644 BRIDGMAX. 



agreement with theory: Beckman's conclusion need not be altered, 

 therefore. 



A mere comparison of the approximate formula with experiment is 

 not at present sufficient to show, however, the correctness of Grii- 

 neisen's fundamental assumption, because the formula is obtained by 



nesflectins; an unknown term, ( - ] , whose presumptive magnitude 



u \dpjs 



might possibly be j of the entire effect. It therefore is pertinent to 

 consider the nature of the assumptions wdiich Griineisen has put into 

 his theory. The general nature of the underlying idea is as follows. 

 It was a cardinal point of Wien's theory that the length of the free path 

 is determined by the motions of the atoms; at higher temperatures the 

 amplitude of atomic vibration becomes greater, and so interferes more 

 with the freedom of electronic motion and decreases the free path. 

 The sign of the pressure effect is explained by showing that as pressure 

 increases at constant temperature the decrease of amplitude of atomic 

 vibration in A-irtue of the increased frequency more than counter- 

 balances the decreased distance between atomic centers due to volume 

 compression, so that free path, and therefore conductivity, increase. 

 The starting point of Wien's theory is the formula already given, 



w = "V^f? • Wien assumes that u and N are both independent of tem- 



perature. It is to be noticed, however, that Wien was concerned only 

 with temperature effects, and for these, as already mentioned, changes 

 of volume may be neglected. W'ien's hypothesis that N is constant 

 must not therefore be understood as committing Wien to the statement 

 that when changes of volume are considered the number of free 

 electrons per cm^ is constant. On the contrary, it is clearly sug- 

 gested, although not explicitly stated, that Wien meant the number 

 of electrons per gm. to remain unaltered. This would mean that Nv 

 is constant. Certainly in the absence of any special examination of 

 the effects of varying electronic dissociation, this is the only plausible 

 hypothesis to make. Now in Griineisen's deduction of the formula 

 he has not assumed either that N or Nv is constant, but has left N in 

 the equation and differentiates it, and arrives at a formula containing 



-r^ ( — — J . This he assumes can be neglected in numerical magnitude 

 N\d'pJ> 



on the basis of experiments of Wagner ^^ on the effect of pressure on 



thermo-electromotive force. But the calculation of ^f ( ^r~ ) from 



N\dpJ, 



Wagner's data proceeds on the assumptions of the gas-free-electron 



