Similar considerations apply to the possible number of natural substances, though we cannot always give precise numerical results. It was recommended by Hatchett[106] that a systematic examination of all alloys of metals should be carried out, proceeding from the binary ones to more complicated ternary or quaternary ones. He can hardly have been aware of the extent of his proposed inquiry. If we operate only upon thirty of the known metals, the number of binary alloys would be 435, of ternary alloys 4060, of quaternary 27,405, without paying 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 would be 11,445,060. An exhaustive investigation of the subject 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 ever be more than fragmentary. [106] *Philosophical Transactions* (1803), vol. xciii. p. 193. The possible variety of definite chemical compounds, again, is enormously great. Chemists have already examined many thousands of inorganic substances, and a still greater number of organic compounds;[107] they have nevertheless made no appreciable impression on the number which may exist. Taking the number of elements at sixty-one, the number of compounds containing different selections of four elements each would be more than half a million (521,855). As the same elements often combine in many different proportions, and some of them, especially carbon, have the power of forming an almost endless number of compounds, it would hardly be possible to assign any limit to the number of chemical compounds which may be formed. There are branches of physical science, therefore, of which it is unlikely that scientific men, with all their industry, can ever obtain a knowledge in any appreciable degree approaching to completeness. [107] Hofmann’s *Introduction to Chemistry*, p. 36. *Higher Orders of Variety.*