RECENT STATISTICAL THEORIES 717 



the curve representing this function should make an acute angle with 

 the axis of E where they intersect at £max- The Maxwellian distribu- 

 tion predicted by the classical statistics for the interior electrons 

 suggests however that the curve in question should approach the 

 axis asymptotically. The new statistics leads also to certain inferences 

 about the shape of the curve for values of E less than £,„ax. A great 

 quantity of data bearing on this subject has been obtained by Ives 

 and his collaborators; but the interpretation is made difficult by the 

 presumption that some allowance must be made for the energy- 

 losses suffered by electrons after they absorb quanta but before they 

 reach the surface, and will require much study. 



Paramagnetism of the Electron-Gas 



The susceptibility of the electron-gas was calculated by Pauli even 

 before the specific heat was evaluated by Sommerfeld, but as it 

 involves an extra complication I have inverted the historical order. 



The complication is due of course to that assumption which is made 

 in order to explain why the electron-gas should be magnetic at all — 

 the assumption that electrons are magnets. Perhaps I am too cautious 

 in referring to it as an assumption, it being so well authenticated 

 by the gyromagnetic effect and by the general usefulness of the 

 "spinning electron" in the explanation of spectra. These phenomena 

 impose a special value on the magnetic moment yuo of the electron, 

 to wit, the value, 



/xo = eh/SwrnoC, (80) 



mo standing for the rest-mass of the electron. Further they require 

 that when the electron is floating in a magnetic field, its moment 

 (considered as a vector) shall be either parallel or anti-parallel to the 

 field. Denote by 6 the angle between the moment of the electron 

 and the magnetic field: then 6 must be either or vr.'^ Now when a 

 magnet of moment M is inclined at an angle ^ to a magnetic field //, 

 its "extra magnetic energy" is — Mil cos 9.^- In dealing with the 

 electron-gas, then, we are in effect assuming that when a field // is 

 applied to it the energy of every electron is either increased or decreased 

 by the amount: 



A = £>////; 8 TTWoC. (81) 



'1 It comes to the same thing, and may on other grounds be preferable, to assign 

 Mo twice the value given in (80), and to 6 the values 60° and 120°. 



12 The magnetic energy, or energy due to the "interaction between the magnet 

 and the field" is put equal to zero when the magnet is transverse to the field, which 

 is consistent with the picture that the field alters the energy of the magnet by speeding 

 up or slowing down the revolving electricity. The formula here given is a first 

 approxinaation. 



