webster. — planck's radiation formula. 137 



(3) m I + | g + f / + / f , , } £ + { f + f / + ^, } £ = « K, 



This equation, being of the standard form for forced harmonic 

 motion with damping, shows at once that the classical theory of the 

 propagation of light through matter is reproducible from this model. 

 For, if the electric force is inclined obliquely to the plane of the mag- 

 neton, the component in the direction perpendicular to this plane will 

 produce practically no effect, on account of the immobility of the 

 charge of the magneton in this direction. Other magnetons, being 

 tipped in other directions, will supply the mobility that is lacking in 

 the one we have considered. 



In the infra-red, where the vibrations of atoms as a whole begin 

 to be of importance, we must superpose the motion of the sort con- 

 sidered above on that of the atom itself. Since each atom has in 

 general very little magnetic moment, it must have magnetons (espe- 

 cially in the groups of eight) turned in all directions. Therefore some 

 of them will always be vibrating with a motion of the center of charge 

 relative to the ring. Their rates of absorption, however, cannot be 

 found from this equation because in a solid or liquid the vibrations of 

 the atoms as a whole will be governed chiefly by collisions with other 

 molecules, while in a liquid or gas the rotation of the molecules will 

 change the direction of the axis of vibration continually and thus 

 prevent the accumulation of large amplitudes. Therefore the rates 

 of absorption are much less than this equation would indicate, as 

 soon as we get to frequencies such influences become noticeable. 

 That this occurs to some extent even in the visible spectrum at ordi- 

 nary temperatures is indicated by the readiness with which absorption 

 of most visible light generally produces heat rather than other effects, 

 such as photo-electric currents or chemical changes, and also by the 

 well known widening of absorption lines by pressure. The fact that 

 such influences may result in a transfer of a certain amount of energy 

 from the vibrations to molecular motions rather than to the steady 

 current of the magnetons, is, as we shall see, entirely immaterial for 

 the derivation of Planck's law, since this derivation depends on con- 

 siderations of probability that are unchanged by this transfer. 



Since each high frequency magneton exposed to radiation will 

 execute a steady vibration, it must store up energy at a constant rate. 

 Likewise at low frequencies, since the oscillations themselves are inde- 

 pendent of the amount already stored, however much they may be 

 affected by molecular motions, the rate of storing will, on the average, 



