In an interesting essay²⁰ on the sources of Newton principles of mechanics, Professor Child expresses the opinion, which he frankly confesses to be a guess, that the inspiration for the preliminary matter of the Principia came from the work of Baliani. He states that his guess would be justified if, "after a careful search into the works that were in Newton's library, there is found a copy of a certain book, especially if it shows signs of having been much used, or if in any of his manuscripts a certain name occurs; and I will gladly acknowledge the error of my ways if such a book is not to be found. The book is De Motu and the author is Baliani." My own reading of the De Motu leaves me with the opinion that any connection between Baliani and Newton is extremely doubtful. His treatment of the problem of forces seems far more limited and obscure than that by Galileo. And the chance that this work by an obscure Italian was known to Newton and his contemporary English natural philosophers is far less likely than that the Dialogues of the most eminent man of science of the age were not familiar to them. The Dialogues on the Two New Sciences had been translated into English in 1665 and, although the edition may have been destroyed in the London fire of the following year, the original or some copies must have been well known and studied.²¹

If we turn to Newton, himself, for the sources of his ideas, we obtain very little information. For his discovery of the problem of the moon's force in 1666, we gather that he developed the law of inverse squares from a direct study of Copernicus and Kepler with the mathematical aid of Descartes, Barrow, and Wallis. In the Principia, he mentions Galileo as the source from which he formulated his first and second laws of motion; and from the work of Wren, Wallis, and Huygens on the laws of impact, he obtained his third law. It is significant of his dislike for Hooke and Descartes that he omits their names. The law of attraction, as being proportional to the inverse square of the distance, he states was surmised by Wren, Hooke, and he specifically mentions that Huygens had compared the force of gravity with the centrifugal forces of revolving bodies. In his correspondence with Halley, the statement is made that Borelli had contributed something to the discovery and had written modestly about it, but Hooke had published Borelli's hypothesis as his own. He also gives credit to Bullialdus for a share in its history. While Descartes should be considered as one of the great contributors to the mechanistic hypothesis and, in fact, elaborated a vast cosmical system on that doctrine, his invention of vortices to carry the planets the about the sun was the chief obstacle to the acceptance of Newtonian mechanics; and Newton took great pains to expose the failure of the vortical theory in a manner which clearly showed his satisfaction.

Although Newton stated explicitly that Borelli and Bullialdus²² had arrived at the correct law of gravitation and also intimated that their views had been of aid to him in his own work, the various commentators of the Principia are quite divided in their opinions as to whether any such conclusions can be derived from the works of those two authors. It seems to me we might accept Newton's testimony rather than their opinion that those authors, whether wittingly or not, had something of real importance to that great discovery. At least we can let them speak for themselves.

Bullialdus (or Bouilleaud, 1605-1694), a French astronomer, was an accurate and voluminous observer whose data on the orbits of the planets were quoted as authoritative by Newton in the Principia. He was an enthusiastic supporter of the Copernican system; and was so convinced, that the success of the new science was dependent on a revival of the Pythagorean and Platonic scientific conceptions, as to name his most important treatise the Astronomia Philolaïca ²² to indicate his belief that Philolaus, the Pythagorean, was the founder of the true astronomy. The work is one of the most important of the period. It contains a valuable summary of the history of astronomy and a wealth of data. While he gives proper credit to Kepler, he accuses him of advancing an erroneous hypothesis of the planetary motions. The portion of the work, which discusses this hypothesis, is contained in the twelfth chapter of the first book, headed An sol moveat planetas. He combats Kepler's idea that the motive force of the planets resided in the sun which was endowed with a species, or effluvium, of a spiritual or magnetical nature, and whirled those inert bodies about him in their orbits. While he adduces four objections, the significant reasons he gives are first; if the planets are thus inert, how do they, the earth and Jupiter for example, move their own satellites and, secondly, he denies that there are any such whirling forces. In the course of his argument, he affirms that the planetary force is one which acts along the line joining the two bodies and decreases inversely as the square of them.²

One of the earliest attempts to explain all phenomena by means of atoms, or corpuscles, which were subject only to mechanical laws, was made by Giovanni Alfonso Borelli²⁵ (1608-1679), a Neapolitan, and the most distinguished member of the Accademia del Cimento. In brief, his fundamental postulate was that all natural actions are caused by a gravitational force on the corpuscles which pulls them towards the centre of the earth according to mechanical laws; but the particular forms of the corpuscles and their mutual linkages divert their downward motion into other directions. Thus, aggregations of corpuscles are like machines whose prime motive force is gravity, but whose construction is so designed as to make them operate in various ways. The dilemma which faces all mechanists is how to give an active principle to atoms which are essentially inert and passive. The problem is really insoluble and the usual method is to create an hypothetical substance which complacently does all those things which may be needed. So Borelli asserts that there are also certain aethereal and living (spirituosa et vivida) particles which were endowed with the attribute of self-motion by God at the creation. The otherwise inert material bodies enmesh in their pores a multitude of these active aethereal corpuscles and so he accounts for the forces of gravity, magnetism, etc. This hypothesis has so many points of resemblance with Newton's speculations on an aether that he very probably was influenced by it. Borelli's contribution to Kepler's problem is found in his study of Jupiter's moons. He remarks that, when a body revolves in an orbit, it has a tendency to recede from its centre of revolution as mud from the rim of a wheel, or a stone whirled by a sling. When this force of recession is equal to a force of attraction pulling it to the centre, the body will neither approach nor recede from the centre but will continually revolve about it, and a planet will appear balanced and floating on the surface of a sphere.

This statement brings us down to the time of the active work of Newton, and may well close our summary of the growth of the mechanistic hypothesis which he completed by his discovery of an universal law of attraction. However much we may respect his predecessors, we cannot fail to recognise that their ideas were vague and that no organised scientific method could be derived from them. If we may personify Nature and give to her the attribute of choice, we may then say that out of all the human race she granted to Newton the unique destiny of disclosing her profoundest secret. All that was needed was a mathematical apparatus capable of expressing the changes of path of a body under a constantly varying motion. The classic geometry, dealing with static problems, was inadequate. But the expansion of mathematical analysis during the Renaissance was even more rapid than was that of astronomy and physics. Descartes made the first great step by his fusion of algebra and geometry. This powerful analysis was developed into the method of solving problems of curvilinear motion by expansion into infinite series; the final step was the invention of the calculus, or summation of infinitesimal variations by Newton and Leibnitz.

19. Horologium Oscillatorium, published in 1673.

20. Isaac Newton, 1642-1727. Ed. by Greenstreet, p. 117.

21. For Professor Child's discussion of this point, cf. Greenstreet, pp. 125-129. As for Newton's manuscripts, I have found no reference in any of them to Baliani; this is not conclusive as it is certain that many of them were destroyed and others have not been discovered. As for his library, since Professor Child wrote his essay Col. de Villamil has found and published the complete catalogue of Newton's books, as inventoried at his death, and no work by Baliani is included. Professor Child makes a slight error when he states that the first book of his De Motu was published in 1639. His guess, also, has not been substantiated.

22. It is interesting to note, in connection with Professor Child's 'guess,' that the works of Borelli are listed in Newton's library, but that none of Bullialdus's is mentioned.

23. Ismaelis Bullialdi Astronomia Philolaïca. Paris, 1645.

24. The passage (Cf. p. 23) is quite explicit although the reasons are specious: Virtus autem illa, qua Sol prehendit seu harpagat planetas, corporalis quae ipsi [Kepler] pro manibus est, lineis rectis in omnem mundi amplitudinem emissa quasi species solis cum illius corpore rotatur: cum ergo sit corporalis imminuitur, & extenuatur in maiori spatio & interuallo, ratio autem huius imminutionis eadem est, ac luminis, in ratione nempe dupla {dropped: interuallorum, sed euersa. Hoc non negauit Keplerus, attamen} virtutem motricem in simpla tantum ratione in[ter]uallorum contendit imminui.

[RAH: More's footnote above drops a significant line in his Latin quotation drawn from Boulliau's Astronomia philolaica, which might be translated: Concerning that force [virtue; power] by which the Sun seizes or takes hold of the planets, and being corporeal behaves in the manner of his [Kepler] hands, it is emitted in straight lines across the entire extent of the cosmos, and as with the species of the sun, it rotates with the body [of the sun]: and thus, because it is corporeal, it becomes weaker and more feeble at a greater distance or interval, and the ratio of this decrease [in strength] is the same as that of light, specifically, as the inverse square of the distances [Or read: the duplicate proportion, inversely, of the distances]. {Kepler does not deny this but claims} the motive force diminishes only in a direct proportion to distance.]

25. His most important works on physics are: Theorica mediceorum planetarum ex causis physicis deducta, Florence, 1666; De motu animalium, opus posthumum, Rome, 1681; De motionibus naturalibus, a gravitate pendentibus, Lugeluni Bataborum, 1686.

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