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 explain the elasticity and compressibility of gases according to Boyle's law, he could explore what he believed might be actual physical reality. But he nonetheless reminded his readers (as in the scholium at the end of section 1) that the condition of resistance that he was discussing was “more a mathematical hypothesis than a physical one.” Even in his final argument against Cartesian vortices (section 9), he admitted the implausibility of the proposed hypothesis that “the resistance . . . is, other things being equal, proportional to the velocity.” Although a scholium to proposition 52 states that “it is in truth probable that the resistance is in a less ratio than that of the velocity,” Newton in fact never explored the consequences of this probable assumption in detail. Such a procedure is in marked contrast to book I, in which Newton examined a variety of conditions of attractive and centripetal forces, but so concentrated on the inverse-square force as to leave the reader in no doubt that this is the chief force acting (insofar as weight is concerned) on the sun, the planets, the satellites, the seas, and all terrestrial objects. Book II differs further from book I in having a separate section devoted to each of the imagined conditions of resistance. In section 1, resistance to the motions of bodies is said to be as “the ratio of the velocity”; in section 2, it is as “the square of their velocities”; and in section 3, it is given as “partly in the ratio of the velocities and partly as the square of the same ratio.” Then, in section 4, Newton introduced the orbital “motion of bodies in resisting mediums,” under the mathematical condition that “the density of a medium” may vary inversely as the distance from “an immovable centre”; the “centripetal force” is said in proposition 15 to be as the square of the said density, but is thereafter arbitrary. In a very short scholium, Newton added that these conditions of varying density apply only to the motions of very small bodies. He supposed the resistance of a medium, “other things being equal,” to be proportional to its “density.” In section 5, Newton went on to discuss some general principles of hydrostatics, including properties of the density and compression of fluids. Historically, the most significant proposition of section 5 is proposition 23, in which Newton supposed “a fluid [to] be composed of particles fleeing from each other,” and then showed that Boyle's law (“the density” of a gas varying directly as “the compression”) is a necessary and a sufficient condition for the centrifugal forces to “be inversely proportional to distances of their [that is, the particles'] centers.” Then, in the scholium to this proposition, Newton generalized the results, showing that for the compressing forces to “be as the cube roots of the power En+2,” where E is “the density of the compressed fluid,” it is both a necessary and sufficient condition that the centrifugal forces be “inversely as any power Dn of the distance [between particles].” He made it explicit that the “centrifugal forces” of particles must “terminate in those particles that are next [to] them, or are diffused not much farther,” and drew upon the example of magnetic bodies. Having set such a model, however, Newton concluded that it would be “a physical question” as to “whether elastic fluids [gases] do really consist of particles so repelling each other,” and stated that he had limited himself to demonstrating “mathematically the property of fluids consisting of particles of this kind, that hence philosophers may take occasion to discuss that question.”157 Section 6 introduces the “motion and resistance of pendulous bodies.” The opening proposition (24) relates the quantity of matter in the bob to its weight, the length of the pendulum, and the time of oscillation in a vacuum. Because, as corollary 5 states, “in general, the quantity of matter in the pendulous body is directly as the weight and the square of the time, and inversely as the length of the pendulum,” a method is at hand for using pendulum experiments to compare directly “the quantity of matter” in bodies, and to prove that the mass of bodies is proportional “to their weight.” Newton added that he had tested this proposition experimentally, then further stated, in corollary 7, that the same experiment may be used for “comparing the weights of the same body in different places, to know the variation of its gravity.”158 This is the first clear recognition that “mass” determines both weight (the amount of gravitational action) and inertia (the measure of resistance to acceleration)--the two properties of which the “equivalence” can, in classical physics, be determined only by experiment. In section 6 Newton also considered the motion of pendulums in resisting mediums, especially oscillations in a cycloid, and gave methods for finding “the resistance of mediums by pendulums oscillating therein.” An account of such experiments makes up the “General Scholium” with which section 6 concludes.159 Among them is an experiment Newton described from memory, designed to confute “the opinion of some that there is a certain aethereal medium, extremely rare and subtile, which freely pervades the pores of all bodies.” Section 7 introduces the “motion of fluids,” and “the resistance made to projected bodies,” and section 8 deals with wave motion. Proposition 42 asserts that “All motion propagated through a fluid Image Size: 240x320 480x640 960x1280 1440x1920 1920x2560 