328 Mr. Baspace on the Influence of Signs 
objects, which consequently recall to the mind the variety of par- 
ticulars of which they consist, some with more, others with less 
vividness according to our previous habits of thought; from this 
cause it sometimes happens that the real ground on which our 
reasoning depends, is with difficulty kept in view by a laborious 
effort of the attention, and is in many instances very indistinctly 
perceived. 
In the use of algebraic signs this mconvenience entirely 
vanishes; we can always so arrange them, that that quality on 
which the whole force of our reasoning turns shall be visible to 
the eye, whilst the numerous others which contribute to form the 
expression we are considering, although thrown into the back 
ground, are still by no means excluded. This species of insulation 
of the property whose consequences we wish to trace, enables 
the mind to apply that attention, which must otherwise be exerted 
in keeping it in view, to the more immediate purpose of tracing 
its connection with other properties that are the objects of our 
research. As an example of these ideas, I would mention the 
word government, upon which we may reason in many different 
directions, either as it secures domestic liberty, or protects from 
foreign attacks, as it discourages vice or promotes commerce: in 
these and in numerous other courses, our reasoning may be pur- 
sued, and the word government will constantly recur without the 
possibility of avoiding it but by the most tedious circumlocution, 
or of restricting the view in which it is regarded but by the most 
unwearied efforts of attention. The word function in analysis 
possesses a still more extensive signification than that which has 
been just mentioned : 
The sign ¥(«, +) 
x 
signifies any symmetrical combination of the two quantities « 
