192 THE PRINCIPLES OF SCIENCE. [chap. 



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 ex- 

 haustive investigation of the subject is therefore out of 

 the question, and unless some laws connecting the proper- 

 ties of the alloy and its components can be discovered, it 

 is not apparent how our knowledge of them can ever be 

 more than fragmentary. 



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 ; ^ they have 

 nevertheless made no appreciable impression on the 

 number which may exist. Takiug 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 

 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. 



Higher Orders of Variety. 



The consideration of the facts already given in this 

 chapter will not produce an adequate notion of the pos- 

 sible variety of existence, unless we consider the com- 

 parative numbers of combinations of different orders. By 

 a combination of a higher order, I mean a combination 

 of groups, which are themselves groups. The immense 

 numbers of compounds of carbon, hydrogen, and oxygen, 



' Hofmann's Introduction to Chemistrij, p. 36. 



