of refraction.* "Now," says Newton, "if the motion of the ray be supposed in this passage to be increased or diminished in a certain proportion, according to the difference of the densities of the ætherial mediums, and the addition or detraction of the motion be reckoned in the perpendicular from the refracting superficies, as it ought to be, the sines of incidence and refraction will be proportional, according to what Descartes has demonstrated." This explanation of refraction is exactly the same as Newton afterwards reproduced in the Principia, though without there pronouncing any opinion on the nature of the disturbing force. It is, however, probable, that in his Memoir he deduced it by simple induction, rather than by a mathematical investigation; for it does not appear that, at this epoch, he was acquainted with the calculation of curvilinear motions. It is, however, important to remark, that from this time he had formed a conception of the doctrine of universal gravitation; for he takes care to point out that the unequal density of the æther, at different distances from the surface of bodies, suffices to determine their mutual tendency towards one another; a consideration which he again brought forward in the Queries annexed to his Optics (in 1704), after he had discovered the laws of the system of the world. Nevertheless we may infer, that in 1675, he had not yet formed the idea of attractions at small distances, since, in his paper addressed to the Royal Society, he imagines that the ascent of liquids in capillary tubes is caused by the air being more rare in confined than in open spaces, and the more rare in proportion as the spaces are more confined. While in the Queries he attributes these phenomena to their true cause, viz. to the reciprocal attractions of the tubes and of the fluid; though, even at this later period, he did not know how to calculate their effect. It was reserved for LAPLACE to complete this investigation.

After having thus considered the simple transmission of rays in ætherial strata of unequal densities, Newton examines the modifications produced during this transmission, by their meeting with undulations originally excited in the æther itself, according as such undulations may favour or oppose the actual motion of the luminous particles;

Birch, Hist. R .S. vol. iii. p. 256.

and by this re-action he is enabled to explain the intermittances in reflection and refraction, which take place in thin plates. We may observe in his Optics, that he has never abandoned this idea; for though in that work he has maintained the most complete reserve with regard to the nature of light, yet, after characterizing the fits as a purely abstract physical property, he gives as a method of rendering it sensible, the same manner of conceiving it that he had given in his Memoir of 1675; the same idea is reproduced in several of the Queries, particularly in the 17th, and those following to the 24th, where Newton asks, as in the paper presented to the Royal Society, if this same æther be not also sufficient to produce universal gravitation, and even all the phenomena of animal motion? Finally, in his paper, he endeavours to apply the same principles to the inflections, undergone by rays of light on passing near the extremities of bodies; which he, in like manner, explains by variations in the density of the æther. It is always thus that he has represented these inflections, both in the Principia, printed in 1687, and in the Queries.

66 seve

From these examples, taken together, we may see that Newton did not ral times change his ideas on light," as has been asserted by some writers, but that, always preserving the same opinion, he has explained it more or less fully, as different occasions demanded.

The phenomena of diffraction, how ever, were still too imperfectly known, and observed with too little detail for enabling Newton to see precisely whether they agreed or not with his hypothesis. We have reason to believe that, in order to study these properties, he then made a number of experiments, to be afterwards inserted at the end of the Optics; for he there introduces them as part of an investigation which he had formerly undertaken, but from which his thoughts were now so far estranged, that he had lost the taste for resuming it. These observations, like all his others, are presented as matters of fact, without relation to any system. When the hypothesis of Newton on the nature of light was presented, in 1675, to the Royal Society, Hooke, as usual, put in his claims to it. Newton, however, did not again waste his time and repose in a controversy on the subject, but contented himself with writing to Oldenburg (21st December), in order to make

him see the injustice of that jealous individual. He first clearly shows that his fundamental idea has nothing in common with that of Hooke, inasmuch as the latter supposes light to consist in the undulations themselves of the æther, transmitted to the organ of vision; while the light of Newton is a substance entirely distinct, which, thrown into the æther, impresses upon, or receives from it, peculiar motions, by means of which it acts upon us. "As to the observations of Hooke on the colours in thin plates, I avow," says Newton, "that I have made use of them, and thank him for the same; but he left me to find out and make such experiments about it, as might inform me of the manner of the production of those colours, to ground an hypothesis on; he having given no further insight to it than this, that the colour depended on some certain thickness of the plate; though what that thickness was at every colour, he confesses, in his Micrography, he had attempted in vain to learn; and, therefore, seeing I was left to measure it myself, I suppose he will allow me to make use of what I took the pains to find out; and this I hope may vindicate me from what Mr. Hooke has been pleased to charge me with."* Happily this time the discussion proceeded no further; and Oldenburg had sufficient influence, as well as sufficient sense, to prevent its obtaining notoriety. From this time till the year 1679, four years afterwards, Newton communicated nothing to the Royal Society. Oldenburg, whose kindness had ever encouraged him, unfortunately died in this interval, and was succeeded in the secretaryship by Hooke, an appointment little likely to remove an apprehension of new disputes. We may imagine, however, that Newton did not remain idle; and, in fact, in this interval, it appears, he was principally occupied with astronomical observations. At last, 28th November, 1679, he had occasion to write to Hooke about a System of Physical Astronomy, on which the Royal Society had asked his opinion. In his letter he proposed, as a matter deserving attention, to verify the motion of the earth by direct experiment, viz. by letting bodies fall from a considerable height, and then observing if they follow exactly a vertical direction; for if the earth

Birch, Hist. R. S. vol. iii. p. 279. † Ibid. vol, iii. p. 512,

turns, since the rotatory velocity at the point of departure must be greater than that at the foot of the vertical, they will be found to deviate from this line towards the east, instead of following it exactly as they would do if the earth did not revolve. This ingenious idea being very favourably received, Hooke was charged to put it into effect. On reflection, Hooke immediately added the remark, that wherever the direction of gravity is oblique to the axis of the earth's rotation, i. e. in all parts of the earth, except at the equator, bodies, in falling, change parallels, and approach the equator: so that in Europe, for instance, the deviation does not take place, rigorously speaking, to the east, but to the south-east of the point of departure. Hooke communicated this remark to Newton, who immediately recognized its correctness in theory; but, in addition to this, Hooke assured the Royal Society that, on repeating the experiment several times, he had actually found that the deviation took place constantly towards the south-east; an accordance which would appear very simple, if Hooke's remarks were merely theoretical; but which must appear very extraordinary if he intended to speak of an actual observed deviation reckoned from the foot of the vertical; for in this case, according to the formula of LAPLACE, the tendency to the south is of the second order, relative to the absolute deviation; and in Hooke's observations this very slight deviation must have been excessively difficult to ascertain, since his experiments were made in the open air. It was this, however, which led Newton to consider whether the elliptical motion of the planets could result from a force varying inversely as the square of the distance, and if so, under what circumstances such a result would ensue. In fact, in proposing to the Royal Society his curious experiment, he had considered the motion of the heavy body as determined by a force of constant intensity, and had concluded the trajectory to be a spiral,* doubtless, because he imagined the body to fall in a resisting medium, such as the air. Hooke, who for a long time had adopted the hypothesis of a force decreasing as the squares of the distance from the centre, replied that the trajectory ought

Vide Newton's original Letters in the Biographia Britannica, article Hooke, p. 2659.

not to be a spiral, but that in a vacuum it would be an excentric ellipse, which would change into an ovoidal curve likewise excentric, if the medium were a resisting one. It is impossible exactly to ascertain how Hooke arrived at these results, for neither then, nor on any subsequent occasion, did he give a demonstration of them; though Halley and Sir Christopher Wren both eagerly pressed him to do so. We might imagine, not without some probability, that the elliptic movement of projectiles was, in his mind, a consequence of the hypothetical, though just, ideas he had formed on the physical cause of the planetary motions; for he attributed them to the existence of a gravitating force, proper to each celestial body, and acting round its centre, with an energy inversely proportional to the square of the distance; so that, in this system, the motion of projectiles round the centre of the earth ought to be elliptical, because, according to observation, the motion of the planets was elliptical round the sun. Hooke had, for some time, turned his thoughts to this kind of speculation; but not being a sufficiently profound mathematician, rigorously to deduce the nature of the force from the form of the orbits, or to show how this form resulted from the supposed law of attraction, he tried to determine its character by direct physical experiments, and actually to produce the motions which resulted from the law, by means of mechanical contrivances. On the 21st March, 1666, he communicated to the Royal Society certain experiments, which he had attempt ed, in order to determine whether the weight of a body undergoes any variation at different distances from the earth's centre, at the greatest altitudes or depths which can be attained. These experiments were made with too little precision to give results on which any reliance could be placed. Hooke himself perceived this, and proposed to employ the more delicate process of using a pendulum clock, and successively observing its rate at different heights. This first attempt, though imperfect, shows the object he had in view, which perhaps is more clearly seen in his own words. "Gravity, though it seems to be one of the most universal, active principles in the world, and consequently ought to be the most considerable, yet has it had the ill fate to have been always, till of late, esteemed otherwise,

even to slighting and neglect. But the inquisitiveness of this latter age hath begun to find sufficient arguments to entertain other thoughts of it. Gilbert began to imagine it a magnetical attractive power, inherent in the parts of the terrestrial globe. The noble Verulam also, in part, embraced this opinion; and Kepler (not without good reason) makes it a property inherent in all celestial bodies,-sun, stars, planets. This supposition we may afterwards more particularly examine; but first it will be requisite to consider, whether this gravitating or attracting power be inherent in the parts of the earth; and, if so, whether it be magnetical, electrical, or of some other nature distant from either. If it be magnetical, any body attracted by it ought to gravitate more, when nearer to its surface, than when further off.*"

Two months afterwards, Hooke made before the Royal Society another experiment, which, as he himself observed, without being an exact representation of the planetary orbits, afforded an example, at that time new and remarkable, of a curvilinear motion produced by the combination of a primitive impulse with an attracting power emanating from a centre. He suspended from the ceiling of a room a long wire, to the end of which was attached a ball of wood, to represent a planetary body. On removing this pendulum from the vertical, and giving it a lateral impulse perpendicular to the plane of deviation, it is acted on by two forces, of which one is the impulse itself, and the other terrestrial gravity, of which the effort, when decomposed perpendicularly to the wire, tends always to bring the body back to the vertical. Now when the lateral impulse was nothing, the ball clearly described a plane orbit, viz. that of its free oscillation; if the impulse, without being nothing, were still very weak, the trajectory became a very much elongated ellipse, having its major axis in the plane of oscillation; with a stronger impulse, a more open ellipse was obtained, which, at a particular point, became an exact circle; and lastly, still stronger impulses produced ellipses, whose major axes were no longer parallel with, but were perpendicular to the plane of free oscillation. Thus these different curves were seen to be produced and to be transformed into each

* Birch, Hist. R. S. vol, ii., p. 70.

other, by merely changing the relative energies of the two forces (the one impulsive, and the other central) which acted on the pendulum. These ellipses, however, differed from the planetary ellipses, inasmuch as the central force produced by the decomposition of gravity is constantly directed towards the centre of the ellipse, and is directly proportional to the distance of the body from that centre; whereas, in the planetary orbits, the central force is constantly directed towards one of the foci of the ellipse, and is reciprocally proportional to the square of the distance of the body from that point. Notwithstanding this fundamental distinction, the experiment of Hooke was important and useful, as it gave a perceptible example of the composition of forces. Eight years later, in 1674, Hooke presented the whole of his ideas in a much more explicit and complete manner, at the end of a dissertation, entitled, "An Attempt to prove the Motion of the Earth from Observations." * I shall," says he, "hereafter explain a system of the world, differing in many particulars from any yet known, answering in all things to the common rules of mechanical motions. This depends upon three suppositions:-first, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, whereby they attract not only their own parts and keep them from flying from them, as we may observe the earth to do, but that they do also attract all the other celestial bodies that are within the sphere of their activity, and consequently, that not only the sun and moon have an influence upon the body and motion of the earth, and the earth upon them, but that Mercury, Venus, Mars, Jupiter, and Saturn also, by their attractive powers, have á considerable influence upon its motion, as in the same manner the corresponding attractive power of the earth hath a considerable influence upon every one of their motions also. The second supposition is this, that all bodies whatsoever, that are put into a direct and simple motion, will so continue to move forward in a straight line, till they are, by some other effectual powers, deflected and bent into a motion describing a circle, ellipsis, or some other more compounded curve line. The third supposition is, that those attractive powers are so much the more

* London, 4to. 1674.

powerful in operating, by how much the nearer the body wrought upon is to their own centres. Now what these seve ral degrees are I have not yet experimentally verified; but it is a notion which, if fully prosecuted, as it ought to be, will mightily assist the astronomers to reduce all the celestial motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the circular pendulum and circular motion will easily understand the whole ground of this principle, and will know where to find directions in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this inquiry, and are not wanting of industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand, which I would first complete, and therefore cannot so well attend it. But this I durst promise the undertaker, that he will find all the great motions of the world to be influenced by this principle, and that the true understanding thereof will be the true perfection of astronomy."

Without lessening the credit due to the distinct expression of such remarkable ideas, it is proper to observe, that we find in Hooke's work no measured result. We do not allude only to the law of force, which is here entirely omitted: we have said that Hooke supposed it to be reciprocal to the square of the distance; but others before him, and among them Bouillaud,* had established the same supposition, on simple metaphysical considerations. Halley again did the same, after Hooke and Bouillaud. We have a convincing proof that Hooke arrived at this conclusion in no other way, from his saying that he had not yet experimentally verified the law of decrease in the attracting force; for he would not have thus expressed himself if he had discovered this law directly, by applying the theorems of Huygens on centrifugal forces to the observed orbits of the planets; for in this case the experiment would have been already made, and the law of the squares, thus obtained, would have needed no other verification. The generalization of the idea of gravity, and its extension to all celestial bodies, decreasing in intensity according to the distance, was formally

* Bullialdus, Astronomia Philolaïca.

expressed by Borelli* in 1666, in his work on the Satellites of Jupiter; and not only did he announce it as a general principle, but he explained very clearly how the planets may be retained and suspended in empty space round the sun, in the same manner as the satellites round their planets, by the action of a power continually and exactly balanced by the centrifugal force caused by their rotation, without having recourse either to the solid heavens of Aristotle, or to the vortices of Descartes. Borelli even endeavoured to deduce from this combination of forces the elliptical motions of the satellites, and the inequalities in their motions, which he considered as being partly produced by the secondary action of the sun; and though, from his being unacquainted both with the law of this force at different distances, and with the Theorems on Central Forces, published by Huygens six years afterwards, he was, of course, unable rigorously to establish these deductions; yet there was much merit in being the first to guess and perhaps to indicate the possibility of doing so. Newton also, we shall presently see, attributes to Borelli the honour of having first formed the idea of extending the principle of gravitation, and of applying it to the planetary motions; and Huygens renders him the same justice in his Kosmotheoros, where he mentions these happy perceptions, immediately before speaking of the demonstrations of Newton. It is not then by any means impossible that Hooke might have been conducted to the same thoughts by similar, that is by purely physical considerations; and we shall presently see reasons that render this conjecture extremely probable. However, in whatever manner he formed these opinions, it is clear that in 1679 he considered them as undoubtedly correct; for, in writing to Newton on the motion of projectiles, he represents the eccentric ellipse as the consequence of a force reciprocal to the squares of the distances from the centre of the earth. This remarkable relation could not fail of striking a mind which had so long and so constantly studied the motions of the heavens. Newton,

Theoric medicearum planetarum ex causis phy sicis deductæ. (Firenze, 1666.) This same Borelli was the author of the celebrated work de Motu Animalium.

† Vid. lib. ii, p. 141. Christianii Hugenii Kosmotheoros, sive de terris cœlestibus, eorumque ornatu conjectura. (4to. Haga Comm. 1698.)

as we have already said, hastened to examine this result, by means of mathematical calculations, and discovered its truth; that is to say, he found that an attractive force, emanating from a centre, and acting reciprocally to the squares of the distances, necessarily compels the body on which it acts, to describe an ellipse, or in general a con c section, in one of whose foci the centre of force resides. The motions produced by such force exactly resemble the planetary motions, both in regard to the form of the orbit and the velocity of the body at each point. This was evidently the secret of the system of the world; but it still remained to account for the singular discordance which the moon's motion had offered to Newton, when, in 1665, he had wished to extend to her the earth's gravity diminished according to this law. Hence it was that, notwithstanding his inference was confirmed by other inductions, he abstained from publishing any thing upon the subject. Three years afterwards, however, (in June, 1682,) Newton being present at a meeting of the Royal Society, in London, the conversation turned on a new measurement of a terrestrial degree, recently executed in France, by Picard, and much credit was given to the care taken in rendering it exact. Newton, having noted down the length of the degree obtained by Picard, returned home immediately, and taking up his former calcu lation of 1665, began to recompute it from the new data. Finding, as he advanced, the manifest tendency of these numbers to produce the long wished for results, he suffered so much nervous excitement, that becoming at length unable to go on with the calculation, he entreated one of his friends to complete it for him. This time the agreement of the computed with the observed result was no longer doubtful. The force of gravity at the earth's surface, as determined by experiments on falling bodies, when applied to the moon, after being diminished proportionally to the square of the distance from the centre of the earth, was found to be very nearly equal to the centrifugal force in the moon, as concluded from its distance and angular velocity obtained by observation. The small difference which still existed between the two results, was in itself a new proof of exactness; for if we suppose an attractive power to emanate from all the celestial bodies inversely proportional to the squares of

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