86 LECTURES AND ESSAYS [1869- 



intersect becomes in the limit a common tangent i.e. 

 the tangent is the substitute for the chord, when the 

 circles come to touch instead of to cut. But evidently 

 the tangent is in no sense a boundary within which the 

 chords lie, nor is any implication of inexactness or approxi 

 mation to be found in the expression. I may observe that 

 the application to the calculus of the idea of a limit is not 

 to be accomplished in a satisfactory way, except in con 

 nection with the idea of rate, which Hegel is quite absolute 

 in refusing to admit. This is the source of all the supposed 

 logical difficulties which he finds to encompass the method 

 of limits, but which really attach to his own refusal to 

 conceive of quantity as generated by flux. 



Now, to Dr. Stirling this refusal is one of Hegel s chief 

 virtues. To call on the philosopher, as I have done, to 

 look at quantity in the Newtonian way, is to introduce 

 &quot; contradictory commixture of the dross and slag of the 

 Vorstellung with the metal of the Begriff,&quot; is to &quot; muddle 

 and puddle the notion the quality that that Newton 

 himself declares independent of quantity by mixed 

 expressions through which the due abstraction only shows 

 but to an eye that is educated.&quot; Or again, Hegel says the 

 same thing as I, reporting Newton, say, only he says it in 

 due abstraction, &quot; in the language of the Begriff.&quot; Now 

 if this were only true, one would be very glad to have it so. 

 If Hegel had understood Newton s notion as Newton 

 himself states it, and then had freed it from unnecessary 

 dross, we could have nothing but admiration for his 

 philosophic skill. But what I object to Hegel is, that he 

 applied his powers of abstraction to Newton s language 

 before he understood its meaning, and so cut himself off 

 from all intelligent contact with Newtonian processes, and 

 fell into the absurd errors which have been sufficiently 

 exposed. In fact, here as elsewhere, Hegel and Dr. 

 Stirling have simply been indulging in that metaphysical 

 pride which goes before a fall. Had they first learned the 

 calculus as Newton teaches it, and condescended to use for 



