30 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Pressure 



Figure 6. Illustrates the 

 method for finding the tem- 

 perature correction of the 

 compressibility. 



rection to bring the compressibility from 40° to G0°. The process- 

 was performed for intervals of 20°, and the results were tabulated 

 and plotted for the twelve liquids. 



The compressibility is most likely to be in error at the lower pres- 

 sures, as was the dilatation. In particular, the compressibility at 



atmospheric pressure can be found from 

 the method outlined above only by a 

 wide extrapolation, and therefore is not 

 accurate. Another method was adopted, 

 therefore, at atmospheric pressure. Of 

 course, the compressibilities ought to be 

 consistent with the tables of volumes, 

 that is, it ought to be possible to compute 

 from the compressibility to the change 

 of volume given in the table. The com- 

 pressibility at atmospheric pressure was 

 accordingly computed so that when com- 

 bined with the compressibility at 500 

 kgm. it should give the proper change of 

 volume between atmospheric pressure and 

 500 kgm. It was assumed in the computation that tlie mean compress- 

 ibility between 1 and 500 kgm. was the average of the compressibilities 

 at 1 and 500 kgm. This is not quite true, because the compressibility 

 varies rapidly with pressure at low pressures. The value computed 

 in this way is likely to be somewhat low. The discrepancy cannot be 

 large, however, and this method was accepted as the best under the 

 circumstances. The compressibility at atmospheric pressure has 

 also been determined in a number of instances by other observers. 

 There is not always, however, very good agreement between other 

 observers even at atmospheric pressure, so that the compressibility 

 at atmospheric pressure might well be the subject for further experi- 

 ment in some cases. The actual disagreement at atmospheric pres- 

 sure and the probable accuracy of the value finally chosen is to be 

 given in the detailed discussion for the separate liquids. 



The Work of Compression. — The mechanical work of compres- 

 sion was the next quantity of thermodynamic interest to be computed. 



This is given by the formula f -r— j = — P[^) ■ '^^ ^"^ ^^^^ ^^*^^ 



quantity of work done from zero up to any given pressure it is evi- 

 dently necessary to integrate the derivative. This integration was 

 performed mechanically with the integraph of the mathematical 



