220 BRIDGMAN. 



(this is merelv the coefficient "a" of the formula — = — ap + op 2 , 



> o 



where p is expressed in kg/ cm 2 ). In the third column is given the 



initial proportional change of compressibility with pressure, or 



) . Here — is 26 of the above formula for change of volume, 



Xdp/o dp 



and Xo is the "a" of the formula. In the fourth column is given the 



/l da N 

 initial proportional change of thermal expansion with pressure 



/da\ 

 In calculating the figures of this column, the derivative I — ) , 



is the same as I — ) or — , was computed from the detailed formulas 

 \dt/o ot 



already given for the compressibility at 30° and 75° merely by sub- 

 tracting the value of "a" at 30° from the value at 75° and dividing by 

 45. The value of a 1 took in most cases from the table in the paper 

 of Richards 1 summarizing his compressibility data. In the fifth 

 column is given the proportional change of expansion of the fourth 

 column divided by the compressibility "a." Finally in the sixth 

 column is given the proportional change of compressibility divided 

 by the compressibility. An examination of the details of the measure- 

 ments will show that less accuracy is to be attached to quantities 

 involving changes with temperature than with pressure. 



In every case the compressibility decreases with increasing pressure. 

 This is entirely what we would expect, but I do not know that there is 

 any necessity here, so that a case of increasing compressibility with 

 pressure would violate any of the laws of physics. In fact it is not at 

 all inconceivable that this may be found to be actually the case for 

 some exceptional substances. For instance, there are a number of 

 cases known in which the polymorphic form with the smaller volume 

 has the larger compressibility, and it is conceivable that a change 

 similar to one which in the case of polymorphism takes place abruptly 

 might in some cases be brought about gradually by increasing pressure, 

 so that the form stable at the higher pressures and therefore with the 

 smaller volume should be the more compressible. In fact for potas- 



1 f dv \ , ,. , . 



sium the proportional compressibility,-! — I , does increase slightly 



at the higher pressures. 



The order of magnitude of the change of compressibility with 

 pressure, when pressure is expressed as here in terms of kilograms per 



