The Chapter begins with a brief summary of the previous chapter, namely with Galileo’s law of free fall. It asserts that if two objects are left from the same point to fall, then, regardless of their masses, both objects will cover the same distance during the same period of time. In particular, both objects will hit the surface of the attracting body at the same time, neglecting the effect of air resistance. In fact, the real, inclined-plane, situation (e.g. to minimize friction) is difficult to establish. The pendulum, on the other hand, more easily allows the experimental confirmation of the law of free fall. Newton used the pendulum not only to test Galileo’s law of free fall and to establish a value for the gravitational constant, but to distinguish mass from weight. Referring to Newton’s experiment on the oscillations of different pendulums in Book III of his Principia, Proposition VI, Du Châtelet remembers that Newton demonstrated that the quantity of matter of bodies is directly proportional to their weight and that the mass of a body is a measure of its quantity (InstPhy, § 322). It is important to note here that we must distinguish with care the heaviness of bodies from their weight (InstPhy, § 324):
la pésanteur, c’est à-dire, cette force, qui anime les corps àdes· cendre vers la terre, agit de même sur tous les corps, quelle que soit leur masse; mais il n’en est pas ainsi de leurs poids, car le poids d’un corps est le produit de la péfanteur par la masse de ce corps. (Amsterdam 1742)
Heaviness, that is to say, that force that animates bodies to descend toward the earth, acts similarly on all bodies, whatever their mass. But it is not the same with their weight: for the weight of a body is the product of the heaviness and the mass of this body. (Copyright © 2018 KB)
In modern terms: Mass is a measure of how much matter an object contains, and weight is a measure of the force of gravity acting on the object. Gravity is the attraction between two objects that have mass. All objects on Earth, regardless of their mass, accelerate due to gravity at the same rate.
In his Horologium oscillatorium (Paris, 1673), Christiaan Hygens generalized Galileo’s law to curvilinear paths: At any point in its fall or rise along a curve, a body will have the same speed as it would have by falling perpendicularly. These experiments were continued and specified by William Derham (“Experiments About the Motion Pendulums in Vacuo,” Philosophical Transactions of the Royal Society of London 24, No. 294 (1705): 1785-89).
Du Châtelet meticulously describes further experiments on resistance to moving bodies. In July 1719, John Theophilus Desaguliers dropped, from the top of the cupola of St Paul’s Church in London, spheres made of hogs’ bladders filled with air. The experiment and experimental result, published in “An Account of Some Experiments Made on the 27th Day of April, 1719 to Find How Much the Resistance of the Air Retards Falling Bodies,” Philosophical Transactions of the Royal Society of London 30, No. 362 (1719): 1071-1078, was that the air by its resistance slowed their fall by about 17 feet in 4½ seconds (InstPhy, § 329). A similar experiment on the fall of bodies from the top of the platform of the Observatory of Paris was carried out by Edme Mariotte (InstPhy, § 330-331). Mariotte’s collision experiments were presented to the French Academy of Sciences in 1671 and subsequently published in 1673 as Traité de la percussion ou choc des corps. Further, Du Châtelet mentions Frenicle de Bessy’s experiments on the time of fall of different bodies, which were falsified by Jean Baptiste DuHamel (Regiae scientiarum Academiae historia Paris 1698). Not to forget: Henri Pitot’s “Remarques sur les rapports des Surfaces des grands & des petits Corps” (Histoire de l’Académie royale des sciences (1728), pp. 369-377), where the relationships between rainfall intensity and resulting surface flow is investigated. These and similar experiments, which demonstrated that bodies fall perpendicularly to the surface of the earth, became most importatnly for Newton, who demonstrated that the heavens (moon and planets) obeyed the same laws as earthly bodies such as falling stones and projectiles.