BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 31 



department of Harvard University. In performing the integration 

 there are two possible methods. We may either integrate p ( ^ 



given above, or we may integrate the equivalent expression ( ^— ) = P- 



The first involves an integration with pressure as the independent vari- 

 able, and the second with volume. The first uses as the integrand the 

 compressibility, which was obtained by computation from the experi- 

 mental data, and the second uses as the integrand the pressure, which 

 is one of the direct experimental data. It is well known that the 

 derivative of an experimental quantity has considerably greater error 

 than the experimental quantity itself. The second method was 

 adopted, therefore, using the volume as the independent variable of 

 integration. It was a fortunate accident that the method could be 

 used without duplication of effort, because the volume had already 

 been plotted against pressure for another purpose. However, the 

 direct results of the integration were not immediately available 

 because it was necessary to obtain the work of compression as a 

 function of pressure instead of as a function of volume. The change 

 of variable was made with the help of the curves of volume against 

 pressure by reading off the pressures corresponding to the given 

 volumes. 



The work of compression was found by the method outlined above 

 at 20° intervals of temperature. It differs only slightly for different 

 temperatures, so slightly that the difference of the work at different 

 temperatures could not be obtained directly from the curves with as 

 great accuracy as was necessary for computing the specific heats. 

 In order to obtain the differences of the work with greater accuracy, 



an independent integration of the quantity Ap[-^j dp was per- 



/dv 



[dp. 



at a given pressure for the interval 20°-40° or 40°-60° or 60°-80. 

 These differences were taken from the tables of compressibility. The 

 integration of the differences was performed with the integrating 

 machine. Tests of the integrating machine showed that the accuracy 

 of this part of the process alone was as high as xV %• The differences 

 found in this way were now used in finding a better mean value for the 

 total work of isothermal compression. For it is evidently possible 

 with these differences to correct the work of compression at 20° or 

 60° or 80° back to 40°. If there were no error all these values should 



\dp 

 formed. The symbol A indicates the difference of the product p 



