32 PROCEEDINGS OF THE AMERICAN ACADEMY. 



agree, but of course complete agreement could not be expected. The 

 agreement of the values corrected to 40° in this way was a few tenths 

 of a per cent. The final value at 40° was taken as the mean of the 

 four corrected values, and is shown in the diagrams. In the lower 

 part of the diagrams the relation between pressure and the difference 

 of the work of compression for 20° intervals is plotted on a larger scale. 

 The Heat of Compression. — The heat of compression was the 

 next quantity to be computed. It is unfortunate that the expression, 

 "heat of compression" is sometimes used in a sense which is not indi- 

 cated by the words themselves; namely, as the rise of temperature 

 when the pressure on a substance is increased adiabatically by the 

 unit amount. But by no stretch of the imagination is it possible to 

 identify a temperature with a "heat." A more descriptive name for 

 this effect would seem to be the "temperature effect of compression." 

 The effect was discussed under this name in the previous paper on 

 water. By "heat of compression" we shall mean in this paper what 

 is naturally suggested by the words, namely the heat, Q, which is 

 given out by a unit quantity of a substance when it is compressed 

 isothermally. It may be computed if the dilatation is known, by 



using the formula ( ^ ] ~ '''i'^) • To find the total heat given out 



by the substance as it is compressed from the initial to the final state 

 it is necessary to integrate this expression. The procedure was exactly 

 analogous to that in computing the work of compression. The inte- 

 gration was performed first for the four temperatures. Then, in 

 order to obtain the differences more accurately, a separate integra- 



fdv\ 

 tion was made of the differences of t ['^r ) for inter\'als of tempera- 

 ture of 20°. With these differences the total heat at any temperature 

 was corrected to 40°, thus giving four values for the heat of compres- 

 sion at 40°, of which the mean was taken for the final value at this 

 temperature. From this final value, the values for the other tempera- 

 tures were found by computing back again with the differences. The 

 magnitude of the differences is much greater than the difl^erences of 

 the mechanical work, so that it was possible to plot the total heat for 

 each temperature without confusing the diagram. 



Change of Internal Energy. — From the heat of compression and 

 the mechanical work of compression we may find at once the change 

 of internal energy when the liquid is compressed isothermally. During 

 compression the liquid receives work from the compressing force 

 and delivers heat. The change of internal energ}- is the difference 



