tions of the same order of generality being both true. If there be a new-discovered comet, and if one astronomer asserts that it will return once in every twenty years, and another, that it will return once in every thirty years, both cannot be right. But if an astronomer says that though its interval was in the last instance 30 years, it will only be 20 years to the next return, in consequence of perturbation and resistance, he may be perfectly right.

And thus, when different and rival explanations of the same phenomena are held, till one of them, though long defended by ingenious men, is at last driven out of the field by the pressure of facts, the defeated hypothesis is transformed before it is extinguished. Before it has disappeared, it has been modified so as to have all palpable falsities squeezed out of it, and subsidiary provisions added, in order to reconcile it with the phenomena. It has, in short, been penetrated, infiltrated, and metamorphosed by the surrounding medium of truth, before the merely arbitrary and erro. neous residuum has been finally ejected out of the body of permanent and certain knowledge,

APPENDIX H.

ON HEGEL'S CRITICISM OF NEWTON'S

PRINCIPIA.

(Cam. Phil. Soc. MAY 21, 1849.)

THE Newtonian doctrine of universal gravitation, as the cause of the motions which take place in the solar system, is so entirely established in our minds, and the fallacy of all the ordinary arguments against it is so clearly understood among us, that it would undoubtedly be deemed a waste of time to argue such questions in this place, so far as physical truth is concerned. But since in other parts of Europe, there are teachers of philosophy whose reputation and influence are very great, and who are sometimes referred to among our own countrymen as the authors of new and valuable views of truth, and who yet reject the Newtonian opinions, and deny the validity of the proofs commonly given of them, it may be worth while to attend for a few minutes to the declarations of such teachers, as a feature in the present condition of European philosophy. I the more readily assume that the Cambridge Philosophical Society will not think a communication on such a subject devoid of interest, in consequence of the favourable reception which it has given to philosophical speculations still more abstract, which I have on previous occasions offered to it. I will therefore proceed to make some remarks on the opinions concerning the Newtonian doctrine of gravitation, delivered by the celebrated Hegel, of Berlin, than whom no philosopher in modern, and perhaps hardly any even in ancient times, has had his teaching received with more reverential submission by his disciples, or been followed by a more numerous and zealous band of scholars bent upon diffusing and applying his principles.

The passages to which I shall principally refer are taken from one of his works which is called the Encyclopædia (Encyklopädie), of which the First Part is the Science of Logic, the Second, the Philosophy of Nature, the Third, the Philosophy of Spirit. The Second Part,

with which I am here concerned, has for an aliter title, Lectures on Natural Philosophy (Vorlesungen über Natur-philosophie), and would through its whole extent offer abundant material for criticism, by referring it to principles with which we are here familiar: but I shall for the present confine myself to that part which refers to the subject which I have mentioned, the Newtonian Doctrine of Gravitation, § 269, 270, of the work. Nor shall I, with regard to this part, think it necessary to give a continuous and complete criticism of all the passages bearing upon the subject; but only such specimens, and such remarks thereon, as may suffice to show in a general manner the value and the character of Hegel's declarations on such questions. I do not pretend to offer here any opinion upon the value and character of Hegel's philosophy in general: but I think it not unlikely that some impression on that head may be suggested by the examination, here offered, of some points in which we can' have no doubt where the truth lies; and I am not at all persuaded that a like examination of many other parts of the Hegelian Encyclopædia would not confirm the impression which we shall receive from the parts now to be considered.

Hegel both criticises the Newtonian doctrines, or what he states as such; and also, not denying the truth of the laws of phenomena which he refers to, for instance Kepler's laws, offers his own proof of these laws. I shall make a few brief remarks on each of these portions of the pages before me. And I would beg it to be understood that where I may happen to put my remarks in a short, and what may seem a peremptory form, I do so for the sake of saving time; knowing 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 glory 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 (a)'. And we have to consider the reasons which he assigns for saying so.

These letters refer to passages in the Translation annexed to this Memoir.

He says (b) 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 phenomenal 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 distance and T the periodic time, is constant. T

A3

A But Newton calls universal gravitation; whence it easily follows T

that gravitation is inversely as A2.

This is Hegel's way of representing Newton's proof. Reading it, any one who had never read the Principia might suppose that

A

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

A

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 curved line: and that in this way, he passes 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 (i) "offers to us a tangled web, formed of the Lines of the mere geometrical construction, to which a

physical meaning of independent forces is given." That a measure of forces is found in such lines as the sagitta of the arc described in a given time, (not such a meaning 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 showing the artificial nature of the Newtonian formulæ, (h) “ Analysis has long been able to derive the Newtonian expression and the laws therewith connected out of the Form of the Keplerian Laws;" an assertion, to verify which he refers to Francœur's Mécanique. This is apparently in order to show that the "lines" of the Newtonian construction are superfluous. We know very well that analysis does not always refer to visible representations of such lines: but we know too, (and Francœur would testify to this also,) that the analytical proofs contain equivalents to the Newtonian lines. We, in this place, are too familiar with the substitution of analytical for geometrical proofs, to be led to suppose that such a substitution affects the substance of the truth proved. The conversion of Newton's geometrical proofs of his discoveries into analytical processes by succeeding writers, has not made them cease to be discoveries: and accordingly, those who have taken the most prominent share in such a conversion, have been the most ardent admirers of Newton's genius and good fortune.

So much for Newton's comparison of the Forces in different circular orbits, and for Hegel's power of understanding and criticising it. Now let us look at the motion in different parts of the same elliptical orbit, as a further illustration of the value of Hegel's criticism. In an elliptical orbit the velocity alternately increases and diminishes. This follows necessarily from Kepler's law of the equal description of the areas, and so Newton explains it. Hegel, however, treats of this acceleration and retardation as a separate fact, and talks of another explanation of it, founded upon Centripetal and Centrifugal Force (o). Where he finds this explanation, I know not; certainly not in Newton, who in the second and third section of the Principia explains the variation of the velocity in a quite different manner, as I have said; and nowhere, I think, employs centrifugal force in his explanations. However, the notion of centrifugal as acting along with centripetal force is introduced in some treatises, and may undoubtedly be used with perfect truth and propriety. How far Hegel can judge when it is so used, we may see from what he says of the confusion produced by such an explanation, which is, he says, a maximum. In the first place, he speaks of the motion being uniformly accelerated and retarded in