ELECTRICAL RESISTANCE UNDER PRESSURE. 151 



exceedingly uncertain, because in addition to the uncertainties in the 

 differences of compressil)ility and thermal expansion between solid 

 and liquid, the compressibilities and thermal expansions of the solids 

 themselves at the melting points are in doubt, the actual measurements 

 having been made in most cases only at room temperature. I have 

 had to guess what the temperature variation of the compressibility 

 might be. However, the uncertainty cannot be so large as to change 

 the sign of the effect for sodium and potassium, for which there can be 

 no doubt that the temperature coefficient at constant volume, as well 

 as the coefficient at constant pressure, is positive. This is the reverse 

 of the behavior of mercury. The data for bismuth are in much more 

 doubt, howe^'er. Assuming the figures shown, the coefficient at 

 constant Aolume is also positive, but the uncertainty is so great that 

 the sign might well be negative. 



The coefficient at constant volume of liquid lithium is of course 

 positive, since the pressure coefficient at constant temperature is 

 abnormal in being positive. The data are not at present known for 

 gallium, so that it is not possible to make any sort of an estimate 

 as to the probable value of its coefficient at constant volume. 



The outcome of this investigation, therefore, for the only two metals 

 for which the results can be sure, is to reverse the behavior previously 

 found for liquid mercury. In this connection it is to be remarked 

 that the temperature coefficient at constant pressure of liquid mercury 

 is abnormal in being very low, and the corresponding coefficients of 

 liquid sodium and potassium are abnormal in being very high. It does 

 not yet appear, therefore, what the probable value of the constant 

 volume coefficient would be for the more usual metals, such as lead. 



The second point of theoretical interest brought out in the previous 

 discussion was the intimate connection between the changes of 

 resistance and the amplitude of atomic vibration. ^^ It appeared that 

 the relative change of resistance, whether brought about by a change 

 of pressure or of temperature, was approximately equal to twice the 

 relative change of amplitude under the same change. The relation 

 was by no means exact, there being failures by as much as a factor of 

 two in some cases, but on the average the agreement was rather good 

 for a large number of metals. The question is whether these new 

 elements also show the same relation? 



In making the computation the following formula for the change" 

 of amplitude with pressure was used 



a\dp/r tv\OT/p 



