Cristiaan Huygens Accepts the Inverse-Square Law But Not Action-at-a-Distance
In my previous post, Gottfried Wilhelm Leibniz Writes Against Barbaric Physics and Gravitational Attraction, I concluded as follows:
For Leibniz, “force is exercised only through an impressed impetus”, i.e., force is only applied when something pushes something else. As for those like Newton, or, as we shall see in the next post, Cristiaan Huygens (1629-1695) in his later years, who accepted the concepts of attractive and repulsive forces acting at a distance, they were bringing barbarism back into physics. The ideological split, the philosophical confrontation, between contact-action and far-action could not be starker.
In researching for the current post, I realized that my assessment of Huygens was incorrect. As we shall see below, he did accept Isaac Newton’s (1643-1727) inverse-square law for gravity, but like Leibniz (1646-1716), did not accept the idea of gravitational attraction. The relevant passages come from Huygens’s 1690 text entitled Discours de la cause de la Pesanteur1, for which I found an English-language translation by Karen Bailey in manuscript form, entitled Discourse on the Cause for Gravity2.
Huygens’s opposition to the idea of gravitational attraction is presented at the end of an extended series of calculations about the shape of the earth, whether it be perfectly spherical or more flattened.
Mr. Newton came up with … that the figure of the Earth differs much more from the spherical, using a completely different calculation that I will not examine here because I am not especially in agreement with a Principle that he supposes in this calculation and others, namely, that all the small parts that we can imagine in two or more different bodies attract one another or tend to approach each other mutually. This I could not concede, because I believe I see clearly that the cause of such an attraction is not explicable either by any principle of mechanics or by the laws of motion. Nor am I at all persuaded of the necessity of the mutual attraction of whole bodies, having shown that, were there no Earth, bodies would not cease to tend toward a center because of what we call their gravity. [p.31, my emphasis]
So Huygens opposes both the idea that the individual particles within two bodies mutually attract each other, as well as the idea that the entire bodies mutually attract each other. It should be understood that although Huygens is explicitly opposing Newton on this question, these ideas can also be found in the Introduction to Johannes Kepler’s (1571-1630) Astronomia Nova. See my post Kepler's First Steps Towards a Theory of Gravity.
In the next paragraph, Huygens accepts Newton’s centripetal force [Vis Centripeta, towards the centre], and notes that it exactly counterbalances the centrifugal force [away from the centre] that Huygens had previously written about. He also notes that Newton’s inverse-square law was new to him.
I have nothing against Vis Centripeta, as Mr. Newton calls it, which causes the planets to weigh (or gravitate [peser]) toward the Sun, and the Moon toward the Earth, but here I remain in agreement without difficulty because not only do we know through experience that there is such a manner of attraction or impulse in nature, but also that it is explained by the laws of motion, as we have seen in what I wrote above on gravity. Because nothing hinders the action of this Vis Centripeta toward the Sun, it would be similar to what pushes bodies that we call heavy to descend toward the Earth. I thought for a long time that the spherical figure of the Sun could be produced by the same thing that, according to me, produces the sphericity of the Earth, but I had not extended the action of gravity to such great distances as from the Sun to the planets, or from the Earth to the Moon, because the vortices of Mr. Descartes, which formerly appeared very likely to me, and which I still had in mind, cut across it [opposed the idea of gravity]. I had not thought at all about the regular diminution of gravity, namely that it is in inverse proportion to the squares of the distances from the center. This is a new and quite remarkable property of gravity, the basis of which is well worth the trouble of investigating. But seeing now from the demonstrations of Mr. Newton that, if one supposes such a gravity towards the Sun that diminishes according to said proportion, it counterbalances the centrifugal force of the planets so well and produces exactly the effect of elliptical motion that Kepler had predicted and verified by observations, I can scarcely doubt that these hypotheses concerning gravity would be true, or that the System of Mr. Newton, insofar as it is founded thereupon, would likewise be true. This should appear so much the more probable as we find in it the solutions of several difficulties that are a problem for the vortices supposed by Descartes. We see now how the eccentricities of the planets are able to remain constantly the same; why the planes of their orbits do not join together, but retain their different inclinations with respect to the plane of the ecliptic; and why the planes of all these orbits necessarily pass through the Sun. We see how the motion of the planets can accelerate and decelerate to the extents that we observe, which could occur in this way with difficulty if they floated in a vortex around the Sun. Finally, we see how comets can pass through our system. For, while we know that they often enter in the region of the planets, we had some difficulty imagining how they could sometimes go in a motion contrary to that of the vortex that had enough force to carry the planets. But this doubt is also removed with the doctrine of Mr. Newton, since nothing prevents the comets from traveling in elliptical paths around the Sun, like the planets, but in more extended paths, and in a figure more different from circular so that these bodies have their own periodic revolutions, as certain ancient and modern planets, but and astronomers had imagined. [pp.31-33, my emphasis]
There is a very interesting and important note for this translation. The first edition of the Principia did not contain Newton’s remark “hypotheses non fingo” [“I do not make any hypotheses”].
Newton’s famous remark, “hypotheses non fingo”, followed in the next sentence by the comment that hypotheses have no place in experimental philosophy, was introduced in the second edition of the Principia; nothing in the first edition displays the aversion to hypotheses that he expressed in the second and third. [p.32, n.57]
So Huygens acknowledges that Newton’s theory of gravity resolves many issues that were problematic with the Cartesian vortices. However, rejecting these vortices would create a number of problems for Huygens, in particular would be inconsistent with his idea of the luminiferous aether, which I wrote about in my post Cristiaan Huygens Explains How Light Waves Advance.
There is only this difficulty: in rejecting the vortices of Mr. Descartes, Mr. Newton claims, in order that the planets and the comets encounter the fewest obstacles in their paths, that the celestial spaces contain only a very rarefied matter. If we suppose that rarity, it does not appear possible to explain either the action of gravity or that of light, at least through the mediums that I have made use of. In order to examine this point then, I propose that the ethereal matter can be supposed rarefied in two ways: either its particles may be distant from each other, with a great deal of empty space between them, or they may touch each other, with the tissue of each being very thin, and with very many small empty spaces mixed with them. I admit without difficulty that there is some void. Moreover, I believe it necessary for the motion of small corpuscles amongst themselves, not being of the sentiment of Mr. Descartes, who claims that extended matter alone is the essence of bodies; but I add perfect hardness to them as well, rendering them impenetrable and incapable of being either broken or impaired. Considering the rarity of the first type, however, I do not see how we could provide a reason for gravity; and, concerning light, it seems to me entirely impossible with such voids to explain its prodigious speed, which must be 600,000 times greater than that of sound according to the demonstration of Mr. Römer, which I reported in the Treatise on Light. This is why I hold that this sort of rarity cannot be thought to suit the celestial spaces. [p.33, my emphasis]
The translation contains the following note, which states that for Newton, who supported the corpuscular theory of light, would have had no problem with the idea “that the celestial spaces contain only a very rarefied matter”.
Because Newton thought light most likely to consist of particles, he had no problem with light being transmitted across empty celestial spaces. Huygens, however, thought light consists of longitudinal waves much like sound waves, and this led him to require a medium for transmitting these waves. [p.33, n.59]
To conclude, Huygens did accept Newton’s inverse-square law for gravity, but like Leibniz, did not accept the idea of gravitational attraction, this for two reasons. First, “the cause of such an attraction is not explicable either by any principle of mechanics or by the laws of motion”; second, Newton’s system would imply the rejection of Descartes’s vortices, and implicitly, Huygens’s idea of the luminiferous aether.
Cristiaan Huygens. Discours de la cause de la pesanteur (1690). In Œuvres complètes, Tome vingt-et-unième: Cosmologie. La Haye: Martinus Nijhoff, 1944. pp.427-509.
Cristiaan Huygens. Discourse on the Cause of Gravity. Translation by Karen Bailey. Annotations by Karen Bailey and George E. Smith. Manuscript, 1997.