98 PROCEEDINGS OF THE AMERICAN ACADEMY. 



itial stages, but of course ultimately diverged greatly from linearity, 

 passing through a maximum. If the straight portion of the curve at 

 the origin represents a region in which the inverse four thirds power 

 law is satisfied, then the tangent to the curve at the origin represents 

 over the entire range of the experiment what the change of energy 

 would have been if the four thirds law had held throughout. The 

 difference between the actual curve and the tangent at the origin is 

 then, according to the above view, equal to the energy which has 

 been stored up as strain inside the molecule. This difference was 

 determined and plotted against volume, in order to find what function 

 of the volume the strain energy might be. For these four liquids, 

 it turned out that the strain energy varies over the entire range approx- 

 imately as the cube of the change of volume reckoned from a suitable 

 origin. The greatest discrepancy is for ether at low pressures. For 

 PCI3 a variation of only 0.01 in the arbitrary zero of volume from 

 which the change is reckoned would wipe out the disci epancy; for 

 amyl alcohol a variation in the zero of 0.005 would give perfect agree- 

 ment; for ethyl iodide a change of 0.01, and for ether a change of 

 0.04. The \'ariation for ether is all below 3000 kgm.; above this 

 the energy of strain is almost exactly proportional to the cube of the 

 change of volume, taking 1.06 as the origin. The zero of volume for 

 phosphorus trichloride is 1.11, for amyl alcohol 1.07, and for ethjd 

 iodide 1.045. All the curves showed slight consistent variations from 

 the cube law; at low pressures the strain energy varies more rapidly 

 than the cube and less rapidly at the high pressures. 



The fact that the internal energy of strain varies as the cube of 

 the change of volume probably does not have very much significance 

 in showing us what the elastic mechanism of the molecule is. If the 

 entire change of volume of the liquid were due to change of volume 

 of the molecules, then we should expect the strain energy to vary as 

 the square of the change of volume, provided the elastic constants 

 of the molecule were unaffected by pressure. If, as is likely, the mole- 

 cule becomes less compressible at high pressure, then the strain 

 energy would vary less rapidly than the square. But the strain 

 energ\- was found to vary as the cube. The reason for this is probably 

 that at low pressures strain energy is stored up in only a few -of the 

 molecules; those molecules which are describing a free path and are 

 not in contact with other molecules have no strain energy of com- 

 pression. With increasing pressure the number of molecules in which 

 strain energy is stored up increases rapidly, and the strain energy of 

 each molecule increases at the same time as the square of the strain, 



