218 THE PRINCIPLES OF SCIENCE. 



into account the semitones, it would become apparent that 

 it is practically impossible to exhaust the variety of 

 music. 



Similar considerations apply to the possible number 

 of natural substances, though we cannot always give 

 precisely numerical results. It was recommended by 

 Hatchett^ that a systematic examination of all alloys 

 of metals should be carried out, proceeding from the 

 most simple binary ones to more complicated ternary 

 or quaternary ones. He can hardly have been aware 

 of the extent of his proposed inquiry. If we operated 

 only upon thirty of the known metals, the number of 

 possible selections of binary alloys would be 435, of 

 ternary alloys 4060, of quaternary 27,405, without 

 paying any regard to the varying proportions of the 

 metals, and only regarding the kind of metal. If we 

 varied all the ternary alloys by quantities not less than 

 one per cent., the number of these alloys only would 

 be 1 1,445,060. An exhaustive investigation of the sub- 

 ject is therefore out of the question, and unless some 

 laws, connecting the properties of the alloy and its 

 components can be discovered, it is not apparent how 

 our knowledge of them can be ever more than most 

 incomplete. 



The possible variety of definite chemical compounds, 

 again, is enormously great. Chemists have already ex- 

 amined many thousands of inorganic substances, and a 

 still greater number of organic compounds ; r they have 

 nevertheless made no appreciable impression on the 

 number which may exist. Taking the number of ele- 

 ments at sixty- one, the number of compounds contain- 

 ing different selections of four elements each would 

 be more than half a million (521,855). As the same 



Q 'Philosophical Transactions' (1803), vol. xciii. p. 193. 

 r Hofmann's ' Introduction to Chemistry/ p. 36. 



