Db. WHEWELL, on HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA. 697 



that among us, upon subjects so familiar, a few words will suffice. For the same reason. I shall 

 take passages from Hegel, not in the order in which they occur, but in the order in which they 

 best illustrate what I have to say. I shall do Hegel no injustice by this mode of proceeding: for 

 I will annex a faithful translation, so far as I can make one, of the whole of the passages referred 

 to, with the context. 



No one will be surprised that a German, or indeed any lover of science, should speak with 

 admiration of the discovery of Kepler's laws, as a great event in the history of Astronomy, and a 

 glorious distinction to the discoverer. But to say that the gloi-y of the discovery of the proof of 

 these laws has been unjustly transferred from Kepler to Newton, is quite another matter. This is 

 what Hegel says («*). And we have to consider the reasons which he assigns for saying so. 



He says (6) that " it is allowed by mathematicians that the Newtonian Formula may be derived 

 from the Keplerian laws," and hence he seems to infer that the Newtonian law is not an additional 

 truth. That is, he does not allow that the discovery of the cause which produces a certain phe- 

 nomenal law is anything additional to the discovery of the law itself. 



"The Newtonian formula may be derived from the Keplerian law." It was professedly so 

 derived ; but derived by introducing the Idea of Force, which Idea and its consequences were not 

 introduced and developed till after Kepler''s time. 



" The Newtonian formula may be derived from the Keplerian law." And the Keplerian law 

 may be derived, and was derived, from the observations of the Greek astronomers and their 

 successors ; but was not the less a new and great discovery on that account. 



But let us see what he says further of this derivation of the Newtonian " formula" from the 

 Keplerian Law. It is evident that by calling it a formula, he means to imply, what he also asserts, 

 that it is no new law, but only a new form (and a bad one) of a previously known truth. 



How is the Newtonian " formula," that is, the law of the inverse squares of the central force, 



derived from the Keplerian law of the cubes of the distances proportional to the squares of the 



times .^ This, says Hegel, is the "immediate derivation." (c). — By Kepler's law, A being the dis- 



A^ A . . 



tance and T the periodic time, — is constant. But Newton calls — universal gravitation ; whence 



it easily follows that gravitation is inversely as A^. 



This is Hegel's way of representing Newton's proof. Beading it, any one who had never read 



the I'rincipia might suppose that Newton defined gravitation to be ~ . We, who have read the 



Principia, know that Newton proves that in circles, the central force (not the universal gravitation) 



is as — ;: that he proves this, by setting out from the idea of force, as that which deflects a body 



from the tangent, and makes it describe a curve line : and that in this way, he pas.ses from Kepler's 

 laws of mere motion to his own law of Force. 



But Hegel does not see any value in this. Such a mode of treating the subject he says (t) 

 " off'ers to us a tangled web, formed of the Lines of the mere geometrical construction, to wiiich a 

 piiysical meaning of independent forces is given." Tiiat a iiierisure of forces is fiioiU in such lines 

 as the sagitta of the arc described in a given time, (not such a metnmig arbitrarily given to them,) 

 is certainly true, and is very distinctly proved in Newton, and in all our elementary books. 



But, says Hegel, as further shewing the artificial nature of the Newtonian formula;, (A) " .Analy- 

 sis has long Ijeen able to derive the Newtonian expression an<i the laws thcrowitli connected out of 

 the Form of the Keplerian Laws;" an assertion, to verify which he refers to I'oisson's Mccatiique. 



• The»e Icllcm refer 10 p»M»gei In ihc Translntion annexed to this Alcnioir. 



