xxix.] EXCEPTIONAL PHENOMENA. 669 



proves to be merely a false, apparent, singular, divergent, 

 or accidental exception, we gain a more minute and ac- 

 curate acquaintance with the effects of laws already known 

 to exist. We have indeed no addition to what was im- 

 plicitly in our possession, but there is much difference 

 between knowing the laws of nature and perceiving all 

 their complicated effects. Should a new fact prove to be a 

 limiting or real exception, we have to alter, in part or in 

 whole, our views of nature, and are saved from errors into 

 which we had fallen. Lastly, the new fact may come 

 under the sixth class, and may eventually prove to be a 

 novel phenomenon, indicating the existence of new laws 

 and forces, complicating but not otherwise interfering with 

 the effects of laws and forces previously known. 



The best instance which I can find of an unresolved 

 exceptional phenomenon, consists in the anomalous vapour- 

 densities of phosphorus, arsenic, mercury, and cadmium. 

 It is one of the most important laws of chemistry, dis- 

 covered by Gay-Lussac, that equal volumes of gases exactly 

 correspond to equivalent weights of the substances. Never- 

 theless phosphorus and arsenic give vapours exactly twice 

 as dense as they should do by analogy, and mercury and 

 cadmium diverge in the other direction, giving vapours 

 half as dense as we should expect. We cannot treat these 

 anomalies as limiting exceptions, and say that the law 

 holds true of substances generally but not of these ; for 

 the properties of gases (p. 60 1), usually admit of the 

 widest generalisations. 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 been maturely considered by chemists, 

 and is found to conflict with all the other analogies of the 

 substances and with the principle of isomorphism. One 

 of the most probable explanations is, that phosphorus and 

 arsenic produce vapour in an allotropic condition, which 

 might perhaps by intense heat be resolved into a simpler 

 gas of half the density ; but facts are wanting to support 

 this hypothesis, and it cannot be applied to the other two 

 exceptions without supposing that gases and vapours 

 generally are capable of resolution into something simpler. 



