596 PROCEEDINGS OF THE AMERICAN ACADEMY. 



volumes be takeu as an approximate criterion, and density seems to be 

 an important factor in determining compressibility.* 



Assuming, then, that oxygen is less compressible than hydrogen, and 

 that the act of polymerization would involve the severing of cohesive 

 attraction of oxygen to hydrogen, and the substitution of the attraction of 

 oxygen for oxygen, the hydrogen, on being freed and but little attracted 

 by its neighboring hydrogen, would expand more than the oxygen could 

 contract. Thus an increase of volume would result, even althoush the 

 energy developed by the oxygen in combining with itself might be con- 

 siderable. Here, as before, it must be borne in mind that a given 

 change of volume in a compressible substance corresponds to a smaller 

 amount of work than the same change of the same volume of a slightly 

 compressible substance. 



In the act of solidification the oxygen-hydrogen cohesion would all be 

 severed, and the system would suffer a sudden expansion in consequence. 

 Thus may be explained the irregular coefficient of expansion of watei", 

 and the abnormal expansion on solidification ; as before, the apparent 

 exception really supports the argument. 



Another although essentially similar case is the somewhat unusual 

 one in which an elementary substance on cooling assumes the form of a 

 phase of less density. The most striking case of this anomaly is that of 

 tin, which possesses at least two different forms with specific gravities of 

 7.3, and 5.8 respectively, the more dense being stable at high tempera- 

 tures, and the lighter at low temperatures.! Even such a case as this 

 is not inexplicable, however ; for if the denser form consists of atoms 

 compressed nearly equally on all sides, an expansion accompanied by 

 evolution of heat might occur through a polymerization involving a 

 greater compression on one side of each atom, with the partial release 

 and consequent expansion of the other side. Because the compressibility 

 diminishes with decreasing volume, the expansion on the sides of the 

 atom partially released might easily exceed the contraction on the com- 

 pressed side of the atom. If this is really the case with tin, one would 

 expect the irregularly constituted gray tin to possess a smaller tenacity 



* According to Dupre's rule, compressibility is inversely as the square of the 

 density. This relation only holds strictly true with analogous compounds, but 

 nevertheless serves as an index of the importance of density. 



t See Cohen, Zeitschr. phys. Chem., 30, GOl (1899), etc. 



The other possible varieties of tin may be explained by arguments similar to 

 these. See Rammelsberg, Jahresbericht, 1870, pp. 358, 724 ; Shepherd, J. Phys. 

 Chem., 6, 519 (1902). 



