340 THE PRINCIPLES OF SCIENCE. 



stances generally but not of these ; for the properties of 

 gases, as previously noticed (vol. ii. p. 250), usually admit 

 of the surest and widest generalizations. Besides, the 

 preciseness of the ratio of divergence points to the real 

 observance of the law in a modified manner. We might 

 endeavour to reduce the exceptions by doubling the atomic 

 weights of phosphorus and arsenic, and halving those of 

 mercury and cadmium. But this step has of course been 

 maturely considered by chemists, and is found to conflict 

 with all the other analogies of the substances and the 

 principles of isomorphism. One of the most probable ex 

 planations is that phosphorus and arsenic produce vapour 

 in an allotropic condition, which might perhaps by intense 

 heat be resolved into a simple gas of half the density ; 

 but facts are wholly wanting to support this hypothesis, 

 and it cannot be applied to the other two exceptions 

 without supposing that gases and vapours generally arc 

 capable of resolution into something simpler. In short, 

 chemists can at present make nothing of these anomalies. 

 As Hofmann distinctly says, Their philosophical inter 

 pretation belongs to the future . . . They may turn out 

 to be typical facts, round which many others of the like 

 kind may come hereafter to be grouped ; and they may 

 prove to be allied with special properties, or dependent on 

 particular conditions as yet unsuspected 8 . 



The expansion of solids and liquids by heat is also a 

 general law, in which we cannot expect to find any real 

 anomalies, any facts indicating too wide generalization, 

 or even any accidental disturbing causes. The con 

 traction of water and several other liquids, even of fusible 

 metal, by heat, together with the few cases in which a 

 solid contracts by heat, must therefore be probably re 

 garded as results of the very law of expansion acting in a 



8 Hofmann s, Introduction to Chemistry, p. 198. 



