A History of the Theories
by Sir Edmund Whittaker F.R.S
This excerpt begins on page 5 of chapter 1
The Theory of the Aether to the Death of Newton
Kepler's teaching provided the chief inspiration of Descartes, whose researches were dominated by a conviction that the theorems of mathematics had a precision, an indubitability and a universal acceptance, which were not to be found in other fields of study. So to these features he attached the highest importance, laying it down as an axiom that clarity and certainty were marks of all genuine knowledge. Now one of the problems of natural philosophy was to account for actions transmitted between bodies not in contact with each other, such as those indicated by the behaviour of magnets, or by the connection between the moon's position on the one hand and the rise and fall of the tides on the other. To accept these as 'occult' influences would have been contrary to his principles; and he conclude that they must be effected by the agency of the only types of action between bodies which were perfectly intelligible, namely, pressure and impact. This implied that bodies can act on each other only when they are contiguous; in other words, he denied action at a distance; and this had the further consequence, that the space between the moon and the earth, and indeed the whole of space, could not be void. It is occupied partly by ordinary material things - air and tangible bodies; but the interstice between the particles of these, and the whole of the rest of space, must be filled with particles of a much more subtle kind, which everywhere press upon, or collide with, each other: they are the contrivance introduced in order to account for all physical happenings. Space is thus, in Descartes' view, a plenum, being occupied by a medium which, though imperceptible to the senses, is capable of transmitting force, and exerting effects on material bodes immersed in it - the aether, as it called. The word had meant originally the blue sky or upper air (as distinguished from the lower air at the level of the earth), and had been borrowed from the Greek by Latin writers, from whom it had passed into French and English in the Middle Ages. In ancient cosmology it was sometimes used in the sense of that which occupied celestial regions; and when the notion of a medium filling the interplanetary void as introduced, aether was the obvious word to sue for it. Before Descartes, it had connoted merely the occupancy of some part of space: he was the first to brining the aether into science, by postulating that it had mechanical properties. In his view, it was to be regarded as the solitary tenant of the universe, save for that infinitesimal fraction of space which is occupied by ordinary matter.
Descartes assumed that the aether particles are continually in motion. As however there was no empty space for moving particles to move into, he inferred that they move by taking the places vacated by other aether particles which are themselves in motion. Thus the movement of a single particle of the aether involved the motion of an entire closed chain of particles; and the motions of these closed chains constituted vortices, which performed important functions in his picture of the cosmos.
Holding, then that the effects produced by means of contacts and collisions were the simplest and most intelligible phenomena in the external world, Descartes admitted no other agencies. He did not claim for his scheme an accurate quantitative agreement with experiment, in the spirit of a modern scientific textbook. He trusted more to the clarity and distinctness of a speculation than to its consistence with observed fact: rather is his work to be regarded as a stupendous effort of the imaginative intellect - a myth, in the same sense as the Timeaeus of Plato is a myth - intended to show that all the contents and happenings of the universe might be exhibited as parts of a logically co-ordinated mechanical scheme, depending solely on very elementary types of physical action, and having (once the premises were accepted) the complete certitude of deduction that had hitherto been associated only with mathematics. Descartes was the originator of the Mechanical Philosophy, i.e. of the doctrine that the external inanimate world may for scientific purposes be regarded as an automatic mechanism, and that it is possible and desirable to imagine a mechanical model of every physical phenomenon.
Such a conception could not well have originated earlier than the Renaissance, because the ancients and the men of the Middle Ages had little or no experience of mechanisms that were self-contained and could work independently of human direction; they were acquainted only with tools, which in order to achieve definite purposes required intelligent guidance. Any manifestation of regularity in performance seemed to our forefathers to indicate, as its directing cause, an activity of mind; indeed it was precisely the order and harmony observed in the movements of the heavenly bodies that led the Geek thinkers to regard them as possessing souls. Movements such as the fall of a material body to the ground were accounted, for, as we have seen by supposing that heavy matter tended to seek its natural place, the centre of the universe. This explanation became unsatisfying when the Copernican theory of the solar system was accepted since the earth was now in motion in infinite space, and no point could be identified as the centre of the universe. It was at this juncture that Descartes put forward his revolutionary suggestion., that the cosmos might be thought of as an immense machine. This entailed the general principle that all happenings in the material world can be predicted by mathematical calculation, and this principle has proved the element of greatest value in the Cartesian philosophy of nature.
Descartes himself seems to have gone further, and to have held the doctrine of epistemological rationalism, that is, the assertion that physics can, like Euclidean geometry, be derived entirely from a priori principles, without any dependence on observation and experiment. At any rate, his general practice was to represent phenomena as the effects of preconceived dispositions and causes. In this respect he departed from the sound doctrines that had been preached a generation earlier by Francis Bacon and Galileo, and he drew down upon himself the criticism of Huygens: 'Descartes,' wrote Huygens, 'who seemed to me to be jealous of the fame of Galileo, had the ambition to be regarded as the author of a new philosophy, to be taught in academies in place of Aristotelianism. He put forward his conjectures a verities, almost as if they could be proved by his affirming them on oath. He ought to have presented his system of physics as an attempt to show what might be anticipated as probable in this science, when no principles but those of mechanics were admitted: this would indeed have been praiseworthy; but he went further, and claimed to have revealed the precise truth, thereby greatly impeding the discovery of genuine knowledge.'
In putting forward an all-embracing theory of the universe before he had studied any of its processes in detail, Descartes was continuing the tradition of the ancient Greeks, rather than treading in the new paths struck out by Tycho, Kepler and Galileo: he never really grasped the principle that true knowledge can only be acquired piecemeal, by the patient interrogation of nature. As further weakness in his system was involved in the assumption that force cannot be communicated except by actual pressure or impact, a principle which compelled him to provide an explicit mechanism in order to account for each of the known forces of nature. This task is evidently much more difficult than that which lies before those who are willing to admit action at distance as an ultimate property of matter.
The many defects of Descartes' method led to the rejection of almost all his theories in less than a century. It must be said, however, that the grandeur of his plan, and the boldness of its execution, stimulated scientific thought to a degree before unparalleled. 'Give me matter and motion,' he cried, 'and I will construct the universe.'
Matter, in the Cartesian philosophy, is characterized not be impenetrability, or by any quality recognizable by the senses, but simply by extension; extension constitutes matter, and matter constitutes space. The basis of all things is a primitive, elementary, unique type of matter, boundless in extent and infinitely divisible. In the process of evolution of the universe three distinct forms of this matter have originated, corresponding respectively to the luminous matter of the sun, the transparent matter of interplanetary space, and the dense opaque matter of the earth. 'The first is constituted by what has been scraped off the other particles of matter when they were rounded; it moves with so much velocity that when it meets other bodies the force of its agitation causes it to be broken and divided by them into a heap of small particles that are of such a figure as to fill exactly all the holes and small interstices which they find around these bodies. The next type includes most of the rest of matter: its particles are spherical, and are very small compared with the bodies we see on the earth; but nevertheless they have a finite magnitude, so that they can be divided into others yet smaller. There exists in addition a third type exemplified by some kinds of matter -- namely, those which, on account of their size and figure, cannot be so easily moved as the preceding. I will endeavor to show that all the bodies of the visible world are composed of these three forms of matter, as of three distinct elements; in fact, that the sun and the fixed stars are formed of the first of these elements, the interplanetary spaces of the second, and the earth, with the planets and comets, of the third. For, seeing that the sun and the fixed stars emit light, the heavens transmit it, and the earth, the planets and the comets reflect it, it appears to me that there is ground for using these three qualities of luminosity, transparency and opacity, in order to distinguish the three elements of the visible world'. (Principia, pt. iii, S52)
According to Descartes' theory, the sun is the centre of an immense vortex formed of the first or subtlest kind of matter. (ed note: It is curious to speculate on the impression which would have been produced had the spirituality of nebulae been discovered before the overthrow of the Cartesian theory of vortices.) 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 intermediated between that of the vortex matter and that of ponderable matter. The globules of the second element, and all the matter of the first element, 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 Meteores, 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 a great discovery which was not fully established until much later.
The general explanation of light on these principles was amplified by a more particular discussion of reflection and refraction. The law of reflection -- that the angles of incidence and reflection are equal -- had been known to the Greeks. Kepler in his Dioptircs (1611) discussed refraction through lenses; he had found experimentally that for glass, when the incidence is almost perpendicular, the angles of incidence and refraction are nearly in the ratio of 3 to 2; and assuming this value, he had found the correct result that the focus of a double convex lens, whose two faces have the same curvature, is the centre of curvature of the side nearest the object. He did not, however, succeed in discovering the general law of refraction -- that the sines of the angles of incidence and refraction are to each other in a ration depending on the media -- which 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 (1591-1676), 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 was 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 motion 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 substantially as follows:
Suppose that a ray of light is refracted across a plane interface from one medium into another. Let a light corpuscle, whose velocity in the first medium is vi, be incident on the interface, making an angle i with the normal to the interface, and let it be refracted at an angle r into the second medium, in which its velocity is vi and vr depends only on the nature of the media: (vr / vi) = u, say. He assumed also that the component of velocity parallel to the interface is unaffected by the refraction, so we have vi sin i = vr sin r
Combining these equations, we have sin i = u sin r which is the law of refraction.
These equations imply that if i > r (e.g. if the refraction is from air into glass) the velocity is greater in the second or denser medium. As we shall see, this consequence of the corpuscular theory in its primitive form is in contradiction with experimental fact. (editors footnote: Descartes' idea can however be modified so as to avoid erroneous consequences in the following way. Instead of considering the velocities of light-corpuscle in the two media, consider its momenta, say pi and pr (for a light-corpuscle, as will be seen later, the momentum is not measured by the product of the mass and the velocity). Let us assume that the ratio of pr to pi depends only on the nature of the media, and that the component of momentum parallel to the interface is unaffected by the transition from one medium to the other, then as in Descartes' proof we have
(pr / pi) = u
Pi sin i = pr sin r
sin i = u sin r
These equations are correct; the momentum is actually greater in the optically denser medium.
Crude though the Cartesian system was in many features, there is no doubt that by presenting definite mechanical conceptions of physical activity, and applying them to so wide a range of phenomena, it stimulated the spirit of inquiry and in some degree prepared the way for the more accurate theories that come after. In its own day it met with great acceptance; the confusion that 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, as we shall see later, did its influence quickly wane.
So far as the theory of light was concerned, Descartes' conceptions
rapidly displaced those which had been current in the Middle Ages. The
validity of his explanation of refraction was, however, called in question
by his fellow-countryman, Pierre de Fermat (1601-65), and a controversy
followed, 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 reflection can
readily be 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 'the 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 arrive 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 suppose light to move more slowly
in dense than in rare media, whereas Descartes had (as we have seen) been
obliged to make the contrary supposition.
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