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Title: Newtonianism or Newtonian Philosophy
Original Title: Newtonianisme ou Philosophie Newtonienne
Volume and Page: Vol. 11 (1765), p. 122
Author: Jean Le Rond D'Alembert
Translator: Terry Stancliffe
Original Version (ARTFL): Link
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URL: http://hdl.handle.net/2027/spo.did2222.0000.981
Citation (MLA): D'Alembert, Jean Le Rond. "Newtonianism or Newtonian Philosophy." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Terry Stancliffe. Ann Arbor: Michigan Publishing, University of Michigan Library, 2015. Web. [fill in today's date in the form 18 Apr. 2009 and remove square brackets]. <http://hdl.handle.net/2027/spo.did2222.0000.981>. Trans. of "Newtonianisme ou Philosophie Newtonienne," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 11. Paris, 1765.
Citation (Chicago): D'Alembert, Jean Le Rond. "Newtonianism or Newtonian Philosophy." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Terry Stancliffe. Ann Arbor: Michigan Publishing, University of Michigan Library, 2015. http://hdl.handle.net/2027/spo.did2222.0000.981 (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Newtonianisme ou Philosophie Newtonienne," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 11:122 (Paris, 1765).

Newtonianism, or Newtonian Philosophy, [1] is the theory of the mechanism of the universe, and particularly of the motions of the heavenly bodies, their laws and their properties, as this has been taught by Mr. Newton. See Philosophy.

The term Newtonian philosophy has been variously applied, and from this, several ideas of the word have arisen.

Some authors understand by it the corpuscular philosophy, as reformed and corrected by the discoveries with which Mr. Newton has enriched it. See Corpuscular.

It is in this sense that Mr. Gravesande calls his elements of physics an Introductio ad philosophiam Newtonianam . [2] In this sense, the Newtonian philosophy is no other than the new philosophy, different from the Cartesian and Peripatetic philosophies, and from the ancient corpuscular philosophies. See Aristotelianism, Peripatetics, Cartesianism, etc.

Others mean by Newtonian philosophy the method which Mr. Newton follows in his philosophy, i.e. the method which consists in deducing his reasoning and his conclusions directly from phenomena, without any previous hypothesis; starting from simple principles; deducing the basic laws of nature from a small number of selected phenomena; and then in using those laws to explain other things. See Laws of Nature (under the word Nature).

In this sense the Newtonian philosophy is no other than experimental physics, and is opposed to the old corpuscular philosophy. See Experimental.

As others understand Newtonian philosophy, it considers physical bodies mathematically, and applies geometry and mechanics to solve [questions about] phenomena. Taken in this sense, Newtonian philosophy is no other than mechanical and mathematical philosophy. See Mechanics and Mathematical Physics.

Others mean, by Newtonian philosophy, that part of physics which Mr. Newton has handled, extended and explained in his book of the Principia . [3]

And still others, finally, understand by Newtonian philosophy the new principles which Mr. Newton has brought into philosophy, the new system he has founded on these principles, and the new explanations of phenomena that he has deduced from them; in a word, what characterises his philosophy and distinguishes it from all the others: and it is in this sense that we shall principally consider it.

The history of this philosophy is quite short; its principles were only published in 1686, by the author, then a fellow of Trinity College, Cambridge; then published again with considerable additions in 1713.

In 1726, a year before the author's death, there was a new edition of his principles, entitled Philosophiae Naturalis Principia Mathematica , an immortal work, and one of the most beautiful that the human spirit has ever produced.

Several authors have tried to make the Newtonian philosophy easier to understand, by leaving out many of its more sublime mathematical results, and replacing them either by simpler reasonings, or by experiments. That is what was mainly done by Whiston in his Praelectiones physico-mathem . [4] and by Gravesande in his Elemens and Institutions . [5]

Mr. Pemberton, a fellow of the Royal Society of London, and editor of the 3rd edition of the Principia, also published a work entitled View of the newtonian philosophy , [6] a kind of commentary by which the author attempts to place this philosophy within reach of the greatest number of geometers [mathematicians] and physicists. Fathers le Seur and Jacquier, of the order of Minims, have also published, in three quarto volumes, [7] Newton's Principia along with a very extensive commentary, which can be most useful to those who wish to read this excellent work of the English philosopher.

To these works should be joined Mr. MacLaurin's Account of Sir Isaac Newton's Philosophical Discoveries , [8] translated into French a few years ago, and the commentary on Newton's Principia that Madame la Marquise du Chatelet left us along with a translation of the same work. [9]

Notwithstanding the great merit of this philosophy and the universal authority that it now has in England, it was at first only very slowly that it became established [in France]; Newtonianism had at first scarcely two or three followers in the whole country: while Cartesianism and Leibnizianism were ruling in full force.

Mr. Newton has set out his philosophy in the third book of the Principia . The two preceding books prepare the way, as it were, and demonstrate the mathematical principles forming the foundation of this philosophy. These are such as the general laws of motion, central and centripetal forces, the heaviness of bodies and the resistance of media. See Central, Gravity, Resistance, etc .

In order to make these results less dry and geometrical, the author illustrated them by philosophical remarks relating mainly to the density and resistance of bodies, the motion of light and sound, about the vacuum, etc .

In the third book the author explains his philosophy, and from the principles that he previously set out he then deduces the structure of the universe, the force of gravity that makes bodies tend towards the Sun and the planets; and it is by this same force that he explains the motions of comets, the theory of the Moon, and the ebb and flow of the tides.

This [third] book, called De Mundi Systemate , was first written in a popular way, as the author tells us; but he then considered that readers who were little used to such principles as his, would perhaps not appreciate the force of the inferences, and would have difficulty in putting aside their old prejudices. To remove this inconvenience, and to prevent his system from being the subject of endless dispute, the author gave the book a mathematical form arranged into propositions, so that one could only read and understand it after becoming familiar with the principles that come before. But it is not necessary to understand them all generally. Several propositions in this work are capable of giving pause even to geometers [mathematicians] of the greatest skill. It is enough to have read the definitions, the laws of motion, and the three first sections of the first book, after which the author himself says that one can pass on to the book De Systemate Mundi .

Different points of this philosophy are explained in this dictionary in articles with special reference to each. See Sun, Moon, Planet, Comet, Earth, Medium, Matter, etc . Here we will be content to give a general idea of the whole, to acquaint the reader with the links that the different parts of this system have with each other.

The great principle at the foundation of this entire philosophy is universal gravitation: but this principle is not new. Kepler long ago gave the first ideas of it in his Introd. ad mot. martis . [10] He even discovered some properties that result from it, and the effects that gravity can produce in the motions of the planets: but the glory of bringing the principle to physical demonstration was reserved to the English philosopher. See Gravity.

What constitutes Mr. Newton's system is the proof of this principle by the phenomena, coupled with the application of the same principle to the phenomena of nature, or the use that the author makes of the principle to explain those phenomena. Here is Mr. Newton's system in summary extract.

I. The phenomena are, 1st, that the satellites of Jupiter describe areas around the planet, [11] which are proportional to the times; and that the times of their [orbital] revolution are in sesquiplicate proportion to their distances from its centre [i.e. in proportion to the one-and-a-half power of the distance, to the square root of its cube]; in which observation all astronomers agree. 2nd. The same phenomenon applies to the satellites of Saturn, considered in relation to Saturn; and to the Moon, considered in relation to the Earth. 3rd. The times of [orbital] revolution of the primary planets around the Sun are in sesquiplicate proportion to their mean distances from the Sun. 4th. The primary planets do not describe areas around the Earth that are proportional to the times: they sometimes appear stationary, and sometimes retrograde, with regard to the Earth. See Satellite, Period.

II. The force that continually turns the satellites of Jupiter away from a rectilinear motion, and retains them in their orbits, is directed towards the centre of Jupiter, and is in reciprocal proportion to the square of the distance from that centre. The same applies to the satellites of Saturn, relative to Saturn; to the Moon, relative to the Earth; and to the primary planets, relative to the Sun. These truths follow from the relationship observed between the distances and the periodic times, and from the proportionality of the areas to the times. See articles Central and Force, where you will find all the principles necessary to draw these inferences.

III. The moon is heavy and weighs towards the Earth, and is retained in its orbit by the force of that gravity: and the same applies to the other satellites with respect to their primary planets, and to the primary planets with respect to the Sun. See Moon and Gravitation.

This proposition is proved as follows in regard to the Moon. The mean distance of the Moon from the Earth is 60 semidiameters of the Earth; its period, relative to the fixed stars, is 27 days, 7 hours, 43 minutes; and then the Earth's circumference is 123,249,600 Paris feet. Let us suppose now that the Moon loses all its motion, and falls towards the Earth with a force equal to that which retains it in its orbit. In one minute of time the Moon would fall 15 1/12 Paris feet (because the arc that the Moon describes by its mean motion around the Earth, in a minute of time, has a versed sine equal to 15 1/12 Paris feet, as calculation easily shows). Now, since the force of gravity increases with approach to the Earth, being in inverse proportion to the square of the distance, it follows that near to the surface of the Earth, it will be 60 x 60 times greater than at the distance of the Moon; thus, a heavy body that is falling, near to the surface of the Earth, would cover, in a minute of time, a distance of 60 x 60 x 15 1/12 Paris feet, and 15 1/12 Paris feet in one second.

But this is in fact the same rate at which heavy bodies fall in a single second, as Huyghens has shown by experiments with pendulums. Thus, the force that retains the Moon in its orbit is the same as what we call gravity ; because if they were different, a body falling near to the surface of the Earth, and impelled by both forces together, would cover double the distance of 15 1/12 feet, i.e. 30 1/6 feet, in a second of time — since on the one hand its heaviness would make it cover 15 feet, and on the other hand the force attracting the Moon, which prevails in the whole space that separates the Moon and the Earth, diminishing as the square of the distance, would also be able to make the body down here cover 15 feet in a second, and would add its effect to that of the heaviness. The proposition in question here has already been demonstrated under the word Gravity, but with less detail and in a slightly different way: we have thought fit not to leave it out, so that our readers may see how in different ways one can arrive at this fundamental truth. See Descent.

As for the other secondary planets, they follow the same laws in relation to their primary planets as the Moon does in relation to the Earth, and analogy alone shows that these laws depend on the same causes. Furthermore, attraction is always mutual, i.e. the reaction is equal to the action, and so the primary planets gravitate towards their secondary planets, the Earth towards the Moon, and the Sun towards all the planets at the same time, and this gravity, in each planet taken separately, is very close in its proportion to the reciprocal of the square of the distance from the common centre of gravity. See Attraction, Reaction, etc .

IV. All bodies gravitate towards all the planets: and their weights towards each planet are, at equal distances, in direct proportion to the quantity of their matter.

The law of the descent of heavy bodies towards the Earth, leaving aside here the resistance of the air, [12] is this: that all bodies at equal distances from the Earth fall by equal distances in equal times.

Let us suppose, for example, that some heavy bodies are taken to the surface of the Moon; and that they and the Moon are deprived at the same time of all progressive motion, and fall back towards the Earth. It is shown that in the same times they would cover the same distances as the Moon. Furthermore, since Jupiter's satellites make their revolutions in times that are in sesquiplicate proportion to their distances from Jupiter, and that thus, when at equal distances, the forces of gravity [13] on them are equal; it follows that in falling by equal heights in equal times, they would cover equal distances precisely as the heavy falling bodies on the Earth, and the same reasoning applies to the primary planets considered in relation to the Sun. Now, the forces by which unequal bodies are equally accelerated, are in proportion to the quantities of matter in them. Thus the weight of bodies towards each planet is as the quantity of matter in each (supposing the distances equal). In the same way, the weights of the primary and secondary planets towards the Sun are in proportion to the quantities of matter in those planets and satellites. See Matter.

V. Gravity extends to all bodies, and the force with which one body draws another is in proportion to the quantity of matter contained in each.

We have already shown that all the planets gravitate towards each other, and that the gravity towards any one of them is in reciprocal proportion to the square of the distance from its centre; consequently, the gravity is proportional to the matter in them. Furthermore, as all the parts of a planet A gravitate towards another planet B, and because the gravity of one part is in the same proportion to the gravity of the whole, as the part is to the whole; and because, finally, the reaction is equal to the action, planet B must gravitate towards all the parts of planet A, and its gravity towards one part will be to its gravity towards the whole planet, as the mass of that part is to the mass of the whole.

From this can be derived a method for finding and comparing the gravities [14] of bodies towards different planets, and for determining the quantity of matter in each planet, and its density. The weights of two equal bodies that revolve around a planet, are in direct proportion to the diameters of their orbits, and inversely as the squares of their periodical times; and their weights at different distances from the centre of the planet are in inverse proportion to the squares of their distances. Now, since the quantities of matter in each planet are in proportion to the force with which they act at a given distance from their centres; and since, lastly, the weights of equal homogeneous bodies towards homogeneous spheres are, at the surface of the spheres, in proportion to their diameters; consequently, the densities of the planets are in proportion to the weights of a body if it were placed on the planets at the distances of their [respective] diameters. In this way Mr. Newton concludes that one can find the masses of those planets that have satellites, thus the Sun, the Earth, Jupiter and Saturn: because it is through the times of revolution of the satellites that one knows the forces with which they are attracted. The great philosopher says that the quantities of matter in the Sun, in Jupiter, in Saturn, and in the Earth, are as 1, 1/1033, 1/2411 and 1/22,512. [15] Since the other planets have no satellites, one cannot know the quantity of their mass. See Density.

VI. The common centre of gravity of the Sun and the planets is at rest; and the Sun, though always in motion, only departs by very little from the common centre of all the planets.

Thus, the matter in the Sun being to that in Jupiter as 1033 to 1; and Jupiter's distance from the Sun to the semi-diameter of the Sun being in a ratio only a little greater; therefore the common centre of gravity of the Sun and of Jupiter will be a point a little outside the surface of the Sun. One finds by the same reasoning that the common centre of gravity of Saturn and the Sun will be a point a little within the surface of the Sun; so that the common centre of gravity of the Sun and the Earth and all the planets will be scarcely as far away from the centre of the Sun as the size of one of its diameters. Now this centre is always at rest: because by virtue of the mutual action of the planets on the Sun and of the Sun on the planets, their common centre of gravity must either be at rest or else must be moving uniformly in a straight line. Now, if it moved uniformly in a straight line, we would be noticeably changing our position in relation to the fixed stars [16]: and as this does not happen, it follows that the centre of gravity of our planetary system is at rest. Consequently, whatever may be the motion of the Sun in one direction or another, according to the different situations of the planets, the Sun can never move very far away from this centre. Thus the common centre of gravity of the Sun, the Earth, and the planets may be taken as the centre of the world. See Sun and Center.

VII. The planets move in ellipses of which the centre of the Sun is the focus; and they describe areas around the Sun which are proportional to the times.

We have already set out this principle a posteriori as a phenomenon: but now that the principle of the celestial motions has been shown, we can demonstrate a priori the phenomenon concerned, and in the following way. Since the weights of the respective planets towards the Sun are in reciprocal proportion to the squares of their distances; if the Sun were at rest and the other planets did not act on each other, each of them would describe around the Sun an ellipse of which the Sun would occupy the focus, and in which the areas would be proportional to the times. But since the mutual actions of the planets are very small, and because the centre of the Sun can be sensed as immobile, it is clear that one can neglect the effect of the action of the planets and the motion of the Sun; thus, etc . [17] See Planet and Orbit.

VIII. [18] It has to be admitted however that the action of Jupiter on Saturn produces a quite considerable effect, and that according to the different situations and distances of those two planets, their orbits can be a little disturbed by it.

The Sun's [apparent] orbit too is a little disturbed by the action of the Moon on the Earth; the common centre of gravity of these two planets describes an ellipse of which the Sun is at the focus, and in which the areas taken around the Sun are proportional to the times. See Earth and Saturn.

IX. The axis of each planet, or the diameter joining its poles, is smaller than the diameter at its equator.

If the planets had no diurnal movement around their centres, they would be spheres, as gravity would act equally all around: but because of their rotation, their parts located at distance away from the axis endeavour to rise up towards the equator, and they would rise up in fact if the matter of the planet were fluid. Jupiter, which rotates very fast around its axis, has been found by the observations to be considerably flattened towards its poles. For the same reason, if our Earth were not higher at the equator than at the poles, the sea would rise up towards the equator, and would inundate everything near that region. See Figure of the Earth.

Mr. Newton also proves a posteriori that the Earth is flattened towards the poles, and this is shown by the oscillations of pendulums, which are of shorter duration [19] under the equator than towards the pole. See Pendulum.

X. All the motions of the Moon, and all the inequalities that one sees in them, follow, according to Mr. Newton, from the same principles, that is, from its tendency or gravitation towards the Earth, combined with its tendency towards the Sun: for example, the unequal velocity of the Moon, and that of its nodes and apogee in the syzygies and in the quadratures; the differences and variations of its eccentricity, [20] etc. See Moon.

XI. The inequalities of the lunar motion can also serve to explain several inequalities that can be seen in the motions of the other satellites. See Satellite, etc .

XII. From all of these principles, especially the action of the Sun and Moon on the Earth, it follows that there must be an ebb and flow of tides, that is, that the sea must rise and subside twice each day. See Ebb and Flow, or Tide.

XIII. From these principles, again, can be deduced the whole theory of comets. The results incude, among other things, that the comets are above the region of the Moon, and in the planetary space; that they shine by the Sun, reflecting its light; that they move in conic sections of which the centre of the Sun occupies the focus; that they describe around the Sun areas proportional to the times; that their orbits or trajectories are almost parabolas; that their bodies are solid, compact, and like those of the planets, and that they must therefore receive in their perihelia an immense heat; that their tails are exhalations that arise from them and surround them like a kind of atmosphere. See Comet.

The objections that have been made against this philosophy are especially targeted against the principle of universal gravitation. Some objectors regard this pretended gravitation as an occult quality. Others view it as a miraculous and supernatural cause which ought to be banned from reasonable philosophy. Others reject it as deducing [21] the [Cartesian] system of vortices, others as assuming the [existence of a] vacuum. The answers of the Newtonians to these objections can be found in the articles Gravity, Attraction, Vortex, etc .

In relation to the system of Mr. Newton on light and colours, see Colour and Light. See also in the articles Algebra, Geometry, Differential, the geometrical [mathematical] discoveries of this great man. Chambers.

We have nothing to add [22] to this article and its exposition of the Newtonian philosophy, except to recommend not to separate it from a reading of the articles under the words Attraction and Gravity. The more that astronomy and analysis receive improvements, the more one perceives the agreement between Mr. Newton's principles and the phenomena. The work of geometers [mathematicians] in the present century has given unshakable support to this admirable system. Details can be seen in the articles Moon, Ebb and Flow, Nutation, Precession, etc .

Mr. Newton has also tried to determine the mass of the Moon by the height of the tides; he finds that it is about one 39th part of the mass of the Earth. [23] On this, see the article Moon.

Notes

1. The French text has a clear if partial antecedent in Chambers’ Cyclopaedia , the article headed ‘NEWTONIAN Philosophy’ — but the French text states, after acknowledging ‘ Chambers ’, ‘We have nothing to add to this article ... ’. Thus, it creates an impression of being no more than a translation. Comparison of sources shows, however, that this is far from the case. The French text has important additions, some deletions, and fresh nuances, nearly throughout, as well as a few errors. Some of the changes in the French version seem to add notable clarity to the arguments, which (in this genre of summary) are so tightly abbreviated, that they can be difficult to follow. The Chambers article had very little modification from its first appearance in 1728 through the 1743 edition (the last that was available to compare for purposes of these notes). A few features of the French text could suggest that its source was closer to the Chambers edition of 1743 than to that of 1728.

2. Willem Jacob 's Gravesande (1688-1742) : Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam (“ Mathematical Elements of Physics, Confirmed by Experiments; or, an Introduction to Newtonian Philosophy ”), Leiden (Lugduni Batavorum), 1720.

3. The title of Newton’s work, Philosophiae Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ), applies to all three editions: London, 1687; Cambridge, 1713; and London, 1726. 1686 was the date of the imprimatur from the Royal Society, not an imprint or publication date. Chambers Cyclopaedia (1728) seems to have been prepared before Newton’s third edition was published. Chambers took material generally from the second (1713) edition (as shown, e.g., by the numbers, updated or changed by Newton from one edition to the next). The French text of ‘Newtonianisme’ does not generally update the material, except to add a citation to Newton’s third edition (as well as citing later works, down to the translation by the marquise du Chatelet, imprint 1756/1759).

4. William Whiston, 1667-1752, Prælectiones physico-mathematicæ Cantabrigiæ in Scholis publicis habitæ , (“ Physico-mathematical lectures given in the public schools at Cambridge ”) Cambridge, 1710. Whiston later published an English version:- Sir Isaac Newton's mathematick philosophy more easily demonstrated , London, 1716.

5. Willem Jacob 's Gravesande, 1688-1742 : see note 2 and: Philosophiae Newtonianae Institutiones, in usus academicos (“ Textbook of Newtonian Philosophy, for academic use ”), Leiden (Lugduni Batavorum), 1723.

6. Henry Pemberton (1694-1771) : A View of Sir Isaac Newton's Philosophy , London, 1728.

7. Newton’s ‘ Principia ’ in the edition of Fathers Thomas Le Seur and Francois Jacquier: Philosophiae Naturalis Principia Mathematica, auctore Isaaco Newton eq.aurato, perpetuis commentariis illustrata, communi studio PP. Thomae Le Seur & Francisci Jacquier, ex Gallicana Minimorum Familia, Matheseos Professorum (Vols. 1-3), (“ Sir Isaac Newton’s Mathematical Principles of Natural Philosophy, with a commentary throughout, from the joint study of Fathers Thomas Le Seur and Francis Jacquier of the Gallican Order of Minims, Professors of Mathematics ”), Geneva, 1739-1742 (reprinted several times, as lately as at Glasgow, 1822 and Glasgow, 1833).

8. Colin MacLaurin (1698-1746) : An Account of Sir Isaac Newton's Philosophical Discoveries, in Four Books, London and Edinburgh, 1748.

9. Émilie (marquise) du Châtelet (1706-1749) : Principes mathématiques de la philosophie naturelle “par feue Madame la Marquise du Chastellet” (“ by the late Mme Marquise du Chastellet ”) (translation), Paris 1756, 1759.

10. This translated paragraph closely matches its English source; but the discussion and citation of Kepler is not a very close match to the content or title of Kepler’s work. Recent scholarship draws attention to a history of confusion and misunderstanding about relationships between Kepler’s work and Newton’s (see e.g. Steffen Ducheyne, The Main Business of Natural Philosophy: Isaac Newton’s Natural-Philosophical Methodology , Dordrecht 2012; and works cited therein). Possibly Chambers’ contributor was unfamiliar with the real details of content and title in Kepler’s works. The nearest would be Johannes Kepler, Astronomia Nova (1609), available in Johannes Keplers Gesammelte Werke , Vol. III, ed. Max Caspar (Munich, 1937), and discussed e.g. in J R Voelkel, The Composition of Kepler's Astronomia Nova (Princeton, 2001). Its major and epoch-making discovery, achieved by Kepler’s study of Mars, was to identify the elliptical orbit and the motion by equal areas in equal times. But it has nothing about the power relationship between orbital size and period (separately found and published by Kepler about 10 years later); and Kepler’s idea of force was something that would produce or maintain velocity, a quite different concept than Newtonian force which produces acceleration; as pointed out by Bruce Stephenson, Kepler’s Physical Astronomy (New York, 1987). The Encyclopédie at this point took its English source at its word.

11. The ‘areas’, as in ‘The satellites of Jupiter describe areas around the planet . . . ’ are the areas that would be covered by a notional straight line that extends radially between the orbitally moving satellite and the centre of the planet. (And so on, in relation also to other pairs of bodies in the same kind of relative motion.)

12. ‘resistance of the air’ is the sense. The French text has ‘art’, Chambers had ‘air’.

13. This paragraph gives one of several signs (see also especially notes 19 and 20) suggesting that the Chambers article was at first put into French by a translator who understood little of the subject, with the translated article then revised and improved by an expert (probably d’Alembert), who however did not pick up all of the errors, perhaps because he did not examine all of it. The French text in this paragraph uses ‘force’ in two contradictory senses: broadly speaking, old and new. Newton often qualified force as ‘accelerative’ force ( vis acceleratrix ), meaning what we would now measure as acceleration, force per unit mass. Modern ‘force’ in this context includes the effect of mass, it is acceleration x mass. The French text tells us first that if Jupiter’s satellites could be placed at equal distances from the planet, then ‘la force de la gravité’ would be the same on each. But the satellites are of different (and unknown) masses, and at equal distances, there would be equal acceleration on each, equal vis acceleratrix , but not an equality of (modern) force. (The Chambers text here, reasonably enough but perhaps not clearly, gives ‘accelerating gravities’, not ‘force of gravity’.) By contrast, in this paragraph, the second French reference to ‘force’ is clear and correct in the modern sense rather than the old: the forces to give equal accelerations to unequal masses are proportional to the masses.

14. Here the French text is like Chambers 1743 edition ‘gravities of bodies’, where the 1728 edition gave ‘weights of bodies’.

15. Newton gave various numbers for the mass of the Earth as a fraction of the Sun’s mass, but 1/22512 is not among them. It is probably a miscopy for 1/227512. The French text otherwise matches Principia in the 1713 edition, which gave for Jupiter, Saturn and the Earth, 1/1033, 1/2411, 1/227512 (Book 3, Proposition 8). (Newton’s estimates for the Earth were much poorer than for Jupiter and Saturn, mainly because the Sun’s distance, and its proxy the solar parallax, was in his time poorly and uncertainly measured relative to that of the Moon: see A van Helden, Measuring the Universe (Chicago, 1985).)

16. The argument for fixity of the solar system’s centre of gravity, based on absence of stellar parallax-like effects, seems to be a curious addition relative to Chambers. It is not in the Principia, where Newton appears rather indifferent to the question whether the solar system centre is at rest or in uniform motion. Thus, he stated the common consensus of rest as a ‘hypothesis’ (Book 3, before Propositions 11 and 12): but the answer, either way, would not affect the rest of Newton’s argumentation.

17. The words at the end of section VII, ‘ donc, etc .’, bring to a premature end a point not in the Chambers article. These words could suggest that d’Alembert was conscious of not having finished his revision of the text. Perhaps he at first intended to return and write out the remainder of this added point: in the event he never did.

18. In the Chambers article, the comment about Jupiter’s perturbation on Saturn had been an unnumbered part of point VII. There had also been a separate argument ‘VIII’, but in the French version this was deleted, its number given to the Jupiter-Saturn point to leave the rest of the numbering unchanged. The deletion is a sign of careful consideration. Original point VIII had been that the aphelia and nodes of the planets are at rest, apart from negligible effects of perturbation by other planets and comets. In Paris in the 1740s, a closely-related point gave rise to hot controversy: the motion of the Moon’s apogee was no longer treated as negligible, and for a time it seemed that the amount of its rate might fundamentally refute rather than confirm the Newtonian gravitational inverse-square law. Eventually, 1749-1750, the difficulty was identified as coming from the inaccuracy of approximate calculations, so that it provided, after all, no evidence that the gravitational law was wrong: see C B Waff, Clairaut and the motion of the lunar apse , pp.35-46 in Planetary Astronomy from the Renaissance to the rise of astrophysics , vol.2B, eds. R Taton and C A Wilson, Cambridge, 1995. Nevertheless, for a French audience, original point VIII, if it had remained, might have been seen as improbable or untrue: its presence might have injured the credibility of the article.

19. This paragraph in the French was a translation of Chambers’ text, and has been garbled, perhaps by an uncomprehending translator. Oscillations of pendulums at the equator are not of shorter duration than towards the pole: the opposite was notoriously true from the 17th century onwards, after the observations of Jean Richer at Cayenne, and Edmund Halley at St.Helena. Near the equator they had found that pendulums beat slower, their lengths had to be shortened to keep the same rates as at Paris or London. Chambers’ text was correct, and it seems unlikely that d’Alembert would have missed this mistake in the French if he had reviewed it with attention.

20. The reference to variations here is another point of garbled translation. Chambers’ text had correctly listed, among lunar inequalities that Newton accounted for, ‘the differences in her Eccentricity, and her Variation, &c’. The term ‘Variation’ applies, here, to a special separate feature of the lunar inequalities, which was discovered by Tycho and named by him (with a most unhelpful name ‘variation’ that promotes confusion between the specific and the general, since practically everything observable in astronomy varies somehow). Clearly, the initial translator of Chambers’ text into French was unfamiliar with this astronomical terminology, and instead gave the phrase in French as if it had been ‘differences and variations of its eccentricity’, with verbal redundancy that makes no sense. It seems very unlikely that d’Alembert would have missed this if he had given attention to the paragraph, since he was himself one of rather few experts in lunar theory of the time (see Jean Le Rond d'Alembert, Oeuvres Complètes , ser.I, vol.6, Premiers textes de mécanique céleste 1747-1749 , ed. Michelle Chapront-Touzé, Paris 2002).

21. The objection was that Newton’s work tended to destroy the system of vortices (which was naturally unwelcome to its adherents). The translation here was either poor or illegibly written: ‘deducing’ ( déduisant ) the system of vortices is a mistake (and not a translation of the word in Chambers’ text), the French translation should have been ‘ détruisant ’.

22. See note 1.

23. The final sentence of the article, mentioning Newton’s (very rough) estimate of the Moon’s mass as a fraction (1/39) of the Earth’s mass, appears as a strange addition. No inferences are drawn from it in the text, and it seems to add little or nothing to the general effect of the arguments. The oddity of its presence here is all the greater, because d’Alembert himself had superseded Newton’s estimate by a much better one — 1/80, in the conclusions published by d’Alembert in his books of 1749 ( Recherches sur la Précession des Equinoxes : p.153) and 1754 (in part 2 of Recherches sur differens points importans du systême du Monde : p.223). There was little doubt at the time that the new measure was more soundly-based than the old. (Newton’s value of 1/39 was by the time of the Encyclopédie clearly an uncertain one, he had started from very rough data about the heights of tides, which were all that was available and relevant in his time; while d’Alembert, and shortly afterwards Euler, used James Bradley’s recent discovery and accurate measurement of the nutation in the direction of the Earth’s polar axis, as well as much-improved methods of developing the Newtonian gravitational analysis. D’Alembert’s value of 1/80 may also be compared in hindsight with the modern measure, close to 1/81.3.) D’Alembert’s work on this subject also afforded further confirmation of Newtonian universal gravitation e.g. by showing further evidence of the Moon’s attraction on the Earth’s equatorial bulge, and it was available enough that it gained a mention elsewhere in the Encyclopédie . Thus the final appended sentence of the French text can seem almost unconsidered: it could with advantage have been either left out or else supplemented with description of the recent results and their support for the principle. Here again, as at note 17, the state of the text could seem to suggest that the article on Newtonianisme as printed may have been essentially unfinished.