USE OF A SYMBOLICAL LANGUAGE. 229 



I(f{x) denote the expression of which a? is a constituent, 

 then f{a) will denote the new expression which is formed 

 by substituting a for x. To take a simple case, let /(a:) 



denote the algebraical expression l-a7 + 5 ; then/(2) 



will denote h 2 + 5, and will be equal to 13 ; /(o) will 



3-2 



denote ho + 5, and will be equal to 7; f[oc—s) ^^ill 



3-0 



denote , ^ + (a'-5)+5, and will be equal to 



3- (^-5) 



-\-x; and so on. 



\—x 



The last symbol f{x—S) warns us of a danger to be 

 carefully guarded against in the introduction of fresh 

 symbols, namely the danger of ambiguity. The meaning 

 here attached to it might in certain cases be confounded 

 with an older and commoner meaning ; for the symbol 

 f{x — s) also denotes the product of the two factors f and 

 X — 5. How is this danger of ambiguity to be guarded 

 against? We might, it is true, guard against it by 

 adopting, instead of /, a totally new symbol of some 

 unwonted shape; but this is a course to be avoided if 

 possible. Strange-looking symbols somehow offend the 

 eye ; and we do not take to them kindly, even when they 

 are of simple and easy formation. Provided we can avoid 

 ambiguity, it is generally better to intrust an old symbol 

 with new duties than to employ the services of a perfect 

 stranger. In the case just considered, and in many 

 analogous cases, the context will be quite sufficient to pre- 

 vent us from confounding one meaning with another, just 

 as in ordinary discourse we run no risk of confoundmg 

 the meanings of the word air in the two statements— 

 ' He assumed an air of authority ,'' and " He resolved the 



