Electron Theory of the Metallic State. 751 



With values for k and p valid for the absolute zero-point, 

 the values for jjl would have been greater by about 1 

 and their mean thus equal to 9 — a value that we will 

 use in our further calculations. As the calculations of 

 Born and Lande applied to the metallic space-lattiee would 

 oive f*=5 also for a cubical symmetry, the derivation of 

 /x = [) from the experiments seems, if our theory holds, 

 to indicate another symmetry as more probable than that of 

 the cube. 



Haber has calculated fi in the same way also for the 

 alkaline metals and found here much smaller values, 

 between 2*4 and 3'5. . As, however, he assumes the 

 alkaline metals to have the same structure as their halogen 

 salt>, which is, at least for Na and Li, not consistent with 

 the results found by Hull by the X-ray analysis, these low 

 values are not as yet in any way definite. 



§ 6. Motions and Kinetic Energy of the Electrons at 

 High .7 emperature. 



To get an understanding of the electric conduction, we 

 must discuss the motions of the electrons in relation to the 

 atom space-lattice — a phenomenon that has hitherto been 

 left unconsidered. It follows from our general assumptions 

 that this motion must be intimately connected with the 

 motions of the atoms. To see this, we may for a moment 

 consider what would be the case if the atoms were at rest. 

 From the equations of §4 it is easily seen that the energy 

 required to overcome the hindering forces from the atoms 

 passed by, when an electron is displaced from one point 

 of equilibrium to another, even though all neighbouring- 

 electrons were supported in the same way, so that no forces 

 from them were to be added, would be more than a hundred 

 times greater than the energy of a gas molecule at ordinary 

 temperatures. The electrons thus would not go very far 

 away from their equilibrium positions. 



In the same way, the thermal oscillations of the atoms 

 cannot have any great amplitudes without a similar motion 

 of the electrons. Now the atomic amplitudes are thought 

 to be considerable, and are, in the neighbourhood of the 

 melting-point, of the same order of magnitude as the atomic 

 distances, so that the atoms* mean velocity is of the order 

 2vB. if v is the frequency and 8 the atomic distance. The 

 velocities of the electrons will then be of the same order. 

 But as the electrons are much smaller and lighter than the 

 atoms, it seems probable that there will be an irregular 

 transport, of electrons, so that the electrons' space-lattice 



