﻿ THE PRINCIPIA - Isaac Newton 1642–1727

# IV. THE PRINCIPIA

The preface explained the title:

Since the ancients (as we are told by Pappus) made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms [of the Scholastics] and occult qualities, have endeavored to subject the phenomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics as far as it regards [natural] philosophy. . . . Therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.

The viewpoint is to be strictly mechanical:

I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.

After laying down some definitions and axioms, Newton formulated three laws of motion:

1. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

2. The change of motion is proportional to the motive force impressed, and is made in the direction of the straight line in which that force is impressed.

3. To every action there is always opposed an equal reaction.

Armed with these laws, and the rule of inverse squares, Newton proceeded to formulate the principle of gravitation. Its current form, that every particle of matter attracts every other particle with a force varying directly as the product of their masses and inversely as the square of the distance between them, is nowhere found in these words in the Principia; but Newton expressed the idea in the general scholium that closes Book II: “Gravity . . . operates . . . according to the quantity of the solid matter which they [the sun and the planets] contain, and propagates its virtue on all sides, . . . decreasing always as the inverse square of the distances.” 33 He applied this principle, and his laws of motion, to the planetary orbits, and found that his mathematical calculations harmonized with the elliptical orbits deduced by Kepler. He argued that the planets are deflected from rectilinear motions, and are kept in their orbits, by a force tending toward the sun and varying inversely as the square of their distances from the center of the sun. On similar principles he explained the attraction of Jupiter upon its satellites, and of the earth upon the moon. He showed that Descartes’ theory of vortices as the first form of the cosmos could not be reconciled with Kepler’s laws. He calculated the mass of each planet, and figured the density of the earth as between five and six times that of water. (The current figure is 5.5.) He accounted mathematically for the flattening of the earth at the poles, and ascribed the bulge of the earth at the equator to the gravitational attraction of the sun. He worked out the mathematics of tides as due to the combined pull of the sun and the moon upon the seas; and by similar “lunisolar” action he explained the precession of the equinoctial points. He reduced the trajectories of comets to regular orbits, and so confirmed Halley’s prediction. By attributing gravitational attraction to all planets and stars, he pictured a universe mechanically far more complex than had been supposed; for now every planet or star was viewed as influenced by every other. But into this complex multitude of heavenly bodies Newton placed law: the most distant star was subject to the same mechanics and mathematics as the smallest particles on the earth. Never had man’s vision of law ventured so far or so boldly into space.

The first edition of the Principia was soon sold out, but no second edition appeared till 1713. Copies became so scarce and hard to secure that one scientist transcribed the whole work with his own hand. 34 It was recognized as an intellectual enterprise of the highest order, but some notes of criticism soured the praise. France, clinging to Descartes’ vortices, rejected the Newtonian system until Voltaire gave it a worshipful exposition in 1738. Cassini and Fontenelle objected that gravitation was just one more occult force or quality; Newton propounded certain relationships among the heavenly bodies, but he had not revealed the nature of gravitation, which remained as mysterious as God. Leibniz argued that unless Newton could show the mechanism by which gravitation could act through apparently empty space upon objects millions of miles away, gravitation could not be accepted as anything more than a word. 35

Even in England the new theory was not readily received. Voltaire claimed that forty years after its first publication hardly twenty scientists could be found favorable to it. Whereas in France critics complained that the theory was insufficiently mechanical as compared with Descartes’ primeval whirlpools, in England the objections were predominantly religious. George Berkeley, in Principles of Human Knowledge (1710), regretted that Newton had thought of space, time, and motion as absolute, apparently eternal, and existing independently of divine support. Mechanism so pervaded the Newtonian system that there seemed no place in it for God.

When Newton, after characteristic delays, agreed to prepare a second edition, he tried to appease his critics. He assured Leibniz and the French that he did not assume a force acting at a distance through empty space; he believed in an intervening medium of transmission, though he would not attempt to describe it; and he frankly confessed that he did not know the nature of gravitation. It was in this connection that he wrote in the second edition the oft misunderstood words “Non fingo hypotheses.36 “Gravity,” he added, “must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers.” 37

To further meet religious objections he appended to the second edition a general scholium on the role of God in his system. He restricted his mechanistic explanations to the physical world; even in that world he saw evidences of divine design; the great machine required some initial source of its motion, which must be God; moreover there were, in the solar system, certain irregularities of behavior which God periodically corrected as they arose. 38 To make room for such miraculous interpositions Newton surrendered the principle of the conservation of energy. The world machine, he now supposed, lost energy in time, and would run down if God did not intervene to restore its force. 39 “This most beautiful system of the sun, planets, and comets,” he concluded, “could only proceed from the counsel and dominion of an intelligent and powerful Being.” 40 Finally he moved toward a philosophy that could be interpreted in either a vitalistic or a mechanistic sense:

And now we might add something concerning a certain most subtle spirit which pervades and hides in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighboring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in a few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates. 41

What was his actual religious faith? His professorship at Cambridge required allegiance to the Established Church, and he attended Anglican services regularly; but, says his secretary, “as for his private prayers, I can say nothing of them; I am apt to believe his intense studies deprived him of the better part.” 42 Yet he studied the Bible as zealously as he studied the universe. An archbishop complimented him—“You know more divinity than all of us put together”; 43 and Locke said of his knowledge of the Scriptures, “I know few his equals.” 44 He left theological writings greater in bulk than all his scientific works.

His studies led him to semi-Arian conclusions much like those of Milton: that Christ, though the Son of God, was not equal in time or power with God the Father. 45 For the rest, Newton was, or became, quite orthodox. He seems to have taken every word of the Bible as the word of God, and to have accepted the books of Daniel and Revelation as literal truth. The greatest scientist of his age was a mystic who lovingly copied out large passages from Jakob Böhme, and who asked Locke to discuss with him the meaning of the “White Horse” in the Apocalypse. He encouraged his friend John Craig to write Theologizae Christianae Principia Mathematica (1699), which sought to prove mathematically the date of Christ’s second coming, and the ratio between the highest attainable earthly happiness and the believer’s rewarding bliss in Paradise. 46 He wrote a commentary on the Apocalypse, and argued that the Antichrist therein predicted was the pope of Rome. Newton’s mind was a mixture of Galileo’s mechanics and Kepler’s laws with Böhme’s theology. We shall not soon see his like again.

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