mct. i.] DISSERTATION SECOND. 43 



tack to sustain in England from a more formidable quarter. 

 Berkeley Bishop of Cloyne, was a man of first-rate talents, 

 distinguished as a metaphysician, a philosopher, and a divine. 

 His geometrical knowledge, however, which, for an attack 

 on the method of fluxions, was more essential than all his 

 other accomplishments, seems to have been little more than 

 elementary. The motive which induced him to enter on 

 discussions so remotely connected with his usual pursuits has 

 been variously represented ; but, whatever it was, it gave 

 rise to the Analyst, in which the author professes to demon- 

 strate, that the new analysis is inaccurate in its principles, 

 and that, if it ever lead to true conclusions, it is from an acci- 

 dental compensation of errors that cannot be supposed al- 

 ways to take place. The argument is ingeniously and plau- 

 sibly conducted, and the author sometimes attempts ridicule 

 with better success than could be expected from the subject ; 

 thus, when he calls ultimate ratios the ghosts of departed 

 quantities, it is not easy to conceive a witty saying more hap« 

 pily fastened on a mere mathematical abstraction. 



The Analyst was answered by Jurin, under the signature 

 of Philalethes ; and to this Berkeley replied in a tract en- 

 titled A Defence of Freethinking in Mathematics. Replies 

 were again made to this, so that the argument assumed the 

 form of a regular controversy ; in which, though the defen- 

 ders of the calculus had the advantage, it must be acknow- 

 ledged that they did not always argue the matter quite fairly, 

 nor exactly meet the reasoning of their adversary. The true 

 answer to Berkeley was, that what he conceived to be an 

 accidental compensation of errors was not at all accidental, 

 but that the two sets of quantities that seemed to him neg- 

 lected in the reasoning were in all cases necessarily equal, 

 and an exact balance for one another. The Newtonian idea 

 of a fluxion contained in it this truth, and so it was argued by 

 Jurin and others, but not in a manner so logical and satisfac- 



