506 Dr. G. J. Stoney's Analysis of 



gives rise to a line in the spectrum, which will become a 

 double line if the partial is exposed to an apsidal shift. It is 

 also shown how the relative sizes, the forms, and other infor- 

 mation about the partials may be obtained from the observa- 

 tions ; and especially how the periodic time of each partial 

 may be deduced from the positions of the two constituents of 

 the double line to which it gives rise. It is found to-be the 

 periodic time which corresponds to the position midway 

 between the two constituents of the double line on a map of 

 oscillation-frequencies. 



Now the periodic times of these partials are not simply a 

 fundamental period and its harmonics, as is the case with the 

 vibrations that produce musical notes. Balmer's Law, how- 

 ever, and the empirical formulae that Rydberg and Professors 

 Kayser and Runge have found to be suitable, suggest that 

 they in some way depend on an event of that simple character. 

 In fact this state of things is represented mathematically by n 

 (the position of the line on a map of oscillation-frequencies) 

 being a function (probably some simple function) of 1/m ; 

 which it is both in Balmer's Law and in the above-mentioned 

 empirical formulae. 



In the case of the hydrogen spectrum this relation is con- 

 spicuously placed in evidence by a very simple diagram. For 

 if we write y for 1/m, and x for n, equation (1) becomes 



f=M ■•(*-*), W 



which, if we regard x and y as running coordinates, is the 

 equation of a parabola. Hence the following rule — Draw the 

 foregoing parabola and place its axis horizontal. Erect an 

 ordinate at the distance k from the vertex. Double this out, 

 and, using its double length as unit, set off upon it the har- 

 monics 1/2, 1/3, 1/4, &c. From the points so determined 

 draw horizontal lines to the curve : these are the values of n 

 for the successive lines of the hydrogen spectrum, on the 

 same scale on which the distance of the ordinate from the 

 vertex represents 274*263, which is the value of k (see 

 Plate VI. fig. 1). 



Now, having regard to the fact that the light monad ele- 

 ments H, Li, Na, K, Rb, Cs have all of them series of double 

 lines which appear to belong to the same general type, we 

 are justified in assuming that Banner's Law is the simplest 

 case of a general law which prevails throughout all the light 

 monads. Hence, if the oscillation-frequencies be all plotted 

 down as the horizontal lines of a diagram constructed as 

 above with x=n and y = l/m, the curve passing through the 



