268 Mr. W. Sutherland on the 



for Li, namely 2*0, may be affected with a relatively large 

 error. Disregarding, then, the possibly deceptive maximum, 

 let us follow the general parallelism of the four rows, and 

 remembering the great diversity of the data used in calcu- 

 lating the first row, with (N— l)m/p ranging from 38 to 14, 

 and mjp from 2 to 56, we must regard the parallelism as 

 significant. It means that though the velocities of light 

 through the atoms, that cause the frequencies in the first row, 

 are 10 5 times those causing p n and u n , the former are nearly 

 proportional to the latter. For other metals the corresponding 

 comparison is as follows': — 



Be. 



Mg. 



Ca, 



Sr. 



Ba. 



Zn. 



Cd. 



149. 



•250. 



•221. 



•200. 



•201. 



•286. 



•200. 







39730 



93890 



30860 



24860 



428S0 



40660 



Here the parallelism is not so close, but under the circum- 

 stance it is close enough to have significance. 



8. Further Analysis of Balmer's Formula and 

 Rydberg's Laics. 



To extend the kinematical study of spectra we can use the 



results of Stoney's important contribution, " On the Cause of 



the Double Lines and of Equidistant Satellites in the Spectra 



of Gases" (Trans. Roy. Dublin Soc iv. 1891). Here he 



takes the electron, which he has done so much to get recog- 



. . . . . 



nized as the atom of electricity, as describing an elliptic orbit, 



which may have perturbations of the nature of progression of 

 the apse, precession, variation of ellipticity, and so on. By 

 a kinematical analysis he shows that such perturbed elliptic 

 motion may be regarded as the resultant of two or more 

 circular motions of different amplitudes and frequencies. 

 Such lie takes to be the origin of the doublets and triplets in 

 spectra. By an extension of Fourier's theorem he proves that 

 any motion of a point in a plane may be regarded as the co- 

 existence and superposition of definite pendulous elliptic 

 motions, and again extends this to the motion of a point in 

 space of three dimensions. If the original motion is periodic 

 with frequency F, then by Fourier's theorem the component 

 elliptic motions into which it maybe resolved have frequencies 



F, 2F. 3F If we simplify these ellipses to circles, 



then the angular velocities of the radius vectors will form a 



series 1, 2, 3 But this gives us only the ordinary 



series of harmonics, corresponding to the usual musical 

 overtones ; whereas for the explanation of spectra we want 

 harmonics analogous to what I have called the undertones of 

 a vibrating circle. The mechanically vibrating atom supplies 



