PRESSURE OX RESISTANCE OF METALS. 645 



theory. One cannot grant that it is permissible to mix in the same 

 equation two theories so opposed in fundamentals. If Griineisen 

 had assumed Xv constant, which seems the only defensible course 

 until an explanation of thermo-electromotive force is provided on the 

 basis of Wien's theory, the compressibility terms would ha\e disap- 

 peared from his formula, with a change in the numerical value of 25%. 



A criticism of Wien's fundamental point of ^-iew is pertinent here. 

 His calculation of the mean free path proceeds on the assumption 

 that the quanta of energy are located in the individual atoms, instead 

 of in the elastic waves, which at present seems to be the accepted 

 conception. It is evident that this change will considerably modify 

 the physical picture of the manner in which the vibrating atoms inter- 

 fere \\ith the motion of the electrons, and might be expected to modify 

 the result. 



Another consideration vitid to Griineisen's theory is the way in 

 which he has "generalized" Wien's expression for the free path. 

 Griineisen's expression is 



= Const ^77 — / ( - — ). 



The important feature about this generalization is the appearance of 

 the atomic volume v. The volume does not enter in the considerations 

 of Wien; its introduction must have been part of Griineisen's process 

 of generalization. It is unfortunate that he gives none of the argu- 

 ment b}' which he reaches the above expression, because the factor v 

 is important, contributing 25% of the total effect, and its appearance 

 in the place where it is involves definite hypotheses about the atomic 

 mechanism. If the free path is proportional to the volume, 

 other things being equal, and if the free path is determined entirely 

 by the vibrations of the atoms, as is supposed in this theory, then the 

 atoms must behave effectively like mathematical points, and not as if 

 they had extension in space. Such a h^^pothesis is at least opposed 

 to the present view of the nature of the atoms in a solid and would 

 seem to require discussion. 



As it now stands, therefore, the theoretical basis for Griineisen's 

 formula requires elaboration in several particulars. But it must not 

 be forgotten that for a first attempt at an explanation of the pres- 

 sure effect the formula works surprisingly well arid must contain 

 a considerable element of truth. It seems to me that the element of 

 truth is to be found essentially in the broad change in the fundamental 



