346 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



W^ = j p It-J^P' It was obtained by a mechanical integration 



from curves similar to the volume curves of Figure 3, drawn on a 

 larger scale. For this purpose the integrating machine owned by the 

 mathematical Department of Harvard University was used. The 





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 Pressure, kgm. / cm.'' x 10' 



Figure 6. The mechanical work of compression at 60°. 



actual value of the mechanical work at any pressure is of course de- 

 pendent on the temperature, but since the variation is so slight that 

 it would have been impossible to show it in the figure (see Figure 6), 

 the work of compression is plotted for only the one temperature, 60°. 

 Although the change of external work with temperature was too slight 

 to show in the diagram, the change with temperature was nevertheless 

 taken account of in making the calculations of the quantities depend- 

 ing on it to be described immediately. After the first 4000 kgm. it is 

 seen that tlie curve becomes very approximately linear. The curve 

 for a substance which retains the same compressibility unchanged 

 over a wide pressure range, as steel for example, is a parabola, the 

 work increasing directly as the square of the pressure. That this 

 curve for water becomes linear, means that the compressibility 

 decreases so fast with increasing pressure that the decrease in the yield 



