510 MR W. ROBERTSON SMITH ON HEGEL 



there would be rest, and no motion ; velocity can be measured only by the space 

 passed through in a definite time" (p. 352). — An appeal to Attwood's machine 

 would probably be too " empirical" for our philosopher, but the law of energy 

 might surely convince Hegel of the reality of a variable velocity dependent on 

 potential energy lost or gained. It is clear, at least, that Hegel lacked the first 

 elements of physical notions, and these were not likely to be supplied by the 

 method of Lagrange to which he adheres, beginning with s=ft, and deducing 

 every other consideration by differentiation. 



The following criticism on a remark of Lagrange is splendid : — " We find, 

 says Lagrange, the motion represented by s = af in the actual fall of bodies. The 

 next simplest motion would be s = ctf, but nature shows no such motion, and we 

 do not know what c could mean." [The ground of this is, of course, to be found 

 in the law of the conservation of energy.] " If so, we have at least a motion 

 whose equation is s 3 = at\ — Kepler's law of planetary motion; and here the 



investigation of the first derived function g-g- , &c, the direct treatment of this 



equation by differentiation, the development of the laws of that absolute move- 

 ment from this starting point, must certainly be a most interesting task, in which 

 analysis would appear in the brightest splendour "[!]. That t and s in Kepler's 

 law are not variables, but constants determined for each planet ; that the equation 

 has no analogy whatsoever with the equation of motion ; that its differentiation 

 would be meaningless unless space were filled with planets; and that then it 

 would have nothing to do with " the determinations of that absolute motion," 

 are considerations that never entered Hegel's head. 



It is rather hard that, from a metaphysical stand-point, a man is still allowed 

 to write about things he has not studied; and more than this, that men so able as 

 Dr Stirling should be found imploring great mathematicians to come and read 

 such utter nonsense as naturally results from the attempt. Certainly Hegel's 

 fame is not likely to rise higher the more his notes on the calculus are studied ; 

 for these notes show quite clearly— first, substantial ignorance of the subject in 

 hand, bolstered up by some hasty glances at the " literature of the subject ; " 

 secondly, great disingenuousness in criticising Newton, without having ever given 

 his views a careful study ; thirdly, almost incredible confusion of mind, in so far 

 as he seems to have thought that he knew his own meaning when he really had 

 no meaning at all ; and lastly, to add nothing more, such a degree of self-compla- 

 cent arrogance as led him to fancy the results of his " half-hour" more valuable 

 than the fruit of the whole life of men like Newton. 



This paper has already grown to such a length that it seems better to say 

 nothing of Hegel's remarks on integration in the closing pages of his second note 

 on the calculus, or of the third note, in which he treats " some other forms con- 

 nected with the qualitative determination of quantity." The subject, in fact, has 



