in Mathematical Reasoning. 361 
difficulties opposed to him; in the one case, the elegance which 
a judicious selection produces, carries the reader pleasantly and 
almost imperceptibly through an abstruse calculation, whilst 
the latent cause, which gives facility to his progress, is rarely 
appreciated, because it is spread uniformly over the whole ques- 
tion: in the other, whose essence often consists in some happy 
substitution, which is always concentrated in some point, the 
effect is too remarkable to escape the least attentive enquirer, 
and its success too striking not to command his admiration. 
Unlimited variety in the use of signs, is as much to be depre- 
cated as too great an adherence to one class of them; the one 
conceals the appearance of relations that really exist, whilst the 
other, affecting to display them too clearly, fails from its want 
of distinctness. It is difficult to point out models of imitation, 
even amongst the most eminent; the same writer, who at one 
time might be safely trusted as a pattern of correct judgement, 
has indulged at another in the most unexampled imnovation ; 
completely setting at defiance many of those principles, whose 
authority I have endeavoured to establish. The fate, which has 
attended the greatest of these proposed reformations, though sanc- 
tioned by the illustrious name of Lagrange, is no slight testimony 
of the validity of those views, which it is the object of several of 
these Essays to advocate*. Having delivered a theory of the diffe- 
rential calculus, which rested on principles entirely new, he intro- 
duced it to the world, clothed in a language of his own creation. 
The value of the present was too great to allow of its utility 
being impeded by the garb with which it was encumbered; and 
the labor of acquirmg the language was compensated by the 
truths which it revealed. Time, however, and experience, con- 
vinced even its immortal author, that the language of signs rests 
* This relates more particularly to an Essay on the Principles of Notation, which is 
not yet published. 
