"Thirdly, I use the word attraction for no other reason but to express an effect which I discovered in Nature--a certain and indisputable effect of an unknown principle--a quality inherent in matter, the cause of which persons of greater abilities than I can pretend to may, if they can, find out."

"What have you, then, taught us?" will these people say further; "and to what purpose are so many calculations to tell us what you yourself do not comprehend?"

"I have taught you," may Sir Isaac rejoin, "that all bodies gravitate towards one another in proportion to their quant.i.ty of matter; that these central forces alone keep the planets and comets in their orbits, and cause them to move in the proportion before set down. I demonstrate to you that it is impossible there should be any other cause which keeps the planets in their orbits than that general phenomenon of gravity. For heavy bodies fall on the earth according to the proportion demonstrated of central forces; and the planets finishing their course according to these same proportions, in case there were another power that acted upon all those bodies, it would either increase their velocity or change their direction. Now, not one of those bodies ever has a single degree of motion or velocity, or has any direction but what is demonstrated to be the effect of the central forces. Consequently it is impossible there should be any other principle."

Give me leave once more to introduce Sir Isaac speaking. Shall he not be allowed to say? "My case and that of the ancients is very different.

These saw, for instance, water ascend in pumps, and said, 'The water rises because it abhors a vacuum.' But with regard to myself; I am in the case of a man who should have first observed that water ascends in pumps, but should leave others to explain the cause of this effect. The anatomist, who first declared that the motion of the arm is owing to the contraction of the muscles, taught mankind an indisputable truth. But are they less obliged to him because he did not know the reason why the muscles contract? The cause of the elasticity of the air is unknown, but he who first discovered this spring performed a very signal service to natural philosophy. The spring that I discovered was more hidden and more universal, and for that very reason mankind ought to thank me the more. I have discovered a new property of matter--one of the secrets of the Creator--and have calculated and discovered the effects of it. After this, shall people quarrel with me about the name I give it?"

Vortices may be called an occult quality, because their existence was never proved. Attraction, on the contrary, is a real thing, because its effects are demonstrated, and the proportions of it are calculated. The cause of this cause is among the _Arcana_ of the Almighty.

"Precedes huc, et non amplius."

(Thus far shalt thou go, and no farther.)

LETTER XVI.--ON SIR ISAAC NEWTON'S OPTICS

The philosophers of the last age found out a new universe; and a circ.u.mstance which made its discovery more difficult was that no one had so much as suspected its existence. The most sage and judicious were of opinion that it was a frantic rashness to dare so much as to imagine that it was possible to guess the laws by which the celestial bodies move and the manner how light acts. Galileo, by his astronomical discoveries, Kepler, by his calculation, Descartes (at least, in his dioptrics), and Sir Isaac Newton, in all his works, severally saw the mechanism of the springs of the world. The geometricians have subjected infinity to the laws of calculation. The circulation of the blood in animals, and of the sap in vegetables, have changed the face of Nature with regard to us. A new kind of existence has been given to bodies in the air-pump. By the a.s.sistance of telescopes bodies have been brought nearer to one another.

Finally, the several discoveries which Sir Isaac Newton has made on light are equal to the boldest things which the curiosity of man could expect after so many philosophical novelties.

Till Antonio de Dominis the rainbow was considered as an inexplicable miracle. This philosopher guessed that it was a necessary effect of the sun and rain. Descartes gained immortal fame by his mathematical explication of this so natural a phenomenon. He calculated the reflections and refractions of light in drops of rain. And his sagacity on this occasion was at that time looked upon as next to divine.

But what would he have said had it been proved to him that he was mistaken in the nature of light; that he had not the least reason to maintain that it is a globular body? That it is false to a.s.sert that this matter, spreading itself through the whole, waits only to be projected forward by the sun, in order to be put in action, in like manner as a long staff acts at one end when pushed forward by the other.

That light is certainly darted by the sun; in fine, that light is transmitted from the sun to the earth in about seven minutes, though a cannonball, which were not to lose any of its velocity, could not go that distance in less than twenty-five years. How great would have been his astonishment had he been told that light does not reflect directly by impinging against the solid parts of bodies, that bodies are not transparent when they have large pores, and that a man should arise who would demonstrate all these paradoxes, and anatomise a single ray of light with more dexterity than the ablest artist dissects a human body.

This man is come. Sir Isaac Newton has demonstrated to the eye, by the bare a.s.sistance of the prism, that light is a composition of coloured rays, which, being united, form white colour. A single ray is by him divided into seven, which all fall upon a piece of linen, or a sheet of white paper, in their order, one above the other, and at unequal distances. The first is red, the second orange, the third yellow, the fourth green, the fifth blue, the sixth indigo, the seventh a violet-purple. Each of these rays, transmitted afterwards by a hundred other prisms, will never change the colour it bears; in like manner, as gold, when completely purged from its dross, will never change afterwards in the crucible. As a superabundant proof that each of these elementary rays has inherently in itself that which forms its colour to the eye, take a small piece of yellow wood, for instance, and set it in the ray of a red colour; this wood will instantly be tinged red. But set it in the ray of a green colour, it a.s.sumes a green colour, and so of all the rest.

From what cause, therefore, do colours arise in Nature? It is nothing but the disposition of bodies to reflect the rays of a certain order and to absorb all the rest.

What, then, is this secret disposition? Sir Isaac Newton demonstrates that it is nothing more than the density of the small const.i.tuent particles of which a body is composed. And how is this reflection performed? It was supposed to arise from the rebounding of the rays, in the same manner as a ball on the surface of a solid body. But this is a mistake, for Sir Isaac taught the astonished philosophers that bodies are opaque for no other reason but because their pores are large, that light reflects on our eyes from the very bosom of those pores, that the smaller the pores of a body are the more such a body is transparent. Thus paper, which reflects the light when dry, transmits it when oiled, because the oil, by filling its pores, makes them much smaller.

It is there that examining the vast porosity of bodies, every particle having its pores, and every particle of those particles having its own, he shows we are not certain that there is a cubic inch of solid matter in the universe, so far are we from conceiving what matter is. Having thus divided, as it were, light into its elements, and carried the sagacity of his discoveries so far as to prove the method of distinguishing compound colours from such as are primitive, he shows that these elementary rays, separated by the prism, are ranged in their order for no other reason but because they are refracted in that very order; and it is this property (unknown till he discovered it) of breaking or splitting in this proportion; it is this unequal refraction of rays, this power of refracting the red less than the orange colour, &c., which he calls the different refrangibility. The most reflexible rays are the most refrangible, and from hence he evinces that the same power is the cause both of the reflection and refraction of light.

But all these wonders are merely but the opening of his discoveries. He found out the secret to see the vibrations or fits of light which come and go incessantly, and which either transmit light or reflect it, according to the density of the parts they meet with. He has presumed to calculate the density of the particles of air necessary between two gla.s.ses, the one flat, the other convex on one side, set one upon the other, in order to operate such a transmission or reflection, or to form such and such a colour.

From all these combinations he discovers the proportion in which light acts on bodies and bodies act on light.

He saw light so perfectly, that he has determined to what degree of perfection the art of increasing it, and of a.s.sisting our eyes by telescopes, can be carried.

Descartes, from a n.o.ble confidence that was very excusable, considering how strongly he was fired at the first discoveries he made in an art which he almost first found out; Descartes, I say, hoped to discover in the stars, by the a.s.sistance of telescopes, objects as small as those we discern upon the earth.

But Sir Isaac has shown that dioptric telescopes cannot be brought to a greater perfection, because of that refraction, and of that very refrangibility, which at the same time that they bring objects nearer to us, scatter too much the elementary rays. He has calculated in these gla.s.ses the proportion of the scattering of the red and of the blue rays; and proceeding so far as to demonstrate things which were not supposed even to exist, he examines the inequalities which arise from the shape or figure of the gla.s.s, and that which arises from the refrangibility. He finds that the object gla.s.s of the telescope being convex on one side and flat on the other, in case the flat side be turned towards the object, the error which arises from the construction and position of the gla.s.s is above five thousand times less than the error which arises from the refrangibility; and, therefore, that the shape or figure of the gla.s.ses is not the cause why telescopes cannot be carried to a greater perfection, but arises wholly from the nature of light.

For this reason he invented a telescope, which discovers objects by reflection, and not by refraction. Telescopes of this new kind are very hard to make, and their use is not easy; but, according to the English, a reflective telescope of but five feet has the same effect as another of a hundred feet in length.

LETTER XVII.--ON INFINITES IN GEOMETRY, AND SIR ISAAC NEWTON'S CHRONOLOGY

The labyrinth and abyss of infinity is also a new course Sir Isaac Newton has gone through, and we are obliged to him for the clue, by whose a.s.sistance we are enabled to trace its various windings.

Descartes got the start of him also in this astonishing invention. He advanced with mighty steps in his geometry, and was arrived at the very borders of infinity, but went no farther. Dr. Wallis, about the middle of the last century, was the first who reduced a fraction by a perpetual division to an infinite series.

The Lord Brouncker employed this series to square the hyperbola.

Mercator published a demonstration of this quadrature; much about which time Sir Isaac Newton, being then twenty-three years of age, had invented a general method, to perform on all geometrical curves what had just before been tried on the hyperbola.

It is to this method of subjecting everywhere infinity to algebraical calculations, that the name is given of differential calculations or of fluxions and integral calculation. It is the art of numbering and measuring exactly a thing whose existence cannot be conceived.

And, indeed, would you not imagine that a man laughed at you who should declare that there are lines infinitely great which form an angle infinitely little?

That a right line, which is a right line so long as it is finite, by changing infinitely little its direction, becomes an infinite curve; and that a curve may become infinitely less than another curve?

That there are infinite squares, infinite cubes, and infinites of infinites, all greater than one another, and the last but one of which is nothing in comparison of the last?

All these things, which at first appear to be the utmost excess of frenzy, are in reality an effort of the subtlety and extent of the human mind, and the art of finding truths which till then had been unknown.

This so bold edifice is even founded on simple ideas. The business is to measure the diagonal of a square, to give the area of a curve, to find the square root of a number, which has none in common arithmetic. After all, the imagination ought not to be startled any more at so many orders of infinites than at the so well-known proposition, viz., that curve lines may always be made to pa.s.s between a circle and a tangent; or at that other, namely, that matter is divisible in _infinitum_. These two truths have been demonstrated many years, and are no less incomprehensible than the things we have been speaking of.

For many years the invention of this famous calculation was denied to Sir Isaac Newton. In Germany Mr. Leibnitz was considered as the inventor of the differences or moments, called fluxions, and Mr. Bernouilli claimed the integral calculus. However, Sir Isaac is now thought to have first made the discovery, and the other two have the glory of having once made the world doubt whether it was to be ascribed to him or them. Thus some contested with Dr. Harvey the invention of the circulation of the blood, as others disputed with Mr. Perrault that of the circulation of the sap.

Hartsocher and Leuwenhoek disputed with each other the honour of having first seen the _vermiculi_ of which mankind are formed. This Hartsocher also contested with Huygens the invention of a new method of calculating the distance of a fixed star. It is not yet known to what philosopher we owe the invention of the cycloid.

Be this as it will, it is by the help of this geometry of infinites that Sir Isaac Newton attained to the most sublime discoveries. I am now to speak of another work, which, though more adapted to the capacity of the human mind, does nevertheless display some marks of that creative genius with which Sir Isaac Newton was informed in all his researches. The work I mean is a chronology of a new kind, for what province soever he undertook he was sure to change the ideas and opinions received by the rest of men.

Accustomed to unravel and disentangle chaos, he was resolved to convey at least some light into that of the fables of antiquity which are blended and confounded with history, and fix an uncertain chronology. It is true that there is no family, city, or nation, but endeavours to remove its original as far backward as possible. Besides, the first historians were the most negligent in setting down the eras: books were infinitely less common than they are at this time, and, consequently, authors being not so obnoxious to censure, they therefore imposed upon the world with greater impunity; and, as it is evident that these have related a great number of fict.i.tious particulars, it is probable enough that they also gave us several false eras.

It appeared in general to Sir Isaac that the world was five hundred years younger than chronologers declare it to be. He grounds his opinion on the ordinary course of Nature, and on the observations which astronomers have made.

By the course of Nature we here understand the time that every generation of men lives upon the earth. The Egyptians first employed this vague and uncertain method of calculating when they began to write the beginning of their history. These computed three hundred and forty-one generations from Menes to Sethon; and, having no fixed era, they supposed three generations to consist of a hundred years. In this manner they computed eleven thousand three hundred and forty years from Menes's reign to that of Sethon.

The Greeks before they counted by Olympiads followed the method of the Egyptians, and even gave a little more extent to generations, making each to consist of forty years.

Now, here, both the Egyptians and the Greeks made an erroneous computation. It is true, indeed, that, according to the usual course of Nature, three generations last about a hundred and twenty years; but three reigns are far from taking up so many. It is very evident that mankind in general live longer than kings are found to reign, so that an author who should write a history in which there were no dates fixed, and should know that nine kings had reigned over a nation; such an historian would commit a great error should he allow three hundred years to these nine monarchs. Every generation takes about thirty-six years; every reign is, one with the other, about twenty. Thirty kings of England have swayed the sceptre from William the Conqueror to George I., the years of whose reigns added together amount to six hundred and forty-eight years; which, being divided equally among the thirty kings, give to every one a reign of twenty-one years and a half very near. Sixty-three kings of France have sat upon the throne; these have, one with another, reigned about twenty years each. This is the usual course of Nature. The ancients, therefore, were mistaken when they supposed the durations in general of reigns to equal that of generations. They, therefore, allowed too great a number of years, and consequently some years must be subtracted from their computation.

Astronomical observations seem to have lent a still greater a.s.sistance to our philosopher. He appears to us stronger when he fights upon his own ground.

You know that the earth, besides its annual motion which carries it round the sun from west to east in the s.p.a.ce of a year, has also a singular revolution which was quite unknown till within these late years. Its poles have a very slow retrograde motion from east to west, whence it happens that their position every day does not correspond exactly with the same point of the heavens. This difference, which is so insensible in a year, becomes pretty considerable in time; and in threescore and twelve years the difference is found to be of one degree, that is to say, the three hundred and sixtieth part of the circ.u.mference of the whole heaven. Thus after seventy-two years the colure of the vernal equinox which pa.s.sed through a fixed star, corresponds with another fixed star.

Hence it is that the sun, instead of being in that part of the heavens in which the Ram was situated in the time of Hipparchus, is found to correspond with that part of the heavens in which the Bull was situated; and the Twins are placed where the Bull then stood. All the signs have changed their situation, and yet we still retain the same manner of speaking as the ancients did. In this age we say that the sun is in the Ram in the spring, from the same principle of condescension that we say that the sun turns round.

Hipparchus was the first among the Greeks who observed some change in the constellations with regard to the equinoxes, or rather who learnt it from the Egyptians. Philosophers ascribed this motion to the stars; for in those ages people were far from imagining such a revolution in the earth, which was supposed to be immovable in every respect. They therefore created a heaven in which they fixed the several stars, and gave this heaven a particular motion by which it was carried towards the east, whilst that all the stars seemed to perform their diurnal revolution from east to west. To this error they added a second of much greater consequence, by imagining that the pretended heaven of the fixed stars advanced one degree eastward every hundred years. In this manner they were no less mistaken in their astronomical calculation than in their system of natural philosophy. As for instance, an astronomer in that age would have said that the vernal equinox was in the time of such and such an observation, in such a sign, and in such a star. It has advanced two degrees of each since the time that observation was made to the present.

Now two degrees are equivalent to two hundred years; consequently the astronomer who made that observation lived just so many years before me.

It is certain that an astronomer who had argued in this manner would have mistook just fifty-four years; hence it is that the ancients, who were doubly deceived, made their great year of the world, that is, the revolution of the whole heavens, to consist of thirty-six thousand years.

But the moderns are sensible that this imaginary revolution of the heaven of the stars is nothing else than the revolution of the poles of the earth, which is performed in twenty-five thousand nine hundred years. It may be proper to observe transiently in this place, that Sir Isaac, by determining the figure of the earth, has very happily explained the cause of this revolution.

All this being laid down, the only thing remaining to settle chronology is to see through what star the colure of the equinoxes pa.s.ses, and where it intersects at this time the ecliptic in the spring; and to discover whether some ancient writer does not tell us in what point the ecliptic was intersected in his time, by the same colure of the equinoxes.