Stoney — Analysis of the Spectrum of Sodium. 207 



which corresponds to the position midway between the two con- 

 stituents 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, however, 

 and the empirical formulae that Eydberg and Professors Kayser 

 and Eunge 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 (pro- 

 bably 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 conspicu- 

 ously placed in evidence by a very simple diagram. For if we 

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



f = ^^-{k-^), (4) 



which, if we regard x and y as running co-ordinates, is the equa- 

 tion of a parabola. Hence the following rule — Draw the fore- 

 going 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 ofi upon it the harmonics 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 Jc. See PI. xvi. fig. 1. 



Now, having regard to the fact that the light monad elements, 

 H, Li, Na, K, Eb, Cs, have all of them series of double lines which 

 appear to belong to the same general type, we are justified in 

 assuming that Balmer'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 = 1/m, the 

 curve passing through the ends of the horizontal lines in the other 

 monads should be some curve of which the parabola is a particular 

 case. This may happen in different ways, but the simplest hypo- 

 thesis is that they are hyperbolas or ellipses. It appeared therefore 



