Descartes' Theory of the Aetherby Edmund Taylor Whittaker
According to Descartes’ theory, the sun is the centre of an immense vortex formed of the first or subtlest kind of matter.
The vehicle of light in interplanetary space is matter of the second kind or element, composed of a closely packed assemblage of globules whose size is intermediate between that of the vortex-matter and that of ponderable matter.
The globules of the second element, and all the matter of the first clement, are constantly straining away from the centres around which they turn, owing to the centrifugal force of the vortices; so that the globules are pressed in contact with each other, and tend to move outwards, although they do not actually so move.
It is the transmission of this pressure which constitutes light; the action of light therefore extends on all sides round the sun and fixed stars, and travels instantaneously to any distance.
In the Dioptrique, vision is compared to the perception of the presence of objects which a blind man obtains by the use of his stick; the transmission of pressure along the stick from the object to the hand being analogous to the transmission of pressure from a luminous object to the eye by the second kind of matter.
Descartes supposed the “diversities of colour and light” to be due to the different ways in which the matter moves.
In the Météores, the various colours are connected with different rotatory velocities of the globules, the particles which rotate most rapidly giving the sensation of red, the slower ones of yellow, and the slowest of green and blue–the order of colours being taken from the rainbow. The assertion of the dependence of colour on periodic time is a curious foreshadowing of one of the great discoveries of Newton.
The general explanation of light on these principles was amplified by a more particular discussion of reflexion and refraction.
The law of reflexion—that the angles of incidence and refraction are equal—had been known to the Greeks; but the law of refraction—that the sines of the angles of incidence and refraction are to each other in a ratio depending on the media—was now published for the first time.
Descartes gave it as his own; but he seems to have been under considerable obligations to Willebrord Snell (b. 1591, d. 1626), Professor of Mathematics at Leyden, who had discovered it experimentally (though not in the form in which Descartes gave it) about 1621.
Snell did not publish his result, but communicated it in manuscript to several persons, and Huygens affirms that this manuscript had been seen by Descartes.
Descartes presents the law as a deduction from theory. This, however, he is able to do only by the aid of analogy; when rays meet ponderable bodies, “they are liable to be deflected or stopped in the same way as the notion of a ball or a stone impinging on a body”; for “it is easy to believe that the action or inclination to move, which I have said must be taken for light, ought to follow in this the same laws as motion."
Thus he replaces light, whose velocity of propagation he believes to be always infinite, by a projectile whose velocity varies from one medium to another. The law of refraction is then proved as follows:—
Let a ball thrown from A meet at B a cloth CBE, so weak that the ball is able to break through it and pass beyond, but with its resultant velocity reduced in some definite proportion, say 1 : k.
Then if BI be a length measured on the refracted ray equal to AB, the projectile will take k times as long to describe BI as it took to describe AB. But the component of velocity parallel to the cloth must be unaffected by the impact; and therefore the projection BE of the refracted ray must be k times as long as the projection BC of the incident
A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf ray. So if i and r denote the angles of incidence and refraction, we have …
or the sines of the angles of incidence and refraction are in a constant ratio; this is the law of refraction.
Desiring to include all known phenomena in his system, Descartes devoted some attention to a class of effects which were at that time little thought of, but which were destined to play a great part in the subsequent development of Physics.
The ancients were acquainted with the curious properties possessed by two minerals, amber (ἣλεκτρον) and magnetic iron ore (ἡ λίθος Μαγνῆτις). The former, when rubbed, attracts light bodies: the latter has the power of attracting iron.
The use of the magnet for the purpose of indicating direction at sea does not seem to have been derived from classical antiquity, but it was certainly known in the time of the Crusades. Indeed, magnetism was one of the few sciences which progressed during the Middle Ages; for in the thirteenth century Petrus Peregrinus, a native of Maricourt in Picardy, made a discovery of fundamental importance.
Taking a natural magnet or lodestone, which had been rounded into a globular form, he laid it on a needle, and marked the line along which the needle set itself. Then laying the needle on other parts of the stone, he obtained more lines in the same way.
When the entire surface of the stone had been covered with such lines, their general disposition became evident; they formed circles, which girdled the stone in exactly the same way as meridians of longitude girdle the earth ; and there were two points at opposite ends of the stone through which all the circles passed, just as all the meridians pass through the Arctic and Antarctic poles of the earth.
Struck by the analogy, Peregrinus proposed to call these two points the poles of the magnet: and he observed that the way in which magnets set themselves and attract each other depends solely on the position of their poles, as if these were the seat of the magnetic power. Such was the origin of those theories of poles and polarization which in later ages have played so great a part in Natural Philosophy.
The observations of Peregrinus were greatly extended not long before the time of Descartes by William Gilbert or Gilbert (b. 1540, d. 1603). Gilbert was born at Colchester: after studying at Cambridge, he took up medical practice in London, and had the honour of being appointed physician to Queen Elizabeth. In 1600 he published a work on Magnetism and Electricity, with which the modern history of both subjects begins.
Of Gilbert’s electrical researches we shall speak later: in magnetism ho made the capital discovery of the reason why magnets set in definite orientations with respect to the earth; which is, that the earth is itself a great magnet, having one of its poles in high northern and the other in high southern latitudes. Thus the property of the compass was seen to be included in the general principle, that the north-seeking pole of every magnet attracts the south-seeking pole of every other magnet, and repels its north-seeking pole.
Descartes attempted to account for magnetic phenomena by his theory of vortices. A vortex of fluid matter was postulated round each magnet, the matter of the vortex entering by one pole and leaving by the other : this matter was supposed to act on iron and steel by virtue of a special resistance to its motion afforded by the molecules of those substances.
Crude though the Cartesian system was in this and many other features, there is no doubt that by presenting definite conceptions of molecular activity, and applying them to so wide a range of phenomena, it stimulated the spirit of inquiry, and prepared the way for the more accurate theories that came after.
In its own day it met with great acceptance: the confusion which had resulted from the destruction of the old order was now, as it seemed, ended by a reconstruction of knowledge in a system at once credible and complete.
Nor did its influence quickly wane; for even at Cambridge it was studied long after Newton had published his theory of gravitation; and in the middle of the eighteenth century Euler and two of the Bernoullis based the explanation of magnetism on the hypothesis of vortices.
Descartes’ theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of refraction was, however, called in question by his fellow-countryman Pierre de Fermat (b. 1601, d. 1665), and a controversy ensued, which was kept up by the Cartesians long after the death of their master. Fermat eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light.
This was the celebrated Principle of Least Time, enunciated in the form, “Nature always acts by the shortest course.” From it the law of reflexion can readily lie derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces. In order to obtain the law of refraction, Fermat assumed that “tho resistance of the media is different,” and applied his “method of maxima and minima” to find the path which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution.
“The result of my work," he writes, “has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established."
His surprise was all the greater, as he had supposed light to move ignore slowly in dense than in rare media, whereas Descartes had (as will be evident from the demonstration given above) been obliged to make the contrary supposition.
Although Fermat’s result was correct, and, indeed, of high permanent interest, the principles from which it was derived were metaphysical rather than physical in character, and consequently were of little use for the purpose of framing a mechanical explanation of light.
Descartes’ theory therefore held the field until the publication in 1667 of the Micrographia of Robert Hooke (b. 1635, d. 1703), one of the founders of the Royal Society, and at one time its Secretary.
Hooke, who was both an observer and a theorist, made two experimental discoveries which concern our present subject; but in both of these, as it appeared, he had been anticipated. The first was the observation of the iridescent colours which are seen when light falls on a thin layer of air between two glass plates or lenses, or on a thin film of any transparent substance.
These are generally known as the “colours of thin plates,” or “Newton’s rings”; they had been previously observed by Boyle Hooke’s second experimental discovery made after the date of the Micrographia, was that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shadow of an opaque body.
This observation had been published in 1665 in a posthumous work of Francesco Maria Grimaldi (b. 1618, d. 1663), who had given to the phenomenon the name diffraction.
Hooke’s theoretical investigations on light were of great importance, representing as they do the transition from the Cartesian system to the fully developed theory of undulations. He begins by attacking Descartes’ proposition, that light is a tendency to motion rather than an actual motion.
“There is," he observes, “no luminous Body but has the parts of it in motion more or less”; and this motion is “exceeding quick.” Moreover, since some bodies (e.g. the diamond when rubbed or heated in the dark) shine for a considerable time without being wasted away, it follows that whatever is in motion is not permanently lost to the body, and therefore that the motion must be of a to-and-fro or vibratory character.
The amplitude of the vibrations must be exceedingly small, since some luminous bodies eg, the diamond again) are very hard, and so cannot yield or bend to any sensible extent.
Concluding, then, that the condition associated with the emission of light by a luminous body is a rapid vibratory motion of very small amplitude, Hooke next inquires how light travels through space.
“The next thing we are to consider," he says, “is the way or manner of the trajection of this motion through the interpos’d pellucid body to the eye: And here it will be easily granted—
“First, that it must be a body susceptible and impartible of this motion that will deserve the name of a Transparent; and next, that the parts of such a body must be homogeneous, or of the same kind.
“Thirdly, that the constitution and motion of the parts must be such that the appulse of the luminous body may be communicated or propagated through it to the greatest imaginable distance in the least imaginable time, though I see no reason to affirm that it must be in an instant.
“Fourthly, that the motion is propagated every way through an Homogeneous medium by direct or straight lines extended every way like Rays from the centre of a Sphere.
“Fifthly, in an Homogeneous medium this motion is propagated every way with equal velocity, whence necessarily every pulse or vibration of the luminous body will generate a Sphere, which will continually increase, and grow bigger, just after the same manner (though indefinitely swifter) as the waves or rings on the surface of the water do swell into bigger and bigger circles about a point of it, where by the sinking of a Stone the motion was begun, whence it necessarily follows, that all the parts of these Spheres undulated through an Homogeneous medium cut the Rays at right angles.”
Here we have a fairly definite mechanical conception. It resembles that of Descartes in postulating a medium as the vehicle of light; but according to the Cartesian hypothesis the disturbance is a statical pressure in this medium, while in Hooke’s theory it is a rapid vibratory motion of small amplitude. In the above extract Hooke introduces, moreover, the idea of the wave-surface, or locus at any instant of a disturbance generated originally at a point, and affirms that it is a sphere, whose centre is the point in question, and whose radii are the rays of light issuing from the point.