SIR ISAAC NEWTON

The little hamlet of Woolsthorpe lies close to the village of Colsterworth, about six miles south of Grantham, in the county of Lincoln. In the manor house of Woolsthorpe, on Christmas Day, 1642, was born to a widowed mother a sickly infant who seemed not long for this world. Two women who were sent to North Witham to get some medicine for him scarcely expected to find him alive on their return. However, the child lived, became fairly robust, and was named Isaac, after his father. What sort of a man this father was we do not know. He was what we may call a yeoman, that most wholesome and natural of all classes. He owned the soil he tilled, and his little estate had already been in the family for some hundred years. He was thirty-six when he died, and had only been married a few months.

Of the mother, unfortunately, we know almost as little. We hear that she was recommended by a parishioner to the Rev. Barnabas Smith, an old bachelor in search of a wife, as “the widow Newton an extraordinary good woman:” and so I expect she was, a thoroughly sensible, practical, homely, industrious, middle-class, Mill-on-the-Floss sort of woman. However, on her second marriage she went to live at North Witham, and her mother, old Mrs. Ayscough, came to superintend the farm at Woolsthorpe, and take care of young Isaac.

By her second marriage his mother acquired another piece of land, which she settled on her first son; so Isaac found himself heir to two little properties, bringing in a rental of about L80 a year.

He had been sent to a couple of village schools to acquire the ordinary accomplishments taught at those places, and for three years to the grammar school at Grantham, then conducted by an old gentleman named Mr. Stokes. He had not been very industrious at school, nor did he feel keenly the fascinations of the Latin Grammar, for he tells us that he was the last boy in the lowest class but one. He used to pay much more attention to the construction of kites and windmills and waterwheels, all of which he made to work very well. He also used to tie paper lanterns to the tail of his kite, so as to make the country folk fancy they saw a comet, and in general to disport himself as a boy should.

It so happened, however, that he succeeded in thrashing, in fair fight, a bigger boy who was higher in the school, and who had given him a kick. His success awakened a spirit of emulation in other things than boxing, and young Newton speedily rose to be top of the school.

Under these circumstances, at the age of fifteen, his mother, who had now returned to Woolsthorpe, which had been rebuilt, thought it was time to train him for the management of his land, and to make a farmer and grazier of him. The boy was doubtless glad to get away from school, but he did not take kindly to the farm especially not to the marketing at Grantham. He and an old servant were sent to Grantham every week to buy and sell produce, but young Isaac used to leave his old mentor to do all the business, and himself retire to an attic in the house he had lodged in when at school, and there bury himself in books.

After a time he didn’t even go through the farce of visiting Grantham at all; but stopped on the road and sat under a hedge, reading or making some model, until his companion returned.

We hear of him now in the great storm of 1658, the storm on the day Cromwell died, measuring the force of the wind by seeing how far he could jump with it and against it. He also made a water-clock and set it up in the house at Grantham, where it kept fairly good time so long as he was in the neighbourhood to look after it occasionally.

At his own home he made a couple of sundials on the side of the wall (he began by marking the position of the sun by the shadow of a peg driven into the wall, but this gradually developed into a regular dial) one of which remained of use for some time; and was still to be seen in the same place during the first half of the present century, only with the gnomon gone. In 1844 the stone on which it was carved was carefully extracted and presented to the Royal Society, who preserve it in their library. The letters WTON roughly carved on it are barely visible.

All these pursuits must have been rather trying to his poor mother, and she probably complained to her brother, the rector of Burton Coggles: at any rate this gentleman found master Newton one morning under a hedge when he ought to have been farming. But as he found him working away at mathematics, like a wise man he persuaded his sister to send the boy back to school for a short time, and then to Cambridge. On the day of his finally leaving school old Mr. Stokes assembled the boys, made them a speech in praise of Newton’s character and ability, and then dismissed him to Cambridge.

At Trinity College a new world opened out before the country-bred lad. He knew his classics passably, but of mathematics and science he was ignorant, except through the smatterings he had picked up for himself. He devoured a book on logic, and another on Kepler’s Optics, so fast that his attendance at lectures on these subjects became unnecessary. He also got hold of a Euclid and of Descartes’s Geometry. The Euclid seemed childishly easy, and was thrown aside, but the Descartes baffled him for a time. However, he set to it again and again and before long mastered it. He threw himself heart and soul into mathematics, and very soon made some remarkable discoveries. First he discovered the binomial theorem: familiar now to all who have done any algebra, unintelligible to others, and therefore I say nothing about it. By the age of twenty-one or two he had begun his great mathematical discovery of infinite series and fluxions now known by the name of the Differential Calculus. He wrote these things out and must have been quite absorbed in them, but it never seems to have occurred to him to publish them or tell any one about them.

In 1664 he noticed some halos round the moon, and, as his manner was, he measured their angles the small ones 3 and 5 degrees each, the larger one 22 deg..35. Later he gave their theory.

Small coloured halos round the moon are often seen, and are said to be a sign of rain. They are produced by the action of minute globules of water or cloud particles upon light, and are brightest when the particles are nearly equal in size. They are not like the rainbow, every part of which is due to light that has entered a raindrop, and been refracted and reflected with prismatic separation of colours; a halo is caused by particles so small as to be almost comparable with the size of waves of light, in a way which is explained in optics under the head “diffraction.” It may be easily imitated by dusting an ordinary piece of window-glass over with lycopodium, placing a candle near it, and then looking at the candle-flame through the dusty glass from a fair distance. Or you may look at the image of a candle in a dusted looking-glass. Lycopodium dust is specially suitable, for its granules are remarkably equal in size. The large halo, more rarely seen, of angular radius 22 deg..35, is due to another cause again, and is a prismatic effect, although it exhibits hardly any colour. The angle 22-1/2 deg. is characteristic of refraction in crystals with angles of 60 deg. and refractive index about the same as water; in other words this halo is caused by ice crystals in the higher regions of the atmosphere.

He also the same year observed a comet, and sat up so late watching it that he made himself ill. By the end of the year he was elected to a scholarship and took his B.A. degree. The order of merit for that year never existed or has not been kept. It would have been interesting, not as a testimony to Newton, but to the sense or non-sense of the examiners. The oldest Professorship of Mathematics at the University of Cambridge, the Lucasian, had not then been long founded, and its first occupant was Dr. Isaac Barrow, an eminent mathematician, and a kind old man. With him Newton made good friends, and was helpful in preparing a treatise on optics for the press. His help is acknowledged by Dr. Barrow in the preface, which states that he had corrected several errors and made some capital additions of his own. Thus we see that, although the chief part of his time was devoted to mathematics, his attention was already directed to both optics and astronomy. (Kepler, Descartes, Galileo, all combined some optics with astronomy. Tycho and the old ones combined alchemy; Newton dabbled in this also.)

Newton reached the age of twenty-three in 1665, the year of the Great Plague. The plague broke out in Cambridge as well as in London, and the whole college was sent down. Newton went back to Woolsthorpe, his mind teeming with ideas, and spent the rest of this year and part of the next in quiet pondering. Somehow or other he had got hold of the notion of centrifugal force. It was six years before Huyghens discovered and published the laws of centrifugal force, but in some quiet way of his own Newton knew about it and applied the idea to the motion of the planets.

We can almost follow the course of his thoughts as he brooded and meditated on the great problem which had taxed so many previous thinkers, What makes the planets move round the sun? Kepler had discovered how they moved, but why did they so move, what urged them?

Even the “how” took a long time all the time of the Greeks, through Ptolemy, the Arabs, Copernicus, Tycho: circular motion, epicycles, and excentrics had been the prevailing theory. Kepler, with his marvellous industry, had wrested from Tycho’s observations the secret of their orbits. They moved in ellipses with the sun in one focus. Their rate of description of area, not their speed, was uniform and proportional to time.

Yes, and a third law, a mysterious law of unintelligible import, had also yielded itself to his penetrating industry a law the discovery of which had given him the keenest delight, and excited an outburst of rapture viz. that there was a relation between the distances and the periodic times of the several planets. The cubes of the distances were proportional to the squares of the times for the whole system. This law, first found true for the six primary planets, he had also extended, after Galileo’s discovery, to the four secondary planets, or satellites of Jupiter .

But all this was working in the dark it was only the first step this empirical discovery of facts; the facts were so, but how came they so? What made the planets move in this particular way? Descartes’s vortices was an attempt, a poor and imperfect attempt, at an explanation. It had been hailed and adopted throughout Europe for want of a better, but it did not satisfy Newton. No, it proceeded on a wrong tack, and Kepler had proceeded on a wrong tack in imagining spokes or rays sticking out from the sun and driving the planets round like a piece of mechanism or mill work. For, note that all these theories are based on a wrong idea the idea, viz., that some force is necessary to maintain a body in motion. But this was contrary to the laws of motion as discovered by Galileo. You know that during his last years of blind helplessness at Arcetri, Galileo had pondered and written much on the laws of motion, the foundation of mechanics. In his early youth, at Pisa, he had been similarly occupied; he had discovered the pendulum, he had refuted the Aristotelians by dropping weights from the leaning tower (which we must rejoice that no earthquake has yet injured), and he had returned to mechanics at intervals all his life; and now, when his eyes were useless for astronomy, when the outer world has become to him only a prison to be broken by death, he returns once more to the laws of motion, and produces the most solid and substantial work of his life.

For this is Galileo’s main glory not his brilliant exposition of the Copernican system, not his flashes of wit at the expense of a moribund philosophy, not his experiments on floating bodies, not even his telescope and astronomical discoveries though these are the most taking and dazzling at first sight. No; his main glory and title to immortality consists in this, that he first laid the foundation of mechanics on a firm and secure basis of experiment, reasoning, and observation. He first discovered the true Laws of Motion.

I said little of this achievement in my lecture on him; for the work was written towards the end of his life, and I had no time then. But I knew I should have to return to it before we came to Newton, and here we are.

You may wonder how the work got published when so many of his manuscripts were destroyed. Horrible to say, Galileo’s own son destroyed a great bundle of his father’s manuscripts, thinking, no doubt, thereby to save his own soul. This book on mechanics was not burnt, however. The fact is it was rescued by one or other of his pupils, Toricelli or Viviani, who were allowed to visit him in his last two or three years; it was kept by them for some time, and then published surreptitiously in Holland. Not that there is anything in it bearing in any visible way on any theological controversy; but it is unlikely that the Inquisition would have suffered it to pass notwithstanding.

I have appended to the summary preceding this lecture the three axioms or laws of motion discovered by Galileo. They are stated by Newton with unexampled clearness and accuracy, and are hence known as Newton’s laws, but they are based on Galileo’s work. The first is the simplest; though ignorance of it gave the ancients a deal of trouble. It is simply a statement that force is needed to change the motion of a body; i.e. that if no force act on a body it will continue to move uniformly both in speed and direction in other words, steadily, in a straight line. The old idea had been that some force was needed to maintain motion. On the contrary, the first law asserts, some force is needed to destroy it. Leave a body alone, free from all friction or other retarding forces, and it will go on for ever. The planetary motion through empty space therefore wants no keeping up; it is not the motion that demands a force to maintain it, it is the curvature of the path that needs a force to produce it continually. The motion of a planet is approximately uniform so far as speed is concerned, but it is not constant in direction; it is nearly a circle. The real force needed is not a propelling but a deflecting force.

The second law asserts that when a force acts, the motion changes, either in speed or in direction, or both, at a pace proportional to the magnitude of the force, and in the same direction as that in which the force acts. Now since it is almost solely in direction that planetary motion alters, a deflecting force only is needed; a force at right angles to the direction of motion, a force normal to the path. Considering the motion as circular, a force along the radius, a radial or centripetal force, must be acting continually. Whirl a weight round and round by a bit of elastic, the elastic is stretched; whirl it faster, it is stretched more. The moving mass pulls at the elastic that is its centrifugal force; the hand at the centre pulls also that is centripetal force.

The third law asserts that these two forces are equal, and together constitute the tension in the elastic. It is impossible to have one force alone, there must be a pair. You can’t push hard against a body that offers no resistance. Whatever force you exert upon a body, with that same force the body must react upon you. Action and reaction are always equal and opposite.

Sometimes an absurd difficulty is felt with respect to this, even by engineers. They say, “If the cart pulls against the horse with precisely the same force as the horse pulls the cart, why should the cart move?” Why on earth not? The cart moves because the horse pulls it, and because nothing else is pulling it back. “Yes,” they say, “the cart is pulling back.” But what is it pulling back? Not itself, surely? “No, the horse.” Yes, certainly the cart is pulling at the horse; if the cart offered no resistance what would be the good of the horse? That is what he is for, to overcome the pull-back of the cart; but nothing is pulling the cart back (except, of course, a little friction), and the horse is pulling it forward, hence it goes forward. There is no puzzle at all when once you realise that there are two bodies and two forces acting, and that one force acts on each body.

If, indeed, two balanced forces acted on one body that would be in equilibrium, but the two equal forces contemplated in the third law act on two different bodies, and neither is in equilibrium.

So much for the third law, which is extremely simple, though it has extraordinarily far-reaching consequences, and when combined with a denial of “action at a distance,” is precisely the principle of the Conservation of Energy. Attempts at perpetual motion may all be regarded as attempts to get round this “third law.”

On the subject of the second law a great deal more has to be said before it can be in any proper sense even partially appreciated, but a complete discussion of it would involve a treatise on mechanics. It is the law of mechanics. One aspect of it we must attend to now in order to deal with the motion of the planets, and that is the fact that the change of motion of a body depends solely and simply on the force acting, and not at all upon what the body happens to be doing at the time it acts. It may be stationary, or it may be moving in any direction; that makes no difference.

Thus, referring back to the summary preceding Lecture IV, it is there stated that a dropped body falls 16 feet in the first second, that in two seconds it falls 64 feet, and so on, in proportion to the square of the time. So also will it be the case with a thrown body, but the drop must be reckoned from its line of motion the straight line which, but for gravity, it would describe.

Thus a stone thrown from O with the velocity OA would in one second find itself at A, in two seconds at B, in three seconds at C, and so on, in accordance with the first law of motion, if no force acted. But if gravity acts it will have fallen 16 feet by the time it would have got to A, and so will find itself at P. In two seconds it will be at Q, having fallen a vertical height of 64 feet; in three seconds it will be at R, 144 feet below C; and so on. Its actual path will be a curve, which in this case is a parabola. (Fi.)

If a cannon is pointed horizontally over a level plain, the cannon ball will be just as much affected by gravity as if it were dropped, and so will strike the plain at the same instant as another which was simply dropped where it started. One ball may have gone a mile and the other only dropped a hundred feet or so, but the time needed by both for the vertical drop will be the same. The horizontal motion of one is an extra, and is due to the powder.

As a matter of fact the path of a projectile in vacuo is only approximately a parabola. It is instructive to remember that it is really an ellipse with one focus very distant, but not at infinity. One of its foci is the centre of the earth. A projectile is really a minute satellite of the earth’s, and in vacuo it accurately obeys all Kepler’s laws. It happens not to be able to complete its orbit, because it was started inconveniently close to the earth, whose bulk gets in its way; but in that respect the earth is to be reckoned as a gratuitous obstruction, like a target, but a target that differs from most targets in being hard to miss.

Now consider circular motion in the same way, say a ball whirled
round by a string. (Fi.)

Attending to the body at O, it is for an instant moving towards A, and if no force acted it would get to A in a time which for brevity we may call a second. But a force, the pull of the string, is continually drawing it towards S, and so it really finds itself at P, having described the circular arc OP, which may be considered to be compounded of, and analyzable into the rectilinear motion OA and the drop AP. At P it is for an instant moving towards B, and the same process therefore carries it to Q; in the third second it gets to R; and so on: always falling, so to speak, from its natural rectilinear path, towards the centre, but never getting any nearer to the centre.

The force with which it has thus to be constantly pulled in towards the centre, or, which is the same thing, the force with which it is tugging at whatever constraint it is that holds it in, is mv^2/r; where m is the mass of the particle, v its velocity, and r the radius of its circle of movement. This is the formula first given by Huyghens for centrifugal force.

We shall find it convenient to express it in terms of the time of one revolution, say T. It is easily done, since plainly T = circumference/speed = 2[pi]r/v; so the above expression for centrifugal force becomes 4[pi]^2mr/T^2.

As to the fall of the body towards the centre every microscopic unit of time, it is easily reckoned. For by Euclid II, and Fi, AP.AA’ = AO^2. Take A very near O, then OA = vt, and AA’ = 2r; so AP = v^2t^2/2r = 2[pi]^2r t^2/T^2; or the fall per second is 2[pi]^2r/T^2, r being its distance from the centre, and T its time of going once round.

In the case of the moon for instance, r is 60 earth radii; more exactly 60.2; and T is a lunar month, or more precisely 27 days, 7 hours, 43 minutes, and 11-1/2 seconds. Hence the moon’s deflection from the tangential or rectilinear path every minute comes out as very closely 16 feet (the true size of the earth being used).

Returning now to the case of a small body revolving round a big one, and assuming a force directly proportional to the mass of both bodies, and inversely proportional to the square of the distance between them: i.e. assuming the known force of gravity, it is

V Mm/r^2

where V is a constant, called the gravitation constant, to be determined by experiment.

If this is the centripetal force pulling a planet or satellite in, it must be equal to the centrifugal force of this latter, viz. (see above).

4[pi]^2mr/T^2

Equate the two together, and at once we get

r^3/T^2 = V/4[pi]^2M;

or, in words, the cube of the distance divided by the square of the periodic time for every planet or satellite of the system under consideration, will be constant and proportional to the mass of the central body.

This is Kepler’s third law, with a notable addition. It is stated above for circular motion only, so as to avoid geometrical difficulties, but even so it is very instructive. The reason of the proportion between r^3 and T^2 is at once manifest; and as soon as the constant V became known, the mass of the central body, the sun in the case of a planet, the earth in the case of the moon, Jupiter in the case of his satellites, was at once determined.

Newton’s reasoning at this time might, however, be better displayed perhaps by altering the order of the steps a little, as thus:

The centrifugal force of a body is proportional to r^3/T^2, but by Kepler’s third law r^3/T^2 is constant for all the planets, reckoning r from the sun. Hence the centripetal force needed to hold in all the planets will be a single force emanating from the sun and varying inversely with the square of the distance from that body.

Such a force is at once necessary and sufficient. Such a force would explain the motion of the planets.

But then all this proceeds on a wrong assumption that the planetary motion is circular. Will it hold for elliptic orbits? Will an inverse square law of force keep a body moving in an elliptic orbit about the sun in one focus? This is a far more difficult question. Newton solved it, but I do not believe that even he could have solved it, except that he had at his disposal two mathematical engines of great power the Cartesian method of treating geometry, and his own method of Fluxions. One can explain the elliptic motion now mathematically, but hardly otherwise; and I must be content to state that the double fact is true viz., that an inverse square law will move the body in an ellipse or other conic section with the sun in one focus, and that if a body so moves it must be acted on by an inverse square law.

This then is the meaning of the first and third laws of Kepler. What about the second? What is the meaning of the equable description of areas? Well, that rigorously proves that a planet is acted on by a force directed to the centre about which the rate of description of areas is equable. It proves, in fact, that the sun is the attracting body, and that no other force acts.

For first of all if the first law of motion is obeyed, i.e. if no force acts, and if the path be equally subdivided to represent equal times, and straight lines be drawn from the divisions to any point whatever, all these areas thus enclosed will be equal, because they are triangles on equal base and of the same height (Euclid, I). See Fi; S being any point whatever, and A, B, C, successive positions of a body.

Now at each of the successive instants let the body receive a sudden blow in the direction of that same point S, sufficient to carry it from A to D in the same time as it would have got to B if left alone. The result will be that there will be a compromise, and it will really arrive at P, travelling along the diagonal of the parallelogram AP. The area its radius vector sweeps out is therefore SAP, instead of what it would have been, SAB. But then these two areas are equal, because they are triangles on the same base AS, and between the same parallels BP, AS; for by the parallelogram law BP is parallel to AD. Hence the area that would have been described is described, and as all the areas were equal in the case of no force, they remain equal when the body receives a blow at the end of every equal interval of time, provided that every blow is actually directed to S, the point to which radii vectores are drawn.

It is instructive to see that it does not hold if the blow is any otherwise directed; for instance, as in Fi, when the blow is along AE, the body finds itself at P at the end of the second interval, but the area SAP is by no means equal to SAB, and therefore not equal to SOA, the area swept out in the first interval.

In order to modify Fi so as to represent continuous motion and steady forces, we have to take the sides of the polygon OAPQ, &c., very numerous and very small; in the limit, infinitely numerous and infinitely small. The path then becomes a curve, and the series of blows becomes a steady force directed towards S. About whatever point therefore the rate of description of areas is uniform, that point and no other must be the centre of all the force there is. If there be no force, as in Fi, well and good, but if there be any force however small not directed towards S, then the rate of description of areas about S cannot be uniform. Kepler, however, says that the rate of description of areas of each planet about the sun is, by Tycho’s observations, uniform; hence the sun is the centre of all the force that acts on them, and there is no other force, not even friction. That is the moral of Kepler’s second law.

We may also see from it that gravity does not travel like light, so as to take time on its journey from sun to planet; for, if it did, there would be a sort of aberration, and the force on its arrival could no longer be accurately directed to the centre of the sun. (See Nature, vol. xlvi., .) It is a matter for accuracy of observation, therefore, to decide whether the minutest trace of such deviation can be detected, i.e. within what limits of accuracy Kepler’s second law is now known to be obeyed.

I will content myself by saying that the limits are extremely
narrow. [Reference may be made also to .]

Thus then it became clear to Newton that the whole solar system depended on a central force emanating from the sun, and varying inversely with the square of the distance from him: for by that hypothesis all the laws of Kepler concerning these motions were completely accounted for; and, in fact, the laws necessitated the hypothesis and established it as a theory.

Similarly the satellites of Jupiter were controlled by a force emanating from Jupiter and varying according to the same law. And again our moon must be controlled by a force from the earth, decreasing with the distance according to the same law.

Grant this hypothetical attracting force pulling the planets towards the sun, pulling the moon towards the earth, and the whole mechanism of the solar system is beautifully explained.

If only one could be sure there was such a force! It was one thing to calculate out what the effects of such a force would be: it was another to be able to put one’s finger upon it and say, this is the force that actually exists and is known to exist. We must picture him meditating in his garden on this want an attractive force towards the earth.

If only such an attractive force pulling down bodies to the earth existed. An apple falls from a tree. Why, it does exist! There is gravitation, common gravity that makes bodies fall and gives them their weight.

Wanted, a force tending towards the centre of the earth. It is to hand!

It is common old gravity that had been known so long, that was perfectly familiar to Galileo, and probably to Archimedes. Gravity that regulates the motion of projectiles. Why should it only pull stones and apples? Why should it not reach as high as the moon? Why should it not be the gravitation of the sun that is the central force acting on all the planets?

Surely the secret of the universe is discovered! But, wait a bit; is it discovered? Is this force of gravity sufficient for the purpose? It must vary inversely with the square of the distance from the centre of the earth. How far is the moon away? Sixty earth’s radii. Hence the force of gravity at the moon’s distance can only be 1/3600 of what it is on the earth’s surface. So, instead of pulling it 16 ft. per second, it should pull it 16/3600 ft. per second, or 16 ft. a minute. How can one decide whether such a force is able to pull the moon the actual amount required? To Newton this would seem only like a sum in arithmetic. Out with a pencil and paper and reckon how much the moon falls toward the earth in every second of its motion. Is it 16/3600? That is what it ought to be: but is it? The size of the earth comes into the calculation. Sixty miles make a degree, 360 degrees a circumference. This gives as the earth’s diameter 6,873 miles; work it out.

The answer is not 16 feet a minute, it is 13.9 feet.

Surely a mistake of calculation?

No, it is no mistake: there is something wrong in the theory, gravity is too strong.

Instead of falling toward the earth 5-1/3 hundredths of an inch every second, as it would under gravity, the moon only falls 4-2/3 hundredths of an inch per second.

With such a discovery in his grasp at the age of twenty-three he is disappointed the figures do not agree, and he cannot make them agree. Either gravity is not the force in action, or else something interferes with it. Possibly, gravity does part of the work, and the vortices of Descartes interfere with it.

He must abandon the fascinating idea for the time. In his own words, “he laid aside at that time any further thought of the matter.”

So far as is known, he never mentioned his disappointment to a soul. He might, perhaps, if he had been at Cambridge, but he was a shy and solitary youth, and just as likely he might not. Up in Lincolnshire, in the seventeenth century, who was there for him to consult?

True, he might have rushed into premature publication, after our nineteenth century fashion, but that was not his method. Publication never seemed to have occurred to him.

His reticence now is noteworthy, but later on it is perfectly astonishing. He is so absorbed in making discoveries that he actually has to be reminded to tell any one about them, and some one else always has to see to the printing and publishing for him.

I have entered thus fully into what I conjecture to be the stages of this early discovery of the law of gravitation, as applicable to the heavenly bodies, because it is frequently and commonly misunderstood. It is sometimes thought that he discovered the force of gravity; I hope I have made it clear that he did no such thing. Every educated man long before his time, if asked why bodies fell, would reply just as glibly as they do now, “Because the earth attracts them,” or “because of the force of gravity.”

His discovery was that the motions of the solar system were due to the action of a central force, directed to the body at the centre of the system, and varying inversely with the square of the distance from it. This discovery was based upon Kepler’s laws, and was clear and certain. It might have been published had he so chosen.

But he did not like hypothetical and unknown forces; he tried to see whether the known force of gravity would serve. This discovery at that time he failed to make, owing to a wrong numerical datum. The size of the earth he only knew from the common doctrine of sailors that 60 miles make a degree; and that threw him out. Instead of falling 16 feet a minute, as it ought under gravity, it only fell 13.9 feet, so he abandoned the idea. We do not find that he returned to it for sixteen years.