed line of the series, whereas 
in the preceding equations »), v» and Ay, A» are quantities not directly obtainable from 
the observations. The arithmetical process of evaluating the other three unknowns is 
thereby greatly facilitated. Lastly, we may write 
er, 1 a eh b 
V—=V  Ay(Ve — v)*(m +p pet ve fo vy (m+ py? : 
(6) 
it ae one 1 a, 
; = == Gea Sea 
equations which will be specially useful in the investigation of the band-series. 
In comparing first our formula with the observed wave-frequencies of line-series, 
we shall make use of equation (2), and apply it in this form to all the series 
mentioned in Professor Kaysrr’s Handbuch der Spectroscopie, vol. u. I may state 
at once that in all cases the constant « was found to be a proper fraction, the 
denominator of which is represented by an entire multiple of 5, or, expressed in 
algebraic symbols , De p and q being integers. As unit of wave-length the 
tenth-metre or Angstrém unit was adopted, while for » the value 108-1 was taken, in 
accordance with Kayser and RunGE and others. When not mentioned otherwise, the 
wave-lengths and oscillation-frequencies are reduced to the Rowland scale. 
A. Ling-SEries. 
Group of Alkali metals.—There are two distinct kinds of series of spectra in the 
elements of this group: the “ principal ” series, consisting of strong and sharply defined 
lmes—the principal lines of the spectrum—which are easily reversible, and one or two 
fainter “subsidiary” series represented by hazy lines, with little or no tendency to reversal. 
These lines have been observed with very different degrees of accuracy. Kayszr’s tables 
contain a column indicating the estimated probable limits of the observational errors 
expressed in units of wave-length. These limits are given in the last columns of the 
following tables, but in units of wave-frequency. Although the estimated uncertainties of 
the observed wave-lengths cannot be considered as quite reliable, they may nevertheless 
convey an approximate idea of the accuracy to be expected in our comparison. 
