80 PROCEEDINGS OF THE AMERICAN ACADEMY. 



It is evident that in order to explain these compHcated facts we 

 shall have to give up the simple picture of things that led us to expect 

 the dilatation always to increase with increasing temperature and to 

 decrease with increasing pressure. A natural way of modifying our 

 conceptions so as to make room for these effects would seem to be as 

 follows. We are to think of the molecules as having complicated 

 shapes, or what for our purposes would amount to the same thing, 

 of being surrounded by fields of force different in different directions. 

 This concept does not seem to be a forced or an unlikely one; it 

 must certainly be the fact for liquids which eventually crystallize 

 under pressure, and for liquids which do not crystallize it is hard to 

 conceive how an assemblage of atoms with unlike chemical affinities 

 can coalesce into a molecule identical in all aspects. The effect of 

 pressure on such an assemblage of molecules may be somewhat as 

 follows. As the molecules are crowded closer together, the localized 

 centers of force on the corners and edges play an increasingly individu- 

 alized part, so that for small volumes we can no longer regard the 

 molecules as centers of force and the cohesional force as a function of 

 the mean distance apart of the molecules, but the orientation of the 

 molecules with respect to each other begins to have its effect. Now we 

 suppose that the natural tendency of the molecules in a liquid under 

 normal conditions is to arrange themselves at haphazard with relation 

 to each other. But as the constraints increase with decreasing volume, 

 the characteristic shape compels an arrangement not entirely at hap- 

 hazard, but such that the molecules fit into each other to some extent. 

 Now it is evident that with the increasing orderliness of the arrange- 

 ment of the molecules the relative positions of the localized centers of 

 force will change. What is more, it is conceivable that the change 

 in position of the force centers will be such that on the average the 

 mean attraction between the molecules shall decrease with decreasing 

 volume instead of increasing as is usual. Still more would this be 

 true if there are centers of both attraction and repulsion in the mole- 

 cule, as seems very likely from our present views of the electrical 

 nature of matter. In this case we should expect the greater dilata- 

 tion to be at the smaller volumes, because the cohesional force is less. 

 But since the smaller volumes correspond to the lower tempera- 

 tures, we have the effect already met, namely, that the dilatation is 

 greater at the lower temperatures. The explanation of the sometimes 

 increasing dilatation with rising pressure is similar. With increasing 

 pressure the molecules may be forced to assume positions more regu- 

 lar in arrangement, of less volume, and of less average attractional 



