Spectra and Planck's Law. 443 



We have supposed, hitherto, that resonance is obtained by 

 the free periods of the electrons in one atom getting modified 

 by the proximity of another. It is conceivable, however, 

 that the same result might be obtained by processes localized 

 in the atom itself and independent of neighbouring atoms. 

 For the atoms of every substance except hydrogen contain 

 more than one unit positive charge, and if the mass of each 

 positive charge is equal to that of the atom of hydrogen, the 

 number of positive charges will be equal to the atomic 

 weight. If the atom is electrically neutral there must be, 

 somewhere or other inside it, an equal number of electrons ; 

 experiment shows, however, that only about half of these 

 are free to exercise any independent effects, the other half 

 must be bound up with the positive charges. If, at long 

 intervals, changes occurred among these positive charges 

 analogous, though on a very much reduced scale, to those 

 which occur in radioactive substances, electrons might be 

 temporarily detached from these charges, though not as in 

 radioactive substances, with such energy as to drive them 

 out of the atom in the form of high-speed /3-ra\s. The 

 displacement of the electrons in the non-radioactive substances 

 would, however, modify the frequency of the vibrations of 

 the electrons in the atom, and would furnish a small supply 

 of atoms whose frequencies differ irregularly from those in 

 the normal atom and which would resonate to vibrations to 

 which the ordinary atom would not respond. 



We have supposed that the periods of the oscillations of 

 the electrons are determined solely by the magnetic forces,. 

 but even when those forces are predominant the electric 

 forces which accompany them will modify, to some extent, 

 the periods, and may make what, if these are neglected, 

 would correspond to a single line become several lines 

 separated by very small intervals. 



It may, perhaps, be worth pointing out that one objection, 

 often raised against the oscillations being due to electrostatic 

 .forces alone, viz. that under such forces, what is primarily 

 given by the equations of motion is the square of the 

 frequency, while the relations given by the series laws relate 

 to the frequency itself and not to its square, does not apply 

 to all types of electrostatic force. If, for example, the force 

 of the positive charge on an electron were represented by 



Ce-~, where is a constant and 6 a function of ?*, then 

 clr ' • 



one set of positions of equilibrium would be determined by 



<£> = ; and if f is the displacement from one of these positions 



