Edmond Halley

Born into a prosperous London family engaged in business, Halley attended Oxford University. While a student there he made astronomical observations and reported his results in the Philosophical Transactions of the Royal Society. In 1676 Halley sailed to St. Helena, the southernmost territory then under English rule. At the request of King Charles II, the East India Company provided for Halley's transportation on one of their ships and for his maintenance on the island. His father paid for his instruments. Halley measured positions of stars and observed eclipses and a transit of Mercury across the face of the Sun. He dedicated his chart of stars of the Southern Hemisphere, with a newly depicted constellation, Robur Carolinum (Charles' Oak), to Charles. Soon after Halley's return to England, the Royal Society elected him a fellow, at the early age of 22.

In 1684 Halley asked Isaac Newton what sort of planetary orbit an inverse square force would produce, a question that led to the Principia. For the second edition of the Principia, Halley in 1695 undertook to calculate comet orbits. He soon realized that the comets of 1531, 1607, and 1682 had similar orbits: it was the same comet revolving around the Sun in an elliptical orbit. Halley died before the predicted return of his comet in 1758. He also died before the predicted transits of Venus of 1761 and 1769, but he left detailed instructions for calculating the size of the solar system from their observation.

In the 1690s Halley discovered from his study of solar and lunar eclipse observations by an Arab astronomer in the ninth century a.d. that the Moon's mean motion had accelerated. And in 1718, Halley announced that a comparison of stellar positions in his day with those measured by Hipparchus revealed that in the course of 1,800 years several of the supposedly fixed stars had altered their places relative to other stars: they had motions of their own.

Halley also found time to undertake the attempted salvage of gold from a sunken ship,

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Not until the third edition, of 1726, did Newton distinguish propositions from hypotheses. He added: "This rule we must follow, that the argument of induction may not be evaded by hypotheses" (Principia III, Rules of Reasoning).

Following the argument of induction, Newton ostensibly began with phenomena. This was the strategy Kepler had adopted in his Astronomía nova in response to criticism for having begun with a priori theory in his earlier Mysterium cosmographicum. Inductivist thinking would become so strongly entrenched after the Principia that even Newton's disciples presumed that he had relied on Kepler's laws as empirical premises. Universal gravitation came to be seen (incorrectly) as an inductive achievement from the facts of planetary motion encapsulated in Kepler's laws.

The first phenomenon listed by Newton was that the radii of Jupiter's moons sweep out equal areas in equal times and the periodic times are as the 3/2 power of their distances. "This we know from observations," Newton wrote (Principia III, Phenomenon I). Observations revealed the same phenomenon for Saturn's moons and for the five planets revolving about the Sun. Here Newton acknowledged Kepler as the first to have observed this proportion. With only one satellite then revolving around the Earth, Kepler's third law, involving ratios for two satellites, was not applicable; but the Moon was observed to sweep out equal areas in equal times.

Next in the Principia came propositions. The implication was that they were induced from the phenomena. For each phenomenon, Newton proposed that the forces by which the moons or planets are "continually drawn off from rectilinear motions, and retained in their proper orbits" tend to the central body (the Sun in the case of the planets; a planet in the case of its moons) and are "inversely as the squares of the distances of the places of those planets [or moons] from that center" (Principia III, Proposition I). Newton also proposed that the planets move in ellipses. In a letter to Halley Newton claimed credit for establishing this proposition. He believed that Tycho Brahe's data were not adequate to warrant or guarantee the hypothesis and that Kepler had merely guessed at the ellipse.

The argument of induction is that from observations or phenomena, theories or propositions follow. After enough observations are accumulated, somehow a theory will appear in the human mind. Does it really matter, though, where a theory comes from? From observation by induction or from out of the mystery of

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which involved improving the diving bell; to survey harbors on the Dalmatian coast for potential use by the British fleet in the anticipated war of the Spanish succession; and to serve for several years as captain (an extremely rare appointment for a civilian) of his Majesty's ship Paramore, carrying out a study of tides in the English Channel and of magnetic variation in the Atlantic Ocean. During his second voyage, Halley discovered and took possession, in his Majesty's name, of a small uninhabited volcanic island in the South Atlantic.

Halley was appointed Savilian Professor of geometry at Oxford in 1704. There he produced editions of several classics of ancient Greek geometry. He was elected Secretary of the Royal Society in 1713 and resigned the position in 1720 when he succeeded John Flamsteed as Astronomer Royal, though he remained active in the Society. Halley carried out astronomical observations until a few months before his death, in 1742.

the human mind by some less rational and less objective process? Justification for a theory is not necessarily to be found in its origin.

Newton's great achievement was to show by deduction that from the theory of universal gravitation all the observed phenomena mathematically follow. Immediately after the propositions, he wrote: "Now that we know the principles on which they [the phenomena] depend, from these principles we deduce the motions of the heavens a priori" (Principia III, Proposition I). This Newton proceeded to do. Not only Kepler's laws, but many additional phenomena fell under Newton's geometrical onslaught.

From ancient observations, Halley had noticed that seemingly the same comet had appeared four times at intervals of 575 years, most recently in 1680. Newton now developed a geometrical procedure for determining from observations the orbit of a comet moving in a parabola. Then he compared observations of several comets with their predicted places computed from his theory. Newton concluded that "from these examples it is abundantly evident that the motions of comets are no less accurately represented by our theory than the motions of the planets commonly are by the theory of them; and, therefore, by means of this theory, we may enumerate the orbits of comets" (Principia III, Proposition XLII, Problem XXII).

The Moon, its motion around the Earth disturbed by the Sun's gravitational force, presented considerable difficulties. It moves faster and its orbit is less curved, and therefore the Moon approaches nearer to the Earth, in the syzygies (when the Moon lies in a straight line with the Earth and the Sun: at opposition or conjunction) than in the quadratures (at 90 degrees from the line joining the Sun and the Earth)—except when the eccentricity of the orbit affects this motion. The eccentricity is greatest when the apogee of the Moon (the point in its orbit farthest from the Earth) is in the syzygies, and least when the apogee is in the quadratures. Moreover, the apogee goes forward, and with an unequal motion: more swiftly forward in its syzygies and more slowly backwards in its quadratures, with a net yearly forward motion. Furthermore, the greatest latitude of the Moon (its angular distance above or below the plane of the Earth and the Sun) is greater in the quadratures than in the syzygies. Also, the mean motion of the Moon is slower when the Earth is at perihelion (nearest the Sun) than at aphelion (farthest from the Sun).

These were the principal inequalities in the motion of the Moon taken notice of by previous astronomers. In a remarkable mathematical tour de force, Newton demonstrated that all these inequalities followed from the principles he had laid down. There remained, however, "yet other inequalities not observed by former astronomers by which the motions of the Moon are so disturbed that to this day we have not been able to bring them under any certain rule" (Principia III, Proposition XXII, Theorem XVIII). Newton also demonstrated geometrically that the flux and reflux of the ocean tides arose from the actions of the Sun and Moon.

Newton's geometrical demonstrations were not restricted to celestial bodies. He also deduced that, other things being equal, the squares of the times of oscillation are as the lengths of pendulums; the weights are inversely as the squares of the times if the quantities of matter are equal; the quantities of matter are as the weights if the times are equal; and if the weights are equal, the quantities of matter are as the squares of the times.

Although a theory can never be absolutely proven because the world could have been made in some different manner that nonetheless has the same set of observational consequences, a theory does gain in confidence with each deduced phenomenon that is observed. Newton had deduced from an inverse square force of gravity an impressive number of effects.

There remained the question, what is gravity? Newton acknowledged that "hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power" (Principia III, General Scholium). Some things Newton did know:

This is certain, that it [gravity] must proceed from a cause that penetrates to the very centres of the Sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances. (Principia III, General Scholium)

But he didn't know what gravity was. In the second and third editions of the Principia, Newton wrote: "But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I feign no hypotheses. . . ." (Principia III, General Scholium).

Writing in Latin, Newton's actual words were "hypotheses non fingo." Sometimes this phrase is translated as "I frame no hypotheses." But Newton meant feign, in the sense of pretend: to present hypotheses that could not be proved and were probably false. Elsewhere he framed hypotheses that could be demonstrated, as all scientists do.

Newton continued. Because in experimental philosophy or science the emphasis should be on observed phenomena, propositions obtained by induction from them, and predicted phenomena deduced from propositions, "whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction" (Principia III, General Scholium).

For justification of experimental philosophy, Newton directed his readers to its remarkable success: "Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered" (Principia III, General Scholium). Newton argued for setting aside the question of what gravity is and instead be content with a mathematical description of its effects. He wrote: "And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea" (Principia III, General Scholium). Newton would have liked to explain the cause of gravity, but he wasn't able to, so he settled for demonstrating that the motions of the celestial bodies could be deduced mathematically from an inverse square force, whatever anyone might imagine the metaphysical or occult qualities of that force to be.

To explain motion Aristotle had attributed it to a final cause or purpose. Newton didn't explain motion; rather he demonstrated that the observed motions could be deduced mathematically from an inverse square force. One should abstain—as Aristotle had not—from speculating about the nature of that force. Moliere's quack doctor might explain the sleep-inducing power of opium in terms of its dormative potency; Newton did not explain gravity.

Also abandoned rather than answered by Newton was the question that had dominated astronomy since Copernicus and was at the center of the Galileo controversy: was the Earth or the Sun at the center of the universe? For Newton, the important center was the center of gravity, and neither the Earth nor the Sun necessarily resided there. (Since most of the mass in our planetary system is contained in the Sun, the Sun very nearly coincides with the center of gravity of the solar system; but they would not coincide in a system with a different distribution of mass.)

Yet another matter completely lost sight of in Newton's new science was the ancient Aristotelian distinction between terrestrial and celestial matter and their physical laws. Newton blithely united the terrestrial and the celestial.

The abandonment of scientific beliefs, values, and worldviews and their replacement with incompatible or even incommensurable new paradigms is the essence of a scientific revolution. Some historians accept the replacement of one theory with a second, incompatible theory as a revolution. Others might withhold the word revolution for the replacement ofone worldview with another worldview so incommensurable that rival proponents cannot agree on common procedures, goals, and measurements of success or failure.

The Ptolemaic and Copernican systems were incompatible but not incommensurable. While they predicted different results, such as the appearance of the phases of Venus, yet they were judged by the mutual standard of how well each saved the phenomena with systems of uniform circular motions.

Descartes' vortex system and Newton's gravity were more incommensurable than incompatible. They had different goals and different measurements of success or failure. Descartes had insisted on an explanation of the cause of gravity. Newton abandoned that quest and argued instead that it was enough that gravity acted according to an inverse-square force law and accounted for all the motions of the celestial bodies. Though Descartes' later followers eventually agreed that any successful vortex theory would have to account for Kepler's laws, Descartes himself had ignored Kepler's discoveries, if indeed he had known of them. Newton, on the other hand, asked that his theory be judged by its success in accounting for Kepler's laws. Descartes'

and Newton's theories were not incompatible, at least initially, with a mutual standard against which they could be judged, but incommensurable: not comparable on any mutually agreed upon basis. Newton established a new world-view and a new way of doing science.

Even poets were impressed. Alexander Pope rhymed:

Nature, and Nature's laws lay hid At Night

God said, Let Newton be!, and All was Light. (Feingold, Newtonian Moment, 144)

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