To Explain the World: The Discovery of Modern Science (35 page)

After laying out Newton’s theories of motion and gravitation, the
Principia
goes on to work out some of their consequences. These go far beyond Kepler’s three laws. For instance, in Proposition 14 Newton explains the precession of planetary orbits measured (for the Earth) by al-Zarqali, though Newton does not attempt a quantitative calculation.

In Proposition 19 Newton notes that the planets must all be oblate, because their rotation produces centrifugal forces that are largest at the equator and vanish at the poles. For instance, the Earth’s rotation produces a centripetal acceleration at its equator equal to 0.11 feet/second per second, as compared with the acceleration 32 feet/second per second of falling bodies, so the centrifugal force produced by the Earth’s rotation is much less than its gravitational attraction, but not entirely negligible, and the Earth is therefore nearly spherical, but slightly oblate. Observations in the 1740s finally showed that the same pendulum will swing more slowly near the equator than at higher latitudes, just as would be expected if at the equator the pendulum is farther from the center of the Earth, because the Earth is oblate.

In Proposition 39 Newton shows that the effect of gravity on the oblate Earth causes a precession of its axis of rotation, the “precession of the equinoxes” first noted by Hipparchus. (Newton had an extracurricular interest in this precession; he used its values along with ancient observations of the stars in an attempt to date supposed historical events, such as the expedition of Jason and the Argonauts.)
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In the first edition of the
Principia
Newton calculates in effect that the annual precession due to the Sun is 6.82° (degrees of arc), and that the effect of the Moon is larger by a factor 6⅓, giving a total of 50.0" (seconds of arc) per year, in perfect agreement with the precession of 50" per year then measured, and close to the modern value of 50.375" per year.
Very impressive, but Newton later realized that his result for the precession due to the Sun and hence for the total precession was 1.6 times too small. In the second edition he corrected his result for the effect of the Sun, and also corrected the ratio of the effects of the Moon and Sun, so that the total was again close to 50" per year, still in good agreement with what was observed.
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Newton had the correct qualitative explanation of the precession of the equinoxes, and his calculation gave the right order of magnitude for the effect, but to get an answer in precise agreement with observation he had to make many artful adjustments.

This is just one example of Newton fudging his calculations to get answers in close agreement with observation. Along with this example, R. S. Westfall
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has given others, including Newton’s calculation of the speed of sound, and his comparison of the centripetal acceleration of the Moon with the acceleration of falling bodies on the Earth’s surface mentioned earlier. Perhaps Newton felt that his real or imagined adversaries would never be convinced by anything but nearly perfect agreement with observation.

In Proposition 24, Newton presents his theory of the tides. Gram for gram, the Moon attracts the ocean beneath it more strongly than it attracts the solid Earth, whose center is farther away, and it attracts the solid Earth more strongly than it attracts the ocean on the side of the Earth away from the Moon. Thus there is a tidal bulge in the ocean both below the Moon, where the Moon’s gravity pulls water away from the Earth, and on the opposite side of the Earth, where the Moon’s gravity pulls the Earth away from the water. This explained why in some locations high tides are separated by roughly 12 rather than 24 hours. But the effect is too complicated for this theory of tides to have been verified in Newton’s time. Newton knew that the Sun as well as the Moon plays a role in raising the tides. The highest and lowest tides, known as spring tides, occur when the Moon is new or full, so that the Sun, Moon, and Earth are on the same line, intensifying the effects of gravitation. But the worst complications come from the fact that any gravitational effects on the
oceans are greatly influenced by the shape of the continents and the topography of the ocean bottom, which Newton could not possibly take into account.

This is a common theme in the history of physics. Newton’s theory of gravitation made successful predictions for simple phenomena like planetary motion, but it could not give a quantitative account of more complicated phenomena, like the tides. We are in a similar position today with regard to the theory of the strong forces that hold quarks together inside the protons and neutrons inside the atomic nucleus, a theory known as quantum chromodynamics. This theory has been successful in accounting for certain processes at high energy, such as the production of various strongly interacting particles in the annihilation of energetic electrons and their antiparticles, and its successes convince us that the theory is correct. We cannot use the theory to calculate precise values for other things that we would like to explain, like the masses of the proton and neutron, because the calculation is too complicated. Here, as for Newton’s theory of the tides, the proper attitude is patience. Physical theories are validated when they give us the ability to calculate enough things that are sufficiently simple to allow reliable calculations, even if we can’t calculate everything that we might want to calculate.

Book III of
Principia
presents calculations of things already measured, and new predictions of things not yet measured, but even in the final third edition of
Principia
Newton could point to no predictions that had been verified in the 40 years since the first edition. Still, taken all together, the evidence for Newton’s theories of motion and gravitation was overwhelming. Newton did not need to follow Aristotle and explain why gravity exists, and he did not try. In his “General Scholium” Newton concluded:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the Sun and planets without any diminution of its power to act, and that acts not in
proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do), but in proportion to the quantity of
solid
matter, and whose action is extended everywhere to immense distances, always decreasing as the inverse squares of the distances. . . . I have not as yet been able to deduce from phenomena the reasons for these properties of gravity, and I do not “feign” hypotheses.

Newton’s book appeared with an appropriate ode by Halley. Here is its final stanza:

Then ye who now on heavenly nectar fare,

Come celebrate with me in song the name

Of Newton, to the Muses dear; for he

Unlocked the hidden treasuries of Truth:

So richly through his mind had Phoebus cast

The radius of his own divinity,

Nearer the gods no mortal may approach.

The
Principia
established the laws of motion and the principle of universal gravitation, but that understates its importance. Newton had given to the future a model of what a physical theory can be: a set of simple mathematical principles that precisely govern a vast range of different phenomena. Though Newton knew very well that gravitation was not the only physical force, as far as it went his theory was universal—every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of their separation. The
Principia
not only deduced Kepler’s rules of planetary motion as an exact solution of a simplified problem, the motion of point masses in response to the gravitation of a single massive sphere; it went on to explain (even if only qualitatively in some cases) a wide variety of other phenomena: the precession of equinoxes, the precession of perihelia, the paths of comets, the motions of moons, the rise and fall of the tides,
and the fall of apples.
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By comparison, all past successes of physical theory were parochial.

After the publication of the
Principia
in 1686–1687, Newton became famous. He was elected a member of parliament for the University of Cambridge in 1689 and again in 1701. In 1694 he became warden of the Mint, where he presided over a reform of the English coinage while still retaining his Lucasian professorship. When Czar Peter the Great came to England in 1698, he made a point of visiting the Mint, and hoped to talk with Newton, but I can’t find any account of their actually meeting. In 1699 Newton was appointed master of the Mint, a much better-paid position. He gave up his professorship, and became rich. In 1703, after the death of his old enemy Hooke, Newton became president of the Royal Society. He was knighted in 1705. When in 1727 Newton died of a kidney stone, he was given a state funeral in Westminster Abbey, even though he had refused to take the sacraments of the Church of England. Voltaire reported that Newton was “buried like a king who had benefited his subjects.”
¹⁷

Newton’s theory did not meet universal acceptance.
¹⁸
Despite Newton’s own commitment to Unitarian Christianity, some in England, like the theologian John Hutchinson and Bishop Berkeley, were appalled by the impersonal naturalism of Newton’s theory. This was unfair to the devout Newton. He even argued that only divine intervention could explain why the mutual gravitational attraction of the planets does not destabilize the solar system,
*
and why some bodies like the Sun and stars shine by their own light, while others like the planets and their satellites are
themselves dark. Today of course we understand the light of the Sun and stars in a naturalistic way—they shine because they are heated by nuclear reactions in their cores.

Though unfair to Newton, Hutchinson and Berkeley were not entirely wrong about Newtonianism. Following the example of Newton’s work, if not of his personal opinions, by the late eighteenth century physical science had become thoroughly divorced from religion.

Another obstacle to the acceptance of Newton’s work was the old false opposition between mathematics and physics that we have seen in a comment of Geminus of Rhodes quoted in
Chapter 8
. Newton did not speak the Aristotelian language of substances and qualities, and he did not try to explain the cause of gravitation. The priest Nicolas de Malebranche (1638–1715) in reviewing the
Principia
said that it was the work of a geometer, not of a physicist. Malebranche clearly was thinking of physics in the mode of Aristotle. What he did not realize is that Newton’s example had revised the definition of physics.

The most formidable criticism of Newton’s theory of gravitation came from Christiaan Huygens.
¹⁹
He greatly admired the
Principia
, and did not doubt that the motion of planets is governed by a force decreasing as the inverse square of the distance, but Huygens had reservations about whether it is true that every particle of matter attracts every other particle with such a force, proportional to the product of their masses. In this, Huygens seems to have been misled by inaccurate measurements of the rates of pendulums at various latitudes, which seemed to show that the slowing of pendulums near the equator could be entirely explained as an effect of the centrifugal force due to the Earth’s rotation. If true, this would imply that the Earth is not oblate, as it would be if the particles of the Earth attract each other in the way prescribed by Newton.

Starting already in Newton’s lifetime, his theory of gravitation was opposed in France and Germany by followers of Descartes and by Newton’s old adversary Leibniz. They argued that an attraction operating over millions of miles of empty space would be
an occult element in natural philosophy, and they further insisted that the action of gravity should be given a rational explanation, not merely assumed.

In this, natural philosophers on the Continent were hanging on to an old ideal for science, going back to the Hellenic age, that scientific theories should ultimately be founded solely on reason. We have learned to give this up. Even though our very successful theory of electrons and light can be deduced from the modern standard model of elementary particles, which may (we hope) in turn eventually be deduced from a deeper theory, however far we go we will never come to a foundation based on pure reason. Like me, most physicists today are resigned to the fact that we will always have to wonder why our deepest theories are not something different.

The opposition to Newtonianism found expression in a famous exchange of letters during 1715 and 1716 between Leibniz and Newton’s disciple, the Reverend Samuel Clarke, who had translated Newton’s
Opticks
into Latin. Much of their argument focused on the nature of God: Did He intervene in the running of the world, as Newton thought, or had He set it up to run by itself from the beginning?
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The controversy seems to me to have been supremely futile, for even if its subject were real, it is something about which neither Clarke nor Leibniz could have had any knowledge whatever.

In the end the opposition to Newton’s theories didn’t matter, for Newtonian physics went from success to success. Halley fitted the observations of the comets observed in 1531, 1607, and 1682 to a single nearly parabolic elliptical orbit, showing that these were all recurring appearances of the same comet. Using Newton’s theory to take into account gravitational perturbations due to the masses of Jupiter and Saturn, the French mathematician Alexis-Claude Clairaut and his collaborators predicted in November 1758 that this comet would return to perihelion in mid-April 1759. The comet was observed on Christmas Day 1758, 15 years after Halley’s death, and reached perihelion on March 13, 1759. Newton’s theory was promoted in the mid-eighteenth
century by the French translations of the
Principia
by Clairaut and by Émilie du Châtelet, and through the influence of du Châtelet’s lover Voltaire. It was another Frenchman, Jean d’Alembert, who in 1749 published the first correct and accurate calculation of the precession of the equinoxes, based on Newton’s ideas. Eventually Newtonianism triumphed everywhere.