336 PROCEEDINGS OF THE AMERICAN ACADEMY. 



interval from 20° to 40°, 3% for the interval 40° to 60°, and 2% from 

 60° to 80°. The order of accuracy to be expected in these thermal 

 measurements is not so great as that in the compressibility determina- 

 tions, therefore, but perhaps the accuracy is as great as could be 

 expected when one considers the smallness of the quantities invohed, 

 and the difficulty of making such measurements at high pressures. 

 At any rate the absolute value of the coefficient cannot be very much 

 in error. This is made probable by the agreement with the known 

 values at atmospheric pressure. The accuracy is at least high enough 

 to enable us to expect a fairly good quantitative description of the vari- 

 ous thermodynamic quantities under high pressure, even those most 

 sensitive to error. The calculation seems to be worth while carrying 

 through in some detail, because such calculations seem never to have 

 been undertaken for any substance, even for the low pressure range up 

 to 3000 kgm., which is the range over which compressibility determi- 

 nations have been previously made. 



Discussion of Results. 



The first necessity for a calculation of the various thermodynamic 

 quantities is as accurate as possible a knowledge of the relation 

 between pressure, temperature and volume over the entire pressure- 

 temperature plane. It may be shown that this is sufficient to com- 

 pletely determine the thermodynamic behavior of the substance if in 

 addition the behavior of the specific heat at constant pressure, for 

 example, is knov.n in its dependence on temperature at atmospheric 

 pressure. This may be assumed to be known well enough for the 

 present purpose. The first and the most important outcome of the 

 present data is, therefore, the construction of a table giving pressure, 

 volume, and temperature at sufficiently close intervals. In con- 

 structing this table the basis of computation was the compressibility 

 as determined at 40°. This, together with the known value of the 

 volume at 40° and atmospheric pressure, gave the volume as a function 

 of the pressure down a line through the middle of the table at 40°. 

 The values of the volume were tabulated for intervals of the pressure 

 of 500 kgm., the values found graphically from smooth curves through 

 the experimental points being so smoothed as to give smooth second 

 differences. The values of the change of volume for intervals of 20° 

 now w^ere combined directly with these values to give the volume 

 as a function of the pressure at 0°, 20°, 60°, and 80°. To find the 

 intermediate values of the volume, smooth curves were drawn through 



