ing 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.

"Procedes 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 circumstance 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 assistance 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 assert 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 staf acts at one end when pushed forward by the other. Thai 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 cannon-ball, which were not to lose any of its

velocity, could not go that distance in less than twentyfive 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 assistance 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 assumes 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 constituent 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 glasses, 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 assisting our eyes by telescopes, can be carried.

Descartes, from a noble 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 assistance 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 glasses 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 glass, and that which arises from the refrangibility. He finds that the object glass 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 glass is above five thousand times less than the error which arises from the refrangibility; and, therefore, that the shape or figure of the glasses 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 assistance 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.