Discovery of Gravitation

A.D. 1666

SIR DAVID BREWSTER

Many admirers of Sir Isaac Newton have asserted that his was the most gigantic intellect ever bestowed on man. He discovered the law of gravitation, and by it explained all the broader phenomena of nature, such as the movements of the planets, the shape and revolution of the earth, the succession of the tides. Copernicus had asserted that the planets moved, Newton demonstrated it mathematically.

His discoveries in optics were in his own time almost equally famous, while in his later life he shared with Leibnitz the honor of inventing the infinitesimal calculus, a method which lies at the root of all the intricate marvels of modern mathematical science.

Newton should not, however, be regarded as an isolated phenomenon, a genius but for whom the world would have remained in darkness. His first flashing idea of gravitation deserves perhaps to be called an inspiration. But in all his other labors, experimental as well as mathematical, he was but following the spirit of the times. The love of science was abroad, and its infinite curiosity. Each of Newton’s discoveries was claimed also by other men who had been working along similar lines. Of the dispute over the gravitation theory Sir David Brewster, the great authority for the career of Newton, gives some account. The controversy over the calculus was even more bitter and prolonged.

It were well, however, to disabuse one’s mind of the idea that Newton’s work was a finality, that it settled anything. As to why the law of gravitation exists, why bodies tend to come together, the philosopher had little suggestion to offer, and the present generation knows no more than he. Before Copernicus and Newton men looked only with their eyes, and accepted the apparent movements of sun and stars as real. Now, going one step deeper, we look with our brains and see their real movements which underlie appearances. Newton supplied us with the law and rate of the movement—but not its cause. It is toward that cause, that great "Why ?" that science has ever since been dimly groping.

In the year 1666, when the plague had driven Newton from Cambridge, he was sitting alone in the garden at Woolsthrope, and reflecting on the nature of gravity, that remarkable power which causes all bodies to descend toward the centre of the earth. As this power is not found to suffer any sensiblediminution at the greatest distance from the earth’s centre to which we can reach—being as powerful at the tops of the highest mountains as at the bottom of the deepest mines—he conceived it highly probable that it must extend much further than was usually supposed. No sooner had this happy conjecture occurred to his mind than he considered what would be the effect of its extending as far as the moon. That her motion must be influenced by such a power he did not for a moment doubt; and a little reflection convinced him that it might be sufficient for retaining that luminary in her orbit round the earth.

Though the force of gravity suffers no sensible diminution at those small distances from the earth’s centre at which we can place ourselves, yet he thought it very possible that, at the distance of the moon, it might differ much in strength from what it is on the earth. In order to form some estimate of the degree of its diminution, he considered that, if the moon be retained in her orbit by the force of gravity, the primary planets must also be carried round the sun by the same power; and by comparing the periods of the different planets with their distances from the sun he found that, if they were retained in their orbits by any power like gravity, its force must decrease in the duplicate proportion, or as the squares of their distances from the sun. In drawing this conclusion, he supposed the planets to move in orbits perfectly circular, and having the sun in their centre. Having thus obtained the law of the force by which the planets were drawn to the sun, his next object was to ascertain if such a force emanating from the earth, and directed to the moon, was sufficient, when diminished in the duplicate ratio of the distance, to retain her in her orbit.

In performing this calculation it was necessary to compare the space through which heavy bodies fall in a second at a given distance from the centre of the earth, viz., at its surface, with the space through which the moon, as it were, falls to the earth in a second of time while revolving in a circular orbit. Being at a distance from books when he made this computation, he adopted the common estimate of the earth’s diameter then in use among geographers and navigators, and supposed that each degree of latitude contained sixty English miles.

In this way he found that the force which retains the moon inher orbit, as deduced from the force which occasions the fall of heavy bodies to the earth’s surface, was one-sixth greater than that which is actually observed in her circular orbit. This difference threw a doubt upon all his speculations; but, unwilling to abandon what seemed to be otherwise so plausible, he endeavored to account for the difference of the two forces by supposing that some other cause must have been united with the force of gravity in producing so great velocity of the moon in her circular orbit. As this new cause, however, was beyond the reach of observation, he discontinued all further inquiries into the subject, and concealed from his friends the speculations in which he had been employed.

After his return to Cambridge in 1666 his attention was occupied with optical discoveries; but he had no sooner brought them to a close than his mind reverted to the great subject of the planetary motions. Upon the death of Oldenburg in August, 1678, Dr. Hooke was appointed secretary to the Royal Society; and as this learned body had requested the opinion of Newton about a system of physical astronomy, he addressed a letter to Dr. Hooke on November 28, 1679. In this letter he proposed a direct experiment for verifying the motion of the earth, viz., by observing whether or not bodies that fall from a considerable height descend in a vertical direction; for if the earth were at rest the body would describe exactly a vertical line; whereas if it revolved round its axis, the falling body must deviate from the vertical line toward the east.

The Royal Society attached great value to the idea thus casually suggested, and Dr. Hooke was appointed to put it to the test of experiment. Being thus led to consider the subject more attentively, he wrote to Newton that wherever the direction of gravity was oblique to the axis on which the earth revolved, that is, in every part of the earth except the equator, falling bodies should approach to the equator, and the deviation from the vertical, in place of being exactly to the east, as Newton maintained, should be to the southeast of the point from which the body began to move.

Newton acknowledged that this conclusion was correct in theory, and Dr. Hooke is said to have given an experimental demonstration of it before the Royal Society in December, 1679.Newton had erroneously concluded that the path of the falling body would be a spiral; but Dr. Hooke, on the same occasion on which he made the preceding experiment, read a paper to the society in which he proved that the path of the body would be an eccentric ellipse in vacuo, and an ellipti-spiral if the body moved in a resisting medium.

This correction of Newton’s error, and the discovery that a projectile would move in an elliptical orbit when under the influence of a force varying in the inverse ratio of the square of the distance, led Newton, as he himself informs us in his letter to Halley, to discover "the theorem by which he afterward examined the ellipsis," and to demonstrate the celebrated proposition that a planet acted upon by an attractive force varying inversely as the squares of the distances, will describe an elliptical orbit in one of whose foci the attractive force resides.

But though Newton had thus discovered the true cause of all the celestial motions, he did not yet possess any evidence that such a force actually resided in the sun and planets. The failure of his former attempt to identify the law of falling bodies at the earth’s surface with that which guided the moon in her orbit, threw a doubt over all his speculations, and prevented him from giving any account of them to the public.

An accident, however, of a very interesting nature induced him to resume his former inquiries, and enabled him to bring them to a close. In June, 1682, when he was attending a meeting of the Royal Society of London, the measurement of a degree of the meridian, executed by M. Picard in 1679, became the subject of conversation. Newton took a memorandum of the result obtained by the French astronomer, and having deduced from it the diameter of the earth, he immediately resumed his calculation of 1665, and began to repeat it with these new data. In the progress of the calculation he saw that the result which he had formerly expected was likely to be produced, and he was thrown into such a state of nervous irritability that he was unable to carry on the calculation. In this state of mind he intrusted it to one of his friends, and he had the high satisfaction of finding his former views amply realized. The force of gravity which regulated the fall of bodies at the earth’s surface, when diminished as the square of the moon’s distance from the earth, was found tobe almost exactly equal to the centrifugal force of the moon as deduced from her observed distance and velocity.

The influence of such a result upon such a mind may be more easily conceived than described. The whole material universe was spread out before him; the sun with all his attending planets; the planets with all their satellites; the comets wheeling in every direction in their eccentric orbits; and the systems of the fixed stars stretching to the remotest limits of space. All the varied and complicated movements of the heavens, in short, must have been at once presented to his mind as the necessary result of that law which he had established in reference to the earth and the moon.

After extending this law to the other bodies of the system, he composed a series of propositions on the motion of the primary planets about the sun, which were sent to London about the end of 1683, and were soon afterward communicated to the Royal Society.

About this period other philosophers had been occupied with the same subject. Sir Christopher Wren had many years before endeavored to explain the planetary motions "by the composition of a descent toward the sun, and an impressed motion; but he at length gave it over, not finding the means of doing it." In January, 1683–1684, Dr. Halley had concluded from Kepler’s law of the periods and distances, that the centripetal force decreased in the reciprocal proportion of the squares of the distances, and having one day met Sir Christopher Wren and Dr. Hooke, the latter affirmed that he had demonstrated upon that principle all the laws of the celestial motions. Dr. Halley confessed that his attempts were unsuccessful, and Sir Christopher, in order to encourage the inquiry, offered to present a book of forty shillings value to either of the two philosophers who should, in the space of two months, bring him a convincing demonstration of it. Hooke persisted in the declaration that he possessed the method, but avowed it to be his intention to conceal it for time. He promised, however, to show it to Sir Christopher; but there is every reason to believe that this promise was never fulfilled.

In August, 1684, Dr. Halley went to Cambridge for the express purpose of consulting Newton on this interesting subject.Newton assured him that he had brought this demonstration to perfection, and promised him a copy of it. This copy was received in November by the doctor, who made a second visit to Cambridge, in order to induce its author to have it inserted in the register book of the society. On December 10th Dr. Halley announced to the society that he had seen at Cambridge Newton’s treatise De Motu Corporum, which he had promised to send to the society to be entered upon their register, and Dr. Halley was desired to unite with Mr. Paget, master of the mathematical school in Christ’s Hospital, in reminding Newton of his promise, "for securing the invention to himself till such time as he can be at leisure to publish it."

On February 25th Mr. Aston, the secretary, communicated a letter from Newton in which he expressed his willingness "to enter in the register his notions about motion, and his intentions to fit them suddenly for the press." The progress of his work was, however, interrupted by a visit of five or six weeks which he made in Lincolnshire; but he proceeded with such diligence on his return that he was able to transmit the manuscript to London before the end of April. This manuscript, entitled Philosophi Naturalis Principia Mathematica, and dedicated to the society, was presented by Dr. Vincent on April 28, 1686, when Sir John Hoskins, the vice-president and the particular friend of Dr. Hooke, was in the chair.

Dr. Vincent passed a just encomium on the novelty and dignity of the subject; and another member added that "Mr. Newton had carried the thing so far that there was no more to be added." To these remarks the vice-president replied that the method "was so much the more to be prized as it was both invented and perfected at the same time." Dr. Hooke took offence at these remarks, and blamed Sir John for not having mentioned "what he had discovered to him "; but the vice-president did not seem to recollect any such communication, and the consequence of this discussion was that "these two, who till then were the most inseparable cronies, have since scarcely seen one another, and are utterly fallen out." After the breaking up of the meeting, the society adjourned to the coffee-house, where Dr. Hooke stated that he not only had made the same discovery, but had given the first hint of it to Newton.

An account of these proceedings was communicated to Newton through two different channels. In a letter dated May 22d Dr. Halley wrote to him "that Mr. Hooke has some pretensions upon the invention of the rule of the decrease of gravity being reciprocally as the squares of the distances from the centre. He says you had the notion from him, though he owns the demonstration of the curves generated thereby to be wholly your own. How much of this is so you know best, as likewise what you have to do in this matter; only Mr. Hooke seems to expect you would make some mention of him in the preface, which it is possible you may see reason to prefix."

This communication from Dr. Halley induced the author, on June 20th, to address a long letter to him, in which he gives a minute and able refutation of Hooke’s claims; but before this letter was despatched another correspondent, who had received his information from one of the members that were present, informed Newton "that Hooke made a great stir, pretending that he had all from him, and desiring they would see that he had justice done him." This fresh charge seems to have ruffled the tranquillity of Newton; and he accordingly added an angry and satirical postscript, in which he treats Hooke with little ceremony, and goes so far as to conjecture that Hooke might have acquired his knowledge of the law from a letter of his own to Huygens, directed to Oldenburg, and dated January 14, 1672–1673. "My letter to Hugenius was directed to Mr. Oldenburg, who used to keep the originals. His papers came into Mr. Hooke’s possession. Mr. Hooke, knowing my hand, might have the curiosity to look into that letter, and there take the notion of comparing the forces of the planets arising from their circular motion; and so what he wrote to me afterward about the rate of gravity might be nothing but the fruit of my own garden."

In replying to this letter Dr. Halley assured him that Hooke’s "manner of claiming the discovery had been represented to him in worse colors than it ought, and that he neither made public application to the society for justice nor pretended that you had all from him." The effect of this assurance was to make Newton regret that he had written the angry postscript to his letter; and in replying to Halley on July 14, 1686, he not only expresses his regret, but recounts the different new ideas whichhe had acquired from Hooke’s correspondence, and suggests it as the best method "of compromising the present dispute" to add a scholium in which Wren, Hooke, and Halley are acknowledged to have independently deduced the law of gravity from the second law of Kepler.

At the meeting of April 28th, at which the manuscript of the Principia was presented to the Royal Society, it was agreed that the printing of it should be referred to the council: that a letter of thanks should be written to its author; and at a meeting of the council on May 19th it was resolved that the manuscript should be printed at the society’s expense, and that Dr. Halley should superintend it while going through the press. These resolutions were communicated by Dr. Halley in a letter dated May 22d; and in Newton’s reply on June 20th, already mentioned, he makes the following observations:

"The proof you sent me I like very well. I designed the whole to consist of three books; the second was finished last summer, being short, and only wants transcribing and drawing the cuts fairly. Some new propositions I have since thought on which I can as well let alone. The third wants the theory of comets. In autumn last I spent two months in calculation to no purpose, for want of a good method, which made me afterward return to the first book and enlarge it with diverse propositions, some relating to comets, others to other things found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious lady that a man had as good be engaged in lawsuits as have to do with her. I found it so formerly, and now I can no sooner come near her again but she gives me warning. The first two books, without the third, will not so well bear the title of Philosophi Naturalis Principia Mathematica; and therefore I had altered it to this: deMoti Corporum, Libri duo. But after second thoughts I retain the former title. ’Twill help the sale of the book, which I ought not to diminish now ’tis yours."

In replying to this letter on June 29th Dr. Halley regrets that our author’s tranquillity should have been thus disturbed by envious rivals, and implores him in the name of the society not to suppress the third book. "I must again beg you," says he, "not to let your resentments run so high as to deprive us of your thirdbook, wherein your applications of your mathematical doctrine to the theory of comets, and several curious experiments which, as I guess by what you write ought to compose it, will undoubtedly render it acceptable to those who will call themselves philosophers without mathematics, which are much the greater number."

To these solicitations Newton seems to have readily yielded. His second book was sent to the society, and presented on March 2, 1687. The third book was also transmitted, and presented on April 6th, and the whole work was completed and published in the month of May, 1687.

Such is the brief account of the publication of a work which is memorable not only in the annals of one science or of one country, but which will form an epoch in the history of the world, and will ever be regarded as the brightest page in the records of human reason. We shall endeavor to convey to the reader some idea of its contents, and of the brilliant discoveries which it disseminated over Europe.

The Principia consists of three books. The first and second, which occupy three-fourths of the work, are entitled On the Motion of Bodies, and the third bears the title On the System of the World. The two first books contain the mathematical principles of philosophy, namely, the laws and conditions of motions and forces; and they are illustrated with several philosophical scholia which treat of some of the most general and best-established points in philosophy, such as the density and resistance of bodies, spaces void of matter, and the motion of sound and light. The object of the third book is to deduce from these principles the constitution of the system of the world; and this book has been drawn up in as popular a style as possible, in order that it may be generally read.

The great discovery which characterizes the Principia is that of the principle of universal gravitation, as deduced from the motion of the moon, and from the three great facts or laws discovered by Kepler. This principle is: That every particle of matter is attracted by or gravitates to every other particle of matter, with a force inversely proportional to the squares of their distances. From the first law of Kepler, namely, the proportionality of the areas to the times of their revolution, Newton inferred that the forcewhich kept the planet in its orbit was always directed to the sun; and from the second law of Kepler, that every planet moves in an ellipse with the sun in one of its foci, he drew the still more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance from the focus. As this law was true in the motion of satellites round their primary planets Newton deduced the equality of gravity in all the heavenly bodies toward the sun, upon the supposition that they are equally distant from its centre; and in the case of terrestrial bodies he succeeded in verifying this truth by numerous and accurate experiments.

By taking a more general view of the subject Newton demonstrated that a conic section was the only curve in which a body could move when acted upon by a force varying inversely as the square of the distance; and he established the conditions depending on the velocity and the primitive position of the body, which were requisite to make it describe a circular, an elliptical, a parabolic, or a hyberbolic orbit.

Notwithstanding the generality and importance of these results, it still remained to be determined whether the forces resided in the centres of the planets or belonged to each individual particle of which they were composed. Newton removed this uncertainty by demonstrating that if a spherical body acts upon a distant body with a force varying as the distance of this body from the centre of the sphere, the same effect will be produced as if each of its particles acted upon the distant body according to the same law. And hence it follows that the spheres, whether they are of uniform density or consist of concentric layers, with densities varying according to any law whatever, will act upon each other in the same manner as if their force resided in their centres alone.

But as the bodies of the solar system are very nearly spherical they will all act upon one another, and upon bodies placed on their surfaces, as if they were so many centres of attraction; and therefore we obtain the law of gravity which subsists between spherical bodies, namely, that one sphere will act upon another with a force directly proportional to the quantity of matter, and inversely as the square of the distance between the centres of the spheres. From the equality of action and reaction, to which noexception can be found, Newton concluded that the sun gravitated to the planets, and the planets to their satellites; and the earth itself to the stone which falls upon its surface, and, consequently, that the two mutually gravitating bodies approached to one another with velocities inversely proportional to their quantities of matter.

Having established this universal law, Newton was enabled not only to determine the weight which the same body would have at the surface of the sun and the planets, but even to calculate the quantity of matter in the sun, and in all the planets that had satellites, and even to determine the density or specific gravity of the matter of which they were composed. In this way he found that the weight of the same body would be twenty-three times greater at the surface of the sun than at the surface of the earth, and that the density of the earth was four times greater than that of the sun, the planets increasing in density as they receded from the centre of the system.

If the peculiar genius of Newton has been displayed in his investigation of the law of universal gravitation, it shines with no less lustre in the patience and sagacity with which he traced the consequences of this fertile principle. The discovery of the spheroidal form of Jupiter by Cassini had probably directed the attention of Newton to the determination of its cause, and consequently to the investigation of the true figure of the earth. The next subject to which Newton applied the principle of gravity was the tides of the ocean.

The philosophers of all ages had recognized the connection between the phenomena of the tides and the position of the moon. The College of Jesuits at Coimbra, and subsequently Antonio de Dominis and Kepler, distinctly referred the tides to the attraction of the waters of the earth by the moon; but so imperfect was the explanation which was thus given of the phenomena that Galileo ridiculed the idea of lunar attraction, and substituted for it a fallacious explanation of his own. That the moon is the principal cause of the tides is obvious from the well-known fact that it is high water at any given place about the time when she is in the meridian of that place; and that the sun performs a secondary part in their production may be proved from the circumstance that the highest tides take place when the sun, the moon,and the earth are in the same straight line; that is, when the force of the sun conspires with that of the moon; and that the lowest tides take place when the lines drawn from the sun and moon to the earth are at right angles to each other; that is, when the force of the sun acts in opposition to that of the moon.

By comparing the spring and neap tides Newton found that the force with which the moon acted upon the waters of the earth was to that with which the sun acted upon them as 4.48 to 1; that the force of the moon produced a tide of 8.63 feet; that of the sun, one of 1.93 feet; and both of them combined, one of 10½ French feet, a result which in the open sea does not deviate much from observation. Having thus ascertained the force of the moon on the waters of our globe, he found that the quantity of matter in the moon was to that in the earth as 1 to 40, and the density of the moon to that of the earth as 11 to 9.

The motions of the moon, so much within the reach of our own observation, presented a fine field for the application of the theory of universal gravitation. The irregularities exhibited in the lunar motions had been known in the time of Hipparchus and Ptolemy. Tycho had discovered the great inequality, called the "variation," amounting to 37’, and depending on the alternate acceleration and retardation of the moon in every quarter of a revolution, and he had also ascertained the existence of the annual equation. Of these two inequalities Newton gave a most satisfactory explanation.

Although there could be little doubt that the comets were retained in their orbits by the same laws which regulated the motions of the planets, yet it was difficult to put this opinion to the test of observation. The visibility of comets only in a small part of their orbits rendered it difficult to ascertain their distance and periodic times; and as their periods were probably of great length, it was impossible to correct approximate results by repeated observations. Newton, however, removed this difficulty by showing how to determine the orbit of a comet, namely, the form and position of the orbit, and the periodic time, by three observations. By applying this method to the comet of 1680 he calculated the elements of its orbit, and, from the agreement of the computed places with those which were observed, he justly inferred that the motions of comets were regulated by the samelaws as those of the planetary bodies. This result was one of great importance; for as the comets enter our system in every possible direction, and at all angles with the ecliptic, and as a great part of their orbits extends far beyond the limits of the solar system, it demonstrated the existence of gravity in spaces far removed beyond the planet, and proved that the law of the inverse ratio of the squares of the distance was true in every possible direction, and at very remote distances from the centre of our system.

Such is a brief view of the leading discoveries which the Principia first announced to the world. The grandeur of the subjects of which it treats, the beautiful simplicity of the system which it unfolds, the clear and concise reasoning by which that system is explained, and the irresistible evidence by which it is supported might have insured it the warmest admiration of contemporary mathematicians and the most welcome reception in all the schools of philosophy throughout Europe. This, however, is not the way in which great truths are generally received. Though the astronomical discoveries of Newton were not assailed by the class of ignorant pretenders who attacked his optical writings, yet they were everywhere resisted by the errors and prejudices which had taken a deep hold even of the strongest minds.

The philosophy of Descartes was predominant throughout Europe. Appealing to the imagination, and not to the reason, of mankind it was quickly received into popular favor, and the same causes which facilitated its introduction, extended its influence and completed its dominion over the human mind. In explaining all the movements of the heavenly bodies by a system of vortices in a fluid medium diffused through the universe Descartes had seized upon an analogy of the most alluring and deceitful kind. Those who had seen heavy bodies revolving in the eddies of a whirlpool or in the gyrations of a vessel of water thrown into a circular motion had no difficulty in conceiving how the planets might revolve round the sun by an analogous movement. The mind instantly grasped at an explanation of so palpable a character and which required for its development neither the exercise of patient thought nor the aid of mathematical skill. The talent and perspicuity with which the Cartesian system wasexpounded, and the show by which it was sustained, contributed powerfully to its adoption, while it derived a still higher sanction from the excellent character and the unaffected piety of its author.

Thus intrenched, as the Cartesian system was, in the strongholds of the human mind, and fortified by its most obstinate prejudices, it was not to be wondered at that the pure and sublime doctrines of the Principia were distrustfully received and perseveringly resisted. The uninstructed mind could not readily admit the idea that the great masses of the planets were suspended in empty space and retained in their orbits by an invisible influence residing in the sun; and even those philosophers who had been accustomed to the rigor of true scientific research, and who possessed sufficient mathematical skill for the examination of the Newtonian doctrines, viewed them at first as reviving the occult qualities of the ancient physics, and resisted their introduction with a pertinacity which it is not easy to explain.

Prejudiced, no doubt, in favor of his own metaphysical views, Leibnitz himself misapprehended the principles of the Newtonian philosophy, and endeavored to demonstrate the truths in the Principia by the application of different principles. Huygens, who above all other men was qualified to appreciate the new philosophy, rejected the doctrine of gravitation as existing between the individual particles of matter and received it only as an attribute of the planetary masses. John Bernouilli, one of the first mathematicians of his age, opposed the philosophy of Newton. Mairan, in the early part of his life, was a strenuous defender of the system of vortices. Cassini and Maraldi were quite ignorant of the Principia, and occupied themselves with the most absurd methods of calculating the orbits of comets long after the Nwetonian method had been established on the most impregnable foundation; and even Fontenelle, a man of liberal views and extensive information, continued, throughout the whole of his life, to maintain the doctrines of Descartes.

The chevalier Louville of Paris had adopted the Newtonian philosophy before 1720; Gravesande had introduced it into the Dutch universities at a somewhat earlier period; and Maupertnis, in consequence of a visit which he paid to England in 1728, became a zealous defender of it; but notwithstanding these andsome other examples that might be quoted, we must admit the truth of the remark of Voltaire, that though Newton survived the publication of the Principia more than forty years, yet at the time of his death he had not above twenty followers out of England.