640 BRIDGMAN. 



experiments that if a metal is warmed from 0° Abs. and pressure is 

 simultaneously applied so as to keep the volume constant, that the 

 change of resistance is very nearly the same as if the metal were 

 allowed to expand freely when heated. But under heating at con- 

 stant volume, the mean free path according to the fundamental point 

 of view must remain constant, and we can explain the facts only by 

 supposing N to decrease proportionally as VT increases. Such a 

 hypothesis is to say the least improbable. 



The classical theory also meets difficulties in explaining the negative 

 pressure coefficient of resistance at constant temperature. As volume 

 decreases with increasing pressure at constant temperature, the mean 

 free path must decrease, and the decreased resistance can be accounted 

 for only by an increase in N. But from work by Wagner ^^ on the 

 effect of pressure on thermo-electromotive force, it appears that N 

 must decrease slightly as pressure increases. 



Dismissing, then, the gas-free-electron theory, we consider several 

 of the recent attempts to improve upon it. Perhaps the most radical 

 of these is the recent revival by J. J. Thomson ^* of a theory of his dat- 

 ing back to 1888, in which he assumed the atoms of a metal to be 

 electric doublets continually emitting and absorbing electrons along 

 their axes. In an electric field there is a resultant orientation in the 

 direction of the field which gives rise to the current. This theory has 

 many formidable difficulties, in fact it seems in certain aspects almost 

 grotesque, but as Lees^^ has remarked, it seems to offer possibility of 

 at least qualitative solution of many of the problems before which 

 the older theory was helpless, and therefore should not be cast lightly 

 aside. It is interesting to see what account this gives of the variation 

 of resistance with pressure. At not low temperatures the formula for 

 conductivity is 



„ _ 1 NepdM 



where N is the number of doubtlets per cm^, e electronic charge, p the 

 number of electrons emitted by an atom per second, d the distance be- 

 tween centers of adjacent atoms, M the moment of the doublet, and k 

 the gas constant. If now pressure is increased at constant tempera- 

 ture, d and M must both decrease, if anything, because of the change 



33 E. Wagner, Ann. Phys. 27, 955-1001 (1908). 



34 J. J. Thomson, Phil. Mag. 30, 192-202 (1915). 



35 C. H. Lees, Nat. 95, 675-677 (1915). 



