HEINRICH HERTZ 367 



the atoms,^ but it shows certain peculiarities there, which 

 are not contained in Maxwell's equations, and still form 

 the subject of continued investigations.* 



Thus Maxwell's equations also have their limits of validity; 

 they relate only to electro-magnetic fields at a sufficient dis- 

 tance from atoms and to all phenomena thus taking place. 

 It is remarkable in this connection that these fields - which 

 alone were known before the discovery of cathode rays, and 

 have been studied since Coulomb's time - never come into 

 existence in any other way than by springing from the in- 

 terior of atoms. No free electric charges are known which 

 do not arise from atoms, within which the elementary parti- 

 cles of positive and negative electricity are found in the 

 closest connection; if charges are to be collected, it is neces- 

 sary somehow to separate sufficiently far from one another 

 the two kinds of electricity, which are found nowhere else 

 than in atoms, and by virtue of the lines of force which con- 

 nect them, always strive to return there. When this is done, 

 the field given by Maxwell's equations comes into being be- 

 tween the two kinds of electricity which have been collected 

 in the form of a very large number of elementary charges. 



The same is true of all magnetic forces which we use, even 

 the strongest, such as those which drive electric railways. 

 They can only be obtained by means of moving electricity 

 obtained from atoms, or directly from atoms (best iron atoms) 

 in which moving electricity is already present, all that is 

 necessary being to arrange the fields of the many such atoms 



^Accordingly, Maxwell's equations can be applied in certain respects 

 to electio-niagnetic fields within matter, for which purpose the constants 

 (di-electric, magnetic, conductivity), appearing in the equations, are re- 

 quired. The dependence of the velocity of propagation (refractive 

 index) upon the wave-length can be coriectly calculated by the equations 

 when the atoms or molecules of matter aie regarded as electric resonators 

 with their own peiiod of oscillation (electro-magnetic theory of disper- 

 sion). 



2 A possible conception of the electric and magnetic lines of force 

 which could also be applied inside the atom, will be found in my publica- 

 tion Vber Ather und Materie, Heidelberg, 191 1. 



