xxix.] EXCEPTIONAL PHENOMENA. 649 



in the crystallisation of iron pyrites and some other sub- 

 stances, that the other four faces become imperceptible and 

 a regular tetrahedron appears to be produced, contrary to 

 the laws of crystallographic symmetry. Many other cry- 

 stalline forms are similarly modified, so as to produce a 

 series of what are called hemihedral forms. 



In tracing out the isomorphic relations of the elements, 

 great perplexity has often been caused by mistaking one 

 substance for another. It was pointed out that though 

 arsenic was supposed to be isomorphous with phosphorus, 

 the arseniate of soda crystallised in a form distinct from 

 that of the corresponding phosphate. Some chemists held 

 this to be a fatal objection to the doctrine of isomorphism ; 

 but it was afterwards pointed out by Clarke, that the 

 arseniate and phosphate in question were not correspond- 

 ing compounds, as they differed in regard to the water 

 of crystallisation. 1 Vanadium again appeared to be an 

 exception to the laws of isomorphism, until it was proved 

 by Professor Eoscoe, that what Berzelius supposed to be 

 metallic vanadium was really an oxide of vanadium. 2 



Apparent but Congruent Exceptions. 



Not unfrequently a law of nature will present results 

 in certain circumstances which appear to be entirely in 

 conflict with the law itself. Not only may the action of 

 the law be much complicated and disguised, but it may 

 in various ways be reversed or inverted, so that careless 

 observers are misled. Ancient philosophers generally 

 believed that while some bodies were heavy by nature, 

 others, such as flame, smoke, bubbles, clouds, &c., were 

 essentially light, or possessed a tendency to move upwards. 

 So acute an inquirer as Aristotle failed to perceive the 

 true nature of buoyancy, and the doctrine of intrinsic 

 lightness, expounded in his works, became the accepted 

 view for many centuries. It is true that Lucretius was 

 aware why flame tends to rise, holding that 



" The flame has weight, though highly rare, 

 Nor mounts but when compelled by heavier air." 



1 Daubeny's J^omic Theory, p. 76. 



2 Bakerian Lecture, Philosophical Transactions (i868\ vol. clviii 

 p. 2. 



