16 LECTURES AND ESSAYS [1869- 



we have been speaking only a very general account of the 

 principles on which he would base the calculus. These 

 general principles are, as Hegel says, &quot; abstract &quot; (we 

 would rather say vague), &quot; and therefore in themselves 

 also easy &quot; (p. 327). The real difficulty lies &quot; in the con 

 crete side,&quot; in the deduction from these generalities of 

 the practical rules of the method. To this subject Hegel 

 devotes his second note, professing to point out a purely 

 analytical method whereby, without any application of 

 the doctrine of limits, everything necessary for practice 

 can be deduced. If we can demonstrate that the ana 

 lytical method is radically unsound, producing results 

 mathematically false, it will surely be vain to appeal in 

 defence to any &quot; deficiency in the judgment of a pure 

 mathematician.&quot; 



The plan that suggests itself is therefore the following : 

 First, to consider the real character of Newton s method, 

 and to show what may, I think, be made quite clear to an 

 unprejudiced mind, that that great man really did know 

 what he was doing ; and, in the second place, to show 

 that Hegel having refused to be instructed by Newton s 

 real knowledge, but having acutely enough caught sight 

 of something like the ghost of an idea, which he could not 

 for want of solid knowledge really make his own, was first 

 ensnared by the plausible but fallacious method of 

 Lagrange, and then, in attempting to improve that 

 method, lost any glimpse of the truth that he had before, 

 and was swamped in hopeless absurdity. 



The ingenuity of a great deal that Hegel has said on 

 this subject I do not wish to dispute. No doubt he, 



&quot; with as delicate a hand, 

 Could twist as tough a rope of sand &quot; 



as any man that ever lived. But the question is, after 

 all, one of plain truth and error ; and however much we 

 may admire the chivalry with which Hegel rushes into an 

 unequal encounter with so gigantic an antagonist as 

 Newton, it will never do to 



