638 BKIDGMAN. 



When the magnitude of the change of volume produced by a pressure 

 of 12000 kg. is considered, however, it does seem that the results 

 acquire a physical significance great enough to justify the extension 

 of the range. The volume of many of the metals at 0°C and 12000 

 kg. is less than the volume at atmospheric pressure at 0° Abs. The 

 resistance of most metals tends towards zero at 0° Abs., but at 0° C at 

 the same volume the resistance is only a few per cent less than under 

 normal conditions. Any valid theorj^ must explain the surprisingly 

 little effect of the element of volume alone apart from the element of 

 temperature. It is furthermore known that at very low temperatures 

 the connection between resistance and temperature changes its char- 

 acter; the relation ceases to be linear, and the resistance curve ap- 

 proaches the origin tangentially to the temperature axis. Whether the 

 abrupt discontinuity shown by several metals a few degrees above 0° 

 Abs. is an effect of a polymorphic transition does not yet seem to be set- 

 tled. It is significant that no trace of any such effect is to be found at 

 room temperature as the volume is decreased toward and beyond its 

 value at 0° Abs. The question whether there is a change in the char- 

 acter of the resistance curves as the volume approaches that at 0° Abs. 

 could not, of course, have been answered by measurements over a small 

 pressure range; it is perhaps some justification of the extension of 

 range that this question can now be answered. 



An estimation as to the comparative volumes at (12000 kg., 0°C) and 

 (0 kg., 0° Abs.) is given in the accompanying Table XXIV. The 

 values of compressibility used in the computations have been taken 

 from Richards ^^, assuming constancy over the pressure range, and the 

 volume at 0° Abs. has been taken from the data of Ch. Lindemann ^^ on 

 linear expansion to 20° Abs. The Table includes all the metals meas- 

 ured by Lindemann to 20°. Linear extrapolation of data of Grii- 

 neisen ^^ to liquid air temperature shows that tin and magnesium also 

 have a smaller volume under 12000 kg. than at 0° Abs., and probably 

 iron does also. The two metals antimony and bismuth which are 

 abnormal with respect to pressure coefficient are also abnormal here; 

 the decrease of volume under 12000 kg. is more than three times as 

 great as that on cooling to 0° Abs. 



Let us now consider the bearing of the facts at high pressures on 

 various proposed theories of electronic conduction in metals. AVe dis- 

 cuss first theii relation to the classical gas-free-electron theory of 



31 Ch. L. Lindemann, Phys. ZS. 12, 1197-1199 (1911). 



32 E. Griineisen, Ann. Phys. 33, 33-78 (1910). 



