246 Mr. W. Sutherland on the 



the periods of the corresponding lines in their spectra is of 

 the order 5 : 4. Now the Cs atom, in addition to its funda- 

 mental vibration, has harmonics, including one whose period, 

 being a sixth of that of the fundamental, is the same as the 

 fundamental of the Li atom. Thus all the elementary atoms 

 have mechanical vibrations of the same or nearly the same 

 frequency, and this mechanical vibration of characteristic 

 frequency is the one which most efficiently forces the vibration 

 of the atomic electrical apparatus. Thus it comes about that 

 the spectra of the elements are only differently accentuated 

 parts, or slightly modified forms, of the spectrum belonging 

 to a certain common standard vibrator. 



As to the nature of the electrical vibrator common to the 

 atoms, it will be shown to consist probably of two parts, 

 whose relative motion produces the luminous vibration. It 

 is on account of this dependence on relative motion that 

 spectra do not show simple harmonic relations, but the 

 complex harmonic relations implied by Balmer's formula. 

 It will be shown that Balmer's formula can be generalized so 

 as to bring out the principle of harmonics in spectra, and a 

 striking harmonic series in the spectrum of magnesium will 

 be demonstrated. The laws of the spectrum discovered by 

 Rydberg will be discussed and extended. The work will be 

 taken in the following order : — 



1. Balmer's law, and optical harmonics as overtones and 

 undertones. 



2. A special series in the magnesium spectrum confirming 

 the existence of optical harmonics. 



"6. A kinematical analysis of Balmer's formula. 



4. Rydberg's laws. 



5. Two supplementary principles. 



6. Demonstration that the atoms of the elements have 

 fundamental mechanical periods of .vibration which are har- 

 monically related to one another. Consequences of this, such 

 as vibrations of electrons forced by mechanical vibrations of 

 atoms. 



7. Free vibrations of the aether of atoms. 



8. Further analysis of Balmer's formula and Bydberg's 

 laws. 



9. Summary. 



1. Balmer's Law, and Optical Harmonics as Overtones 

 and Undertones. 



From the labours of spectroscopists there have recently 

 resulted discoveries as to the laws regulating the structure of 

 spectra, the most important of which are Balmer's formula 



