2 Mr. W. Sutherland on the 



matter, if we imagine the electrons associated in pairs con- 

 sisting of one negative and one positive electron revolving 

 around one another in such a way that each pair has an 

 average electric moment, then if these moments are similarly 

 directed, the atom as a whole will have an electric moment, 

 and can be investigated as a uniformly electrized sphere. 

 From the laws of molecular attraction we find that there are 

 definite broad principles giving the types of external electric 

 field belonging to different classes of atoms. It will be shown 

 in the present paper that the corresponding internal electric 

 fields cause atomic vibrations in much the same way as the 

 Earth's gravitational field causes the oscillations of pendulums, 

 and its magnetic field causes the oscillations of galvanometer 

 needles. Just as the compound pendulum for many purposes 

 can be schematically reduced to the simple equivalent pen- 

 dulum, so the real atomic vibrator can be reduced to the 

 single electron of the theory of the Zeeman effect, although 

 it is much more complex. The matters to be discussed 

 will be taken under the headings : 1. The Fundamental 

 Constant of Atomic Vibration. 2» A Theory of Dielectric 

 Capacity. 3. A Kinematical Analysis of Balmer's Formula. 

 4. Summary. 



1. The Fundamental Constayd of Atomic Vibration. 



The most notable general fact yet brought out concerning 

 spectra is that for the elements they all depend upon one 

 constant which first made its appearance in the formula of 

 Balmer for wave-length in the hydrogen spectrum. This 

 appears as b in Rydberg's extension of Balmer's formula,, 

 namely 



n — n — b/(m-t-fjiy, 



where n is the number of wave-lengths in a cm. belonging 

 to a line in a series, m is an integer, and yu, like n is a para- 

 meter characteristic of the series. Rydberg, having dis- 

 covered that b has nearly the same value for other elements 

 as for hydrogen, assumed it to be an absolute constant of 

 Nature. Others have found empirical convenience in allow- 

 ing b to vary from one element to another ; for instance, in 

 " The Cause of the Structure of Spectra " (loc. cit.) in the Li 

 family of metals b ranges from 108800 for Rb to 113950 for 

 Cs. For 11 other elements it ranges from 100000 to 110100, 

 so that for 16 elements it ranges from 100000 to 113950. 

 But for Sr it appears to be 96232, and for Ba 89540, the 

 value for Ca being 100000 and for Mg 104320. Even if 

 these variations of b are genuine, and not merely the acci- 



