i87s] STIRLING AND HEGEL 77 



fluxion by a process analytically, technically, algebraically, 

 formally correct. To Dr. Stirling, this seems a small 

 matter, a matter of logic rather than of mathematics, a 

 matter not amounting to real error. But to Newton, and 

 to all Newtonians, the charge is of the gravest order ; 

 for they know that with the deduction of this fluxion the 

 whole calculus, in its concrete applications as well as in 

 its theory, must fall, and that Newton s grand scheme 

 of subduing the unconquered realms of geometry by a 

 method rivalling the logical precision of the ancients, 

 must be reckoned as a vain chimsera. But they know, 

 too, that Newton s plan is no chimaera, that his method 

 does possess every particle of the precision of the ancient 

 method of exhaustions, and therefore they regard with 

 contempt, rather than with anger, the attempt of Hegel 

 to subvert the insubvertible. And, strange to say, they 

 have Dr. Stirling on their side. For it is now admitted 

 that the expedient which in The Secret of Hegel, and in 

 letter after letter in the Courant, was declared utterly 

 indefensible, is, as a matter of fact, &quot; unimpeachable, and 

 in its simplicity and efficiency does the usual honour 

 to Newton s extraordinary penetration and unrivalled 

 resource &quot; (p. 129). 



In admitting for himself and Hegel a &quot; misleading &quot; 

 on this point, Dr. Stirling is careful to observe that his 

 admission &quot; is wholly unavailable in excuse of Mr. Smith, 

 who has utterly failed to see what Hegel meant, whether 

 arithmetically or analytically.&quot; But perhaps the recollec 

 tion of former persistency for so many years in one error, 

 may dispose a man so candid as Dr. Stirling to contemplate 

 the possibility of his having misrepresented me as well as 

 Newton. He may possibly be aided in this contemplation 

 by the statements of the present paper ; and he may even 

 be inclined to admit that the fact that I and the other 

 mathematicians, whose utterances are characterised as 

 &quot; rabid nonsense,&quot; have always upheld the view which 

 Dr. Stirling now admits to be right, creates an appreciable 



