292 OPERATIONS SUBSIDIARY TO INDUCTION. 



the two already treated of, appears to be the most 

 valuable which the language of science can possess. 

 Of this quality a general notion may be conveyed by 

 the following aphorism: 



Whenever the nature of the subject permits our 

 reasoning process to be, without danger, carried on 

 mechanically, the language should be constructed on 

 as mechanical principles as possible; while in the 

 contrary case, it should be so constructed that there 

 shall be the greatest possible obstacles to a merely 

 mechanical use of it. 



I am conscious that this maxim requires much 

 explanation, which I shall at once proceed to give. 

 And first, as to what is meant by using a language 

 mechanically. The complete or extreme case of the 

 mechanical use of language, is when it is used with- 

 out any consciousness of a meaning, and with only 

 the consciousness of using certain visible or audible 

 marks in conformity to technical rules previously laid 

 down. This extreme case is, so far as I am aware, 

 nowhere realized except in the figures of arithmetic 

 and the symbols of algebra, a language unique in 

 its kind, and approaching as nearly to perfection, for 

 the purposes to which it is destined, as can, perhaps, 

 be said of any creation of the human mind. Its per- 

 fection consists in the completeness of its adaptation 

 to a purely mechanical use. The symbols are mere 

 counters, without even the semblance of a meaning 

 apart from the convention which is renewed each time 

 they are employed, and which is altered at each renewal, 

 the same symbol a or x being used on different occa- 

 sions to represent things which (except that, like all 

 things, they are susceptible of being numbered) have 

 no property in common. There is nothing, therefore, 

 to distract the mind from the set of mechanical opera- 



