420 PROCEEDINGS OF THE AMERICAN ACADEMY § 1 6 



insufficient, for the time being, to carry them out of the 

 sphere of their mutual attraction; and that no matter how 

 low the temperature may be, there will always be some 

 which are free to move under the influence of external 

 forces.* 



It follows that in liquids, solid particles, in solids, liquid 

 particles must always be present. 



What distinguishes a solid from a liquid is not, therefore, 

 according to this theory, the fact that all particles are 

 either solid or liquid; but simply that the rate of solid- 

 ification or of liquefaction, as the case may be, is in excess; 

 so that a structure once set up is capable, in solids, of 

 maintaining itself, while in liquids it never attains more than 

 indefinitely small dimensions. 



The existence, however, of an indefinite number of these 

 indefinitely small solid particles is easily seen to have a 

 inarked influence on the volume whenever in the solid 

 state the density is considerably diflerent from that of the 

 liquid. 



Conspicuous amongst all liquids in this respect stands 

 water, which expands greatly on solidif3'ing. In all such 

 liquids, the continual formation of solid particles, be it only 

 for an instant, must tend to increase the volume, and the 

 colder the liquid becomes, the greater will be the propor- 

 tion of solid particles at any instant; so that, other things 

 being equal, the liquid will expand by cooling. 



On the other hand, if the solid be denser than the liquid, 

 the rate of expansion with the temperature will be in- 

 creased by the gradual disappearance of solid particles. 



The existence, therefore, of exceptions to the general 

 law of expansion does not militate in any way against the 

 validity of the reasoning by which it was established. 



As in the case of vapor tensions, the quantitative appli- 

 cation of the theory of probability is beset with mathe- 



• The practical effect is seen, undoubtedly, in the slow yielding of the hardest rocks to 

 enormous pressures, discussed in Geology, and in the so-called viscosity of ice. 



