74 LECTURES AND ESSAYS [1869- 



into serious errors of fact as to the malign influence which 

 he supposes me to have exercised over the opinions of the 

 leaders of physical science in Scotland. It is asserted at 

 p. 127 that a supposed mistake in my paper (which I shall 

 presently show to be no mistake) &quot; misled &quot; these gentle 

 men into their statements before the Royal Society of 

 Edinburghstatements we have seen made months before 

 my paper was written, and nearly a year before it was 

 published. 1 



Let us pass, however, to take up on their own merits 

 the questions in dispute. The dispute, it has been seen, 

 turned in the first instance on a single point on the 

 correctness of the process by which Newton derives the 

 fluxion of a product. But, as every mathematician knows, 

 this point is so cardinal that any flaw in the deduction 

 necessarily vitiates the whole processes of the fluxional 

 calculus. When Hegel, therefore, in this connection speaks 

 of an operation performed by Newton which, though 

 elementary, is nevertheless incorrect ; when he talks of 

 the pressing necessity which could bring a Newton to palm 

 on himself the deception of such a proof, he, in fact, teaches 

 that the whole proof of the algebraic relation between 

 fluent and fluxion is deceptive and unsound. Dr. Stirling 

 does not seem to see this ; but I think it may be possible 

 to convince him of so much on Hegel s own showing. 

 &quot; The whole method of the calculus,&quot; says Hegel at the 

 commencement of his second mathematical note, 2 &quot; is 

 settled in the proposition that dx n = nx n ~ l dx . . . the 

 derivation of the following forms of the differential of a 



1 Still more extraordinary is the liberty which Dr. Stirling has 

 allowed himself in suspecting my influence in certain utterances of 

 Professor Tait with regard to Leibnitz a suspicion utterly ungrounded, 

 and which can have occurred only as the development of a fixed idea, by 

 which Dr. Stirling has come to conceive of me as the evil genius of 

 Scottish physicists. 



2 Werke (Ed. 1841), vol. iii. p. 316. The paging of this edition differs 

 from that of the edition quoted by Dr. Stirling and formerly by myself. 

 Passages cited from the book now before me will be found about eleven 

 pages further on in the other edition. 



