564 Mr. Savidge and Prof. Nicholson on the 



successive members of a series, the numerical solution of a 

 troublesome biquadratic equation, to several significant 

 figures, is essential; and when the process must be repeated 

 with various selections of three lines from a list, the labour 

 is sometimes almost prohibitive. 



When the components of a series form doublets, moreover, 

 one member of the doublet is usually very much weaker than 

 the other; and unless the spectrum is developed very strongly 

 — this development being controlled sometimes by circum- 

 stances not sufficiently understood to enable it to be performed 

 at will, — the weaker member cannot be seen and measured. 

 One of us has shown recently that this is the underlying 

 cause of the apparent non-existence of series in the spectra 

 of an important group of chemical elements, which actually 

 contain series of the usual type, so that the laws of spectra 

 are in all probability of a universal application. This work 

 has not yet been published, but it is mentioned here on 

 account of the fact that the existence of the Table published 

 in this paper alone rendered such a conclusion possible. 



When, in a complicated spectrum, the type of regularity 

 typified by the recurrence of doublets is in this manner 

 apparently absent, there is no real guide to the probable 

 series lines, and a beginning towards their detection can 

 only be made by the use of a graph or Table, with which any 

 two lines can be compared, and an immediate determination 

 made of the third member of their possible series. Graphs 

 are used frequently in this manner by spectroscopists ; but 

 their use is somewhat limited, for they cannot give the 

 necessary degree of accuracy. When a graph leads to the 

 conclusion that three lines may belong to a series, the ensuing 

 verification by a tedious calculation is always necessary, the 

 utility of the graph being limited to the rejection of unlikely 

 cases. 



The need for a Table has always been urgent, and the 

 Table has now been calculated by Mr. Savidge. It has 

 the advantage of being applicable equally to the ordinary 

 arc series with Bydberg's constant N, and to the " enhanced 

 line " type of series recently discovered by Prof. Fowler *, 

 in which this constant is 4N. It can also be applied to 

 series in which this constant may be any other multiple of N. 

 In series spectra developed in the arc, the wave number n of 

 a line is given very closely by the formula 



* Bakerian Lecture, Hoy. Soc. Phil. Trans. 1914. 



