Chapter XXV (2)

33. Descartes, in his new theory of the solar system, aspired to explain the secret springs of nature, while Kepler and Galileo had merely showed their effects. By what force the heavenly bodies were impelled, by what law they were guided, was certainly a very different question from that of the orbit they described or the period of their revolution. Kepler had evidently some notion of that universally mutual gravitation which Hooke saw more clearly, and Newton established on the basis of his geometry.[623] But Descartes rejected this with contempt. “For,” he says “to conceive this we must not only suppose that every portion of matter in the universe is animated, and animated by several different souls which do not obstruct one another, but that those souls are intelligent and even divine; that they may know what is going on in the most remote places, without any messenger to give them notice, and that they may exert their powers there.”[624] Kepler, who took the world for a single animal, a leviathan that roared in caverns and breathed in the ocean tides, might have found it difficult to answer this, which would have seemed no objection at all to Campanella. If Descartes himself had been more patient towards opinions which he had not formed in his own mind, that constant divine agency, to which he was, on other occasions, apt to resort, could not but have suggested a sufficient explanation of the gravity of matter, without endowing it with self-agency. He had, however, fallen upon a complicated and original scheme; the most celebrated, perhaps, though not the most admirable, of the novelties which Descartes brought into philosophy.

[623] “If the earth and moon,” he says, “were not retained in
their orbits, they would fall one on another, the moon moving
about 33/34 of the way, the earth the rest, supposing them
equally dense.” By this attraction of the moon he accounts for
tides. He compares the attraction of the planets towards the sun
to that of heavy bodies towards the earth.

[624] Vol. x., p. 560.

|Cartesian theory of the world.|

34. In a letter to Mersenne, January 9th, 1639, he shortly states that notion of the material universe, which he afterwards published in the Principia Philosophiæ. “I will tell you,” he says, “that I conceive, or rather I can demonstrate, that besides the matter which composes terrestrial bodies, there are two other kinds; one very subtle, of which the parts are round or nearly round like grains of sand, and this not only occupies the pores of terrestrial bodies, but constitutes the substance of all the heavens; the other incomparably more subtle, the parts of which are so small and move with such velocity, that they have no determinate figure, but readily take at every instant that which is required to fill all the little intervals which the other does not occupy.”[625] To this hypothesis of a double æther he was driven by his aversion to admit any vacuum in nature; the rotundity of the former corpuscles having been produced, as he fancied, by their continual circular motions, which had rubbed off their angles. This seems at present rather a clumsy hypothesis, but it is literally that which Descartes presented to the world.

[625] Vol. viii., p. 73.

35. After having thus filled the universe with different sorts of matter, he supposes that the subtler particles, formed by the perpetual rubbing off of the angles of the larger in their progress towards sphericity, increased by degrees till there was a superfluity that was not required to fill up the intervals; and this, flowing towards the centre of the system, became the sun, a very subtle and liquid body, while in like manner, the fixed stars were formed in other systems. Round these centres the whole mass is whirled in a number of distinct vortices, each of which carries along with it a planet. The centrifugal motion impels every particle in these vortices of each instant to fly off from the sun in a straight line; but it is retained by the pressure of those which have already escaped and form a denser sphere beyond it. Light is no more than the effect of particles seeking to escape from the centre, and pressing one on another, though perhaps without actual motion.[626] The planetary vortices contain sometimes smaller vortices, in which the satellites are whirled round their principal.

[626] J’ai souvent averti que par la lumière je n’entendois pas
tant le mouvement que cette inclination ou propension que ces
petits corps ont à se mouvoir, et que ce que je dirois du
mouvement, pour être plus aisément entendu, se devoit rapporter à
cette propension; d’où il est manifeste qua selon moi l’on ne
doit entendre autre chose par les couleurs que les différentes
variétés qui arrivent en ces propensions. Vol. vii., p. 193.

36. Such, in a few words, is the famous Cartesian theory, which, fallen in esteem as it now is, stood its ground on the continent of Europe, for nearly a century, till the simplicity of the Newtonian system, and, above all, its conformity to the reality of things, gained an undisputed predominance. Besides the arbitrary suppositions of Descartes, and the various objections that were raised against the absolute plenum of space and other parts of his theory, it has been urged that his vortices are not reconcilable, according to the laws of motion in fluids, with the relation, ascertained by Kepler, between the periods and distances of the planets; nor does it appear why the sun should be in the focus, rather than in the centre of their orbits. Yet, within a few years it has seemed not impossible, that a part of his bold conjectures will enter once more with soberer steps into the schools of philosophy. His doctrine as to the nature of light, improved as it was by Huygens, is daily gaining ground over that of Newton; that of a subtle æther pervading space, which in fact is nearly the same thing, is becoming a favourite speculation, if we are not yet to call it an established truth; and the affirmative of a problem, which an eminent writer has started, whether this æther has a vorticose motion round the sun, would not leave us very far from the philosophy it has been so long our custom to turn into ridicule.

|Transits of Mercury and Venus.|

37. The passage of Mercury over the sun was witnessed by Gassendi in 1631. This phenomenon, though it excited great interest in that age, from its having been previously announced, so as to furnish a test of astronomical accuracy, recurs too frequently to be now considered as of high importance. The transit of Venus is much more rare. It occurred on December 4, 1639, and was then only seen by Horrox, a young Englishman of extraordinary mathematical genius. There is reason to ascribe an invention of great importance, though not perhaps of extreme difficulty, that of the micrometer, to Horrox.

|Laws of Mechanics.|

|Statics of Galileo.|

38. The satellites of Jupiter and the phases of Venus are not so glorious in the scutcheon of Galileo as his discovery of the true principles of mechanics. These, as we have seen in the former volume, were very imperfectly known till he appeared; nor had the additions to that science since the time of Archimedes been important. The treatise of Galileo, Della Scienza Mecanica, has been said, I know not on what authority, to have been written in 1592. It was not published, however, till 1634, and then only in a French translation by Mersenne, the original not appearing till 1649. This is chiefly confined to statics, or the doctrine of equilibrium; it was in his dialogues on motion, Della Nuova Scienza, published in 1638, that he developed his great principles of the science of dynamics, the moving forces of bodies. Galileo was induced to write his treatise on mechanics, as he tells us, in consequence of the fruitless attempts he witnessed in engineers to raise weights by a small force, “as if with their machines they could cheat nature, whose instinct as it were by fundamental law is that no resistance can be overcome except by a superior force.” But as one man may raise a weight to the height of a foot by dividing it into equal portions, commensurate to his power, which many men could not raise at once, so a weight, which raises another greater than itself, may be considered as doing so by successive instalments of force, during each of which it traverses as much space as a corresponding portion of the larger weight. Hence the velocity, of which space uniformly traversed in a given time is the measure, is inversely as the masses of the weights; and thus the equilibrium of the straight lever is maintained, when the weights are inversely as their distance from the fulcrum. As this equilibrium of unequal weights depends on the velocities they would have if set in motion, its law has been called the principle of virtual velocities. No theorem has been of more important utility to mankind. It is one of those great truths of science, which combating and conquering enemies from opposite quarters, prejudice and empiricism, justify the name of philosophy against both classes. The waste of labour and expense in machinery would have been incalculably greater in modern times, could we imagine this law of nature not to have been discovered; and as their misapplication prevents their employment in a proper direction, we owe in fact to Galileo the immense effect which a right application of it has produced. It is possible, that Galileo was ignorant of the demonstration given by Stevinus of the law of equilibrium in the inclined plane. His own is different; but he seems only to consider the case when the direction of the force is parallel to that of the plane.

|His Dynamics.|

39. Still less was known of the principles of dynamics than of those of statics, till Galileo came to investigate them. The acceleration of falling bodies, whether perpendicularly or on inclined planes, was evident; but in what ratio this took place, no one had succeeded in determining, though many had offered conjectures. He showed that the velocity acquired was proportional to the time from the commencement of falling. This might now be demonstrated from the laws of motion; but Galileo, who did not perhaps distinctly know them, made use of experiment. He then proved by reasoning that the spaces traversed in falling were as the squares of the times or velocities; that their increments in equal times were as the uneven numbers, 1, 3, 5, 7, and so forth; and that the whole space was half what would have been traversed uniformly from the beginning with the final velocity. These are the great laws of accelerated and retarded motion, from which Galileo deduced most important theorems. He showed that the time in which bodies roll down the length of inclined planes is equal to that in which they would fall down the height, and in different planes is proportionate to the height; and that their acquired velocity is in the same ratios. In some propositions he was deceived; but the science of dynamics owes more to Galileo than to any one philosopher. The motion of projectiles had never been understood; he showed it to be parabolic; and in this he not only necessarily made use of a principle of vast extent, that of compound motion, which, though it is clearly mentioned in one passage by Aristotle[627] and may probably be implied in the mechanical reasonings of others, does not seem to have been explicitly laid down by modern writers, but must have seen the principle of curvilinear deflection by forces acting in infinitely small portions of time. The ratio between the times of vibration in pendulums of unequal length, had early attracted Galileo’s attention. But he did not reach the geometrical exactness of which this subject is capable.[628] He developed a new principle as to the resistance of solids to the fracture of their parts, which, though Descartes as usual treated it with scorn, is now established in philosophy. “One forms, however,” says Playfair, “a very imperfect idea of this philosopher from considering the discoveries and inventions, numerous and splendid as they are, of which he was the undisputed author. It is by following his reasonings, and by pursuing the train of his thoughts, in his own elegant, though somewhat diffuse exposition of them, that we become acquainted with the fertility of his genius, with the sagacity, penetration, and comprehensiveness of his mind. The service which he rendered to real knowledge is to be estimated not only from the truths which he discovered, but from the errors which he detected; not merely from the sound principles which he established, but from the pernicious idols which he overthrew. Of all the writers who have lived in an age which was yet only emerging from ignorance and barbarism, Galileo has most entirely the tone of true philosophy, and is most free from any contamination of the times, in taste, sentiment, and opinion.”[629]

[627] Drinkwater’s Life of Galileo, p. 80.

[628] Fabroni.

[629] Preliminary Dissertation to Encyclop. Britain.

|Mechanics of Descartes.|

40. Descartes, who left nothing in philosophy untouched, turned his acute mind to the science of mechanics, sometimes with signal credit, sometimes very unsuccessfully. He reduced all statics to one principle, that it requires as much force to raise a body to a given height, as to raise a body of double weight to half the height. This is the theorem of virtual velocities in another form. In many respects he displays a jealousy of Galileo, and an unwillingness to acknowledge his discoveries, which puts himself often in the wrong. “I believe,” he says, “that the velocity of very heavy bodies which do not move very quickly in descending increases nearly in a duplicate ratio; but I deny that this is exact, and I believe that the contrary is the case when the movement is very rapid.”[630] This recourse to the air’s resistance, a circumstance of which Galileo was well aware, in order to diminish the credit of a mathematical theorem, is unworthy of Descartes; but it occurs more than once in his letters. He maintained also, against the theory of Galileo, that bodies do not begin to move with an infinitely small velocity, but have a certain degree of motion at the first instance, which is afterwards accelerated.[631] In this too, as he meant to extend his theory to falling bodies, the consent of philosophers has decided the question against him. It was a corollary from these notions that he denies the increments of spaces to be according to the progression of uneven numbers.[632] Nor would he allow that the velocity of a body augments its force, though it is a concomitant.[633]

[630] Œuvres de Descartes, vol. viii., p. 24.

[631] Il faut savoir, quoique Galilée et quelques autres disent
au contraire, que les corps qui commencent à descendre, ou à se
mouvoir en quelque façon que ce soit, ne passent point par tous
les degrés de tardiveté; mais que des le premier moment ils ont
certaine vitesse qui s’augmente après de beaucoup, et c’est de
cette augmentation que vient la force de la percussion. viii.,
181.

[632] Cette proportion d’augmentation selon les nombres impairs,
1, 3, 5, 7, &c., qui est dans Galilée et que je crois vous avoir
aussi écrite autrefois, ne peut être vraie, qu’en supposant deux
ou trois choses qui sont très fausses, dont l’une est que le
mouvement croisse par degrés depuis le plus lent, ainsi que le
songe Galilée, et l’autre que la résistance de l’air n’empêche
point. Vol. ix., p. 349.

[633] Je pense que la vitesse n’est pas la cause de
l’augmentation de la force, encore qu’elle l’accompagne toujours.
Id. p. 356, See also vol. viii., p. 14. He was probably perplexed
by the metaphysical notion of causation, which he knew not how to
ascribe to mere velocity. The fact that increased velocity is a
condition or antecedent of augmented force could not be doubted.

|Law of motion laid down by Descartes.|

41. Descartes, however, is the first who laid down the laws of motion; especially that all bodies persist in their present state of rest or uniform rectilineal motion till affected by some force. Many had thought, as the vulgar always do, that a continuance of rest was natural to bodies, but did not perceive that the same principle of inertia or inactivity was applicable to them in rectilineal motion. Whether this is deducible from theory, or depends wholly on experience, by which we ought to mean experiment, is a question we need not discuss. The fact, however, is equally certain; and hence Descartes inferred that every curvilinear deflection is produced by some controlling force, from which the body strives to escape in the direction of a tangent to the curve. The most erroneous part of his mechanical philosophy is contained in some propositions as to the collision of bodies, so palpably incompatible with obvious experience that it seems truly wonderful he could ever have adopted them. But he was led into these paradoxes by one of the arbitrary hypotheses which always governed him. He fancied it a necessary consequence from the immutability of the divine nature that there should always be the same quantity of motion in the universe; and rather than abandon this singular assumption he did not hesitate to assert, that two hard bodies striking each other in opposite directions would be reflected with no loss of velocity; and, what is still more outrageously paradoxical, that a smaller body is incapable of communicating motion to a greater; for example, that the red billiard-ball cannot put the white into motion. This manifest absurdity he endeavoured to remove by the arbitrary supposition, that when we see, as we constantly do, the reverse of his theorem take place, it is owing to the air, which, according to him, renders bodies more susceptible of motion, than they would naturally be.

|Also those of compound forces.|

42. Though Galileo, as well as others, must have been acquainted with the laws of the composition of moving forces, it does not appear that they had ever been so distinctly enumerated as by Descartes, in a passage of his Dioptrics.[634] That the doctrine was in some measure new may be inferred from the objections of Fermat; and Clerselier, some years afterwards, speaks of persons “not much versed in mathematics, who cannot understand an argument taken from the nature of compound motion.”[635]

[634] Vol. v., p. 18.

[635] Vol. vi., p. 508.

|Other discoveries in mechanics.|

43. Roberval demonstrated what seems to have been assumed by Galileo, that the forces on an oblique or crooked lever balance each other, when they are inversely as the perpendiculars drawn from the centre of motion to their direction. Fermat, more versed in geometry than physics, disputed this theorem which is now quite elementary. Descartes, in a letter to Mersenne, ungraciously testifies his agreement with it.[636] Torricelli, the most illustrious disciple of Galileo, established that when weights balance each other in all positions, their common centre of gravity does not ascend or descend, and conversely.

[636] Je suis de l’opinion, says Descartes, de ceux qui disent
que _pondera sunt in æquilibrio quando sunt in ratione reciproca
linearum perpendicularium_, &c., vol. xi., p. 357. He would not
name Roberval; one of those littlenesses which appear too
frequently in his letters and in all his writings. Descartes in
fact could not bear to think that another, even though not an
enemy, had discovered anything. In the preceding page he says:
C’est une chose ridicule que de vouloir employer la raison du
levier dans la poulie, ce qui est, si j’ai bonne mémoire, une
imagination de Guide Ubalde. Yet this imagination is demonstrated
in all our elementary books on mechanics.

|In Hydrostatics and pneumatics.|

44. Galileo, in a treatise entitled, Delle Cose che stanno nell’Acqua, lays down the principles of hydrostatics already established by Stevin, and among others what is called the hydrostatical paradox. Whether he was acquainted with Stevin’s writings, may be perhaps doubted; it does not appear that he mentions them. The more difficult science of hydraulics was entirely created by two disciples of Galileo, Castellio and Torricelli. It is one everywhere of high importance, and especially in Italy. The work of Castellio, Della Misura dell’Acque Correnti, and a continuation, were published at Rome, in 1628. His practical skill in hydraulics, displayed in carrying off the stagnant waters of the Arno, and in many other public works, seems to have exceeded his theoretical science. An error, into which he fell, supposing the velocity of fluids to be as the height down which they had descended, led to false results. Torricelli proved that it was as the square root of the altitude. The latter of these two was still more distinguished by his discovery of the barometer. The principle of the syphon or sucking-pump, and the impossibility of raising water in it more than about thirty-three feet, were both well known; but even Galileo had recourse to the clumsy explanation that nature limited her supposed horror of a vacuum to this altitude. It occurred to the sagacity of Torricelli that the weight of the atmospheric column pressing upon the fluid which supplied the pump was the cause of this rise above its level; and that the degree of rise was consequently the measure of that weight. That the air had weight was known, indeed, to Galileo and Descartes; and the latter not only had some notion of determining it by means of a tube filled with mercury, but in a passage which seems to have been much overlooked, distinctly suggests as one reason why water will not rise above eighteen _brasses_ in a pump, “the weight of the water which counterbalances that of the air.”[637] Torricelli happily thought of using mercury, a fluid thirteen times heavier, instead of water, and thus invented a portable instrument by which the variations of the mercurial column might be readily observed. These he found to fluctuate between certain well known limits, and in circumstances which might justly be ascribed to the variations of atmospheric gravity. This discovery he made in 1643; and in 1648, Pascal, by his celebrated experiment on the Puy de Dome, established the theory of atmospheric pressure beyond dispute. He found a considerable difference in the height of the mercury at the bottom and the top of that mountain; and a smaller yet perceptible variation was proved on taking the barometer to the top of one of the loftiest churches in Paris.

[637] Vol. vii., p. 437.

|Optics.--Discoveries of Kepler.|

|Invention of the telescope.|

45. The science of optics was so far from falling behind other branches of physics in this period, that, including the two great practical discoveries which illustrate it, no former or later generation has witnessed such an advance. Kepler began, in the year 1604, by one of his first works, Paralipomena ad Vitellionem, a title somewhat more modest than he was apt to assume. In this supplement to the great Polish philosopher of the middle ages, he first explained the structure of the human eye, and its adaptation to the purposes of vision. Porta and Maurolycus had made important discoveries, but left the great problem untouched. Kepler had the sagacity to perceive the use of the retina as the canvas on which images were painted. In his treatise, says Montucla, we are not to expect the precision of our own age; but it is full of ideas novel and worthy of a man of genius. He traced the causes of imperfect vision in its two principal cases, where the rays of light converge to a point before or behind the retina. Several other optical phenomena are well explained by Kepler; but he was unable to master the great enigma of the science, the law of refraction. To this he turned his attention again in 1611, when he published a treatise on Dioptrics. He here first laid the foundation of that science. The angle of refraction, which Maurolycus had supposed equal to that of incidence, he here assumed to be one third of it; which, though very erroneous as a general theorem, was sufficiently accurate for the sort of glasses he employed. It was his object to explain the principle of the telescope; and in this he well succeeded. That admirable invention was then quite recent. Whatever endeavours have been made to carry up the art of assisting vision by means of a tube to much more ancient times, it seems to be fully proved that no one had made use of combined lenses for that purpose. The slight benefit which a hollow tube affords by obstructing the lateral ray, must have been early familiar, and will account for passages which have been construed to imply what the writers never dreamed of.[638] The real inventor of the telescope is not certainly known. Metius of Alkmaer long enjoyed that honour; but the best claim seems to be that of Zachary Jens, a dealer in spectacles at Middleburg. The date of the invention, or at least of its publicity, is referred, beyond dispute, to 1609. The news of so wonderful a novelty spread rapidly through Europe; and in the same year, Galileo, as has been mentioned, having heard of the discovery, constructed, by his own sagacity, the instrument which he exhibited at Venice. It is, however, unreasonable to regard himself as the inventor; and in this respect his Italian panegyrists have gone too far. The original sort of telescope, and the only one employed in Europe for above thirty years, was formed of a convex object-glass with a concave eye-glass. This, however, has the disadvantage of diminishing too much the space which can be taken in at one point of view; “so that,” says Montucla, “one can hardly believe that it could render astronomy such service as it did in the hands of a Galileo or a Scheiner.” Kepler saw the principle upon which another kind might be framed with both glasses convex. This is now called the astronomical telescope, and was first employed a little before the middle of the century. The former, called the Dutch telescope, is chiefly used for short spying-glasses.

[638] Even Dutens, whose sole aim is to depreciate those whom
modern science has most revered, cannot pretend to show that the
ancients made use of glasses to assist vision. Origine des
Découvertes, i., 218.

|Of the microscope.|

46. The microscope has also been ascribed to Galileo; and so far with better cause, that we have no proof of his having known the previous invention. It appears, however, to have originated, like the telescope, in Holland, and perhaps at an earlier time. Cornelius Drebbel, who exhibited the microscope in London about 1620, has often passed for the inventor. It is suspected by Montucla that the first microscopes had concave eye-glasses; and that the present form with two convex glasses is not older than the invention of the astronomical telescope.

|Antonio de Dominis.|

47. Antonio de Dominis, the celebrated archbishop of Spalatro, in a book published in 1611, though written several years before, De Radiis Lucis in Vitris Perspectivis et Iride, explained more of the phenomena of the rainbow than was then understood. The varieties of colour had baffled all inquirers, though the bow itself was well known to be the reflection of solar light from drops of rain. Antonio de Dominis, to account for these, had recourse to refraction, the known means of giving colour to the solar ray; and guiding himself by the experiment of placing between the eye and the sun a glass bottle of water, from the lower side of which light issued in the same order of colours as in the rainbow, he inferred that after two refractions and one intermediate reflection within the drop, the ray came to the eye tinged with different colours, according to the angle at which it had entered. Kepler, doubtless ignorant of De Dominis’s book, had suggested nearly the same. “This, though not a complete theory of the rainbow, and though it left a great deal to occupy the attention, first of Descartes, and afterwards of Newton, was probably just, and carried the explanation as far as the principles then understood allowed it to go. The discovery itself may be considered as an anomaly in science, as it is one of a very refined and subtle nature, made by a man who has given no other indication of much scientific sagacity or acuteness. In many things, his writings show great ignorance of principles of optics well known in his time, so that Boscovich, an excellent judge in such matters, has said of him, ‘Homo opticarum rerum supra quod patiatur ea ætas imperitissimus.’”[639] Montucla is hardly less severe on De Dominis, who, in fact, was a man of more ingenious than solid understanding.

[639] Playfair, Dissertation on Physical Philosophy, p. 119.

|Dioptrics of Descartes.--Law of refraction.|

48. Descartes announced to the world in his Dioptrics, 1637, that he had at length solved the mystery which had concealed the law of refraction. He showed that the sine of the angle of incidence at which the ray enters, has, in the same medium, a constant ratio to that of the angle at which it is refracted, or bent in passing through. But this ratio varies according to the medium; some having a much more refractive power than others. This was a law of beautiful simplicity as well as extensive usefulness; but such was the fatality, as we would desire to call it, which attended Descartes, that this discovery had been indisputably made twenty years before by a Dutch geometer of great reputation, Willibrod Snell. The treatise of Snell had never been published; but we have the evidence both of Vossius and Huygens, that Hortensius, a Dutch professor, had publicly taught the discovery of his countryman. Descartes had long lived in Holland; privately, it is true, and by his own account reading few books; so that in this, as in other instances, we may be charitable in our suspicions; yet it is unfortunate that he should perpetually stand in need of such indulgence.

|Disputed by Fermat.|

49. Fermat did not inquire whether Descartes was the original discoverer of the law of refraction but disputed its truth. Descartes, indeed, had not contented himself with experimentally ascertaining it, but, in his usual manner, endeavoured to show the path of the ray by direct reasoning. The hypothesis he brought forward seemed not very probable to Fermat, nor would it be permitted at present. His rival, however, fell into the same error; and starting from an equally dubious supposition of his own, endeavoured to establish the true law of refraction. He was surprised to find that, after a calculation founded upon his own principle, the real truth of a constant ratio between the sines of the angles came out according to the theorem of Descartes. Though he did not the more admit the validity of the latter’s hypothetical reasoning, he finally retired from the controversy with an elegant compliment to his adversary.

|Curves of Descartes.|

50. In the Dioptrics of Descartes, several other curious theorems are contained. He demonstrated that there are peculiar curves, of which lenses may be constructed, by the refraction from whose superficies all the incident rays will converge to a focal point, instead of being spread, as in ordinary lenses, over a certain extent of surface, commonly called its spherical aberration. The effect of employing such curves of glass would be an increase of illumination, and a more perfect distinctness of image. These curves were called the ovals of Descartes; but the elliptic or hyperbolic speculum would answer nearly the same purpose. The latter kind has been frequently attempted; but, on account of the difficulties in working them, if there were no other objection, none but spherical lenses are in use. In Descartes’s theory, he explained the equality of the angles of incidence and reflection in the case of light, correctly as to the result, though with the assumption of a false principle of his own, that no motion is lost in the collision of hard bodies such as he conceived light to be. Its perfect elasticity makes his demonstration true.

|Theory of the rainbow.|

51. Descartes carried the theory of the rainbow beyond the point where Antonio de Dominis had left it. He gave the true explanation of the outer bow, by a second intermediate reflection of the solar ray within the drop: and he seems to have answered the question most naturally asked, though far from being of obvious solution, why all this refracted light should only strike the eye in two arches with certain angles and diameters, instead of pouring its prismatic lustre over all the rain-drops of the cloud. He found that no pencil of light continued, after undergoing the processes of refraction and reflection in the drop, to be composed of parallel rays, and consequently to possess that degree of density which fits it to excite sensation in our eyes, except the two which make those angles with the axis drawn from the sun to an opposite point at which the two bows are perceived.