PRESSURE ON RESISTANCE OF METALS. 641 



of dimensions. X will increase for the same reason, but this increase is 

 sufficient to account for not over 25% of the effect. Hence most of the 

 increase of conductivity must be due to an increase in p. Now this is a 

 most unfortunate member to call on to do the brunt of the work, be- 

 cause it is already sorely overburdened. In fact, one may calculate p 

 from data in a recent paper of Richardson ^^ for tungsten at 2000°. 

 It turns out that p is about 1.7X10^^. Since the figures given by 

 Richardson lead to a minimum value of p it seems evident that parts 

 of the theory must be radically recast. I owe the idea that p is im- 

 probably large to a remark of Professor E. H. Hall. 



Another recently suggested theory which seems to have possibilities 

 is that of F. A. Lindemann.^' According to this theory the electrons 

 are rigidly arranged in the nodes of a space lattice between the atoms. 

 The state of the electrons is therefore that of a perfect solid rather 

 than of a perfect gas. Since however this theory gives essentially the 

 same account of pressure effects as does Wien's recent theory as modi- 

 fied by Griineisen, we may omit special discussion of this and pass to 

 the Wien-Griineisen theory. 



The only serious attempt that has been made to bring pressure 

 effects within the range of an electron theory has been by Griineisen.^ 

 His starting point is the theory of Wien,'^^ who supposes that the elec- 

 tron velocity is independent of temperature. With this assumption, 

 combined with assumption of the quantum distribution of energy, 

 Wien finds a function proportional to the mean free path. Starting 

 with Wien's value of the free path, which he "generalizes", and with 



the help of his theorem that along a line at constant entropy ^ 



remains constant, Griineisen finds a value for the pressure coefficient 

 in terms of quantities most of which are known. There is reason to 

 except that the unknown quantities are not as important as the others, 

 and by neglecting them a formula is obtained for pressure coefficient 

 in terms of compressibility, thermal expansion, specific heat, and 

 temperature coefficient of resistance. The formula follows; 



1 /dw\ ^ 1 fdu\ _ 2 (dN\ _ 1 /dv\ _ J_ fdv\ 

 w\dpjt u\dpjs N\dpJs v\dpjs Cp\dTjp 



w\d 1 /p 



The first two terms, which represent the change of electronic velocity 



36 O. W. Richardson, Phil. Mag. 30, 295-299 (1915). 



37 F. A. Lindemann, Phil. Mag. 29, 127-140 (1915). 



38 W. Wien, Columbia Lectures, (1913), p. 29. 



