RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 593 



76 kilojoules, and by Bertlielot and IMantignon as 226 kilojoules.* In 

 sucli cases one is at a loss as to the true value, without new experi- 

 mental data, and is unable to apply intelligently the principles under 

 consideration. 



It is not to be expected, however, that even when all the data have 

 been correctly determined the agreement should be mathematically pre- 

 cise, especially when solids are concerned, on account of the complexity 

 of the problem, and the fact that a given substance often assumes differ- 

 ent solid forms. In nearly all cases, it is true, the relation of the differ- 

 ent solid phases of a given substance accords qualitatively with the 

 principles above : — the formation of the more compact phase evolves 

 heat, and hence this phase gives a less heat of reaction with other sub- 

 stances,t indicating a state of greater compression. This is true, for 

 example, in the case of sulphur, phosphorus, and carbon. In such cases, 

 the output of heat of allotropic modification has the same sign as the 

 contraction in volume, and these quantities add respectively to the heat 

 evolved, and to the change of volume during any reaction, not affecting 

 the qualitative relation. 



In some cases, however, the act of polymerization or of solidification 

 seems to involve an anomalous expansion of volume, an apparent incon- 

 sistency which needs further discussion. There can be no doubt that the 

 explanation given in a previous paper | aifords the most probable interpre- 

 tation of this fact. The explanation runs as follows, — it will be amplified 

 below : — 



'■' In those cases where there is a transition from a more compressible 

 union to a stabler, less compressible one, involving more work of com- 

 pression, solidification would involve increase of volume, as in the case 

 of water." 



This possibility might be discussed as an abstraction ; but it becomes 

 much clearer when a specific case is considered. Of course, such a con- 

 sideration presupposes a knowledge of the nature of the molecular 

 change which takes place in the substances, and but little is known con- 

 cerning such changes. Hence, the evidence must in most cases be vague 

 and rather unsatisfactory. It seems to me, however, that enough is 

 known concerning at least a single case, that of the solidification of 

 water, to allow its interpretation to serve as a type ; and if the dis- 

 cussion is viewed as a possible concrete example of a general principle, 



* See Ostwald, Lehrbuch, 2 (1), 175 (1893). 

 t Petersen, Zeitschrift fiir pliysikalisclie Cliemie, 8, Gil (1891). 

 t Richards, Tliese Proceedings, 37, 407 (1902). 

 VOL. XXXI X. — .38 



