COMBINATIONS AND PERMUTATIONS. 219 



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 combinations of simpler 

 groups. The almost unlimited number of compounds 

 of carbon, hydrogen, and oxygen, described in organic 

 chemistry, are combinations of a second order, for the 

 atoms are groups of groups. The wave of sound pro- 

 duced by a musical instrument may be regarded as a 

 combination of motions ; the body of sound proceeding 

 from a large orchestra is therefore a complex aggregate 

 of sounds each in itself a complex combination of move- 

 ments. All literature may be said to be developed 

 out of the difference of white paper and black ink. 

 From the almost unlimited number of marks which 

 might be chosen we select twenty-six customary letters. 

 The pronounceable combinations of letters are probably 

 some trillions in number. Now, as a sentence is a cer- 

 tain selection of words, the possible sentences must be 

 indefinitely more numerous than the words of which 

 it may be composed. A book is a combination of 



