A History of the Theories of Aether and Electricity/Chapter 1

by Edmund Taylor Whittaker

 

THEORIES OF AETHER AND ELECTRICITY.

 

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CHAPTER I.

THE THEORY OF THE AETHER IN THE SEVENTEENTH CENTURY.

The observation of the heavens, which has been pursued continually from the earliest ages, revealed to the ancients the regularity of the planetary motions, and gave rise to the conception of a universal order. Modern research, building on this foundation, has shown how intimate is the connection between the different celestial bodies. They are formed of the same kind of matter; they are similar in origin and history; and across the vast spaces which divide them they hold perpetual intercourse.

Until the seventeenth century the only influence which was known to be capable of passing from star to star was that of light. Newton added to this the force of gravity; and it is now recognized that the power of communicating across vacuous regions is possessed also by the electric and magnetic attractions.

It is thus erroneous to regard the heavenly bodies as isolated in vacant space; around and between them is an incessant conveyance and transformation of energy. To the vehicle of this activity the name aether has been given.

The aether is the solitary tenant of the universe, save for that infinitesimal fraction of space which is occupied by ordinary matter. Hence arises a problem which has long engaged attention, and is not yet completely solved: What relation subsists between the medium which fills the interstellar void and the condensations of matter that are scattered throughout it?

The history of this problem may be traced back continuously to the earlier half of the seventeenth century. It first emerged clearly in that reconstruction of ideas regarding the physical universe which was effected by René Descartes.

Descartes was born in 1596, the son of Joachim Descartes, Counsellor to the Parliament of Brittany. As a young man he followed the profession of arms, and served in the campaigns of Maurice of Nassau, and the Emperor; but his twenty-fourth year brought a profound mental crisis, apparently not unlike those which have been recorded of many religious leaders; and he resolved to devote himself thenceforward to the study of philosophy.

The age which preceded the birth of Descartes, and that in which he lived, were marked by events which greatly altered the prevalent conceptions of the world. The discovery of America, the circumnavigation of the globe by Drake, the overthrow of the Ptolemaic system of astronomy, and the invention of the telescope, all helped to loosen the old foundations and to make plain the need for a new structure. It was this that Descartes set himself to erect. His aim was the most ambitious that can be conceived; it was nothing less than to create from the beginning a complete system of human knowledge.

Of such a system the basis must necessarily be metaphysical; and this part of Descartes' work is that by which he is most widely known. But his efforts were also largely devoted to the mechanical explanation of nature, which indeed he regarded as one of the chief ends of Philosophy.^[1]

The general character of his writings may be illustrated by a comparison with those of his most celebrated contemporary.^[2] Bacon clearly defined the end to be sought for, and laid down the method by which it was to be attained; then, recognizing that to discover all the laws of nature is a task beyond the powers of one man or one generation, he left to posterity the work of filling in the framework which he had designed. Descartes, on the other hand, desired to leave as little as possible for his successors to do; his was a theory of the universe, worked out as far as possible in every detail. It is, however, impossible to derive such a theory inductively unless there are at hand sufficient observational data on which to base the induction; and as such data were not available in the age of Descartes, he was compelled to deduce phenomena from preconceived principles and causes, after the fashion of the older philosophers. To the inherent weakness of this method may be traced the errors that at last brought his scheme to ruin.

The contrast between the systems of Bacon and Descartes is not unlike that between the Roman republic and the empire of Alexander. In the one case we have a career of aggrandizement pursued with patience for centuries; in the other a growth of fungus-like rapidity, a speedy dissolution, and an immense influence long exerted by the disunited fragments. The grandeur of Descartes' plan, and the boldness of its execution, stimulated scientific thought to a degree before unparalleled; and it was largely from its ruins that later philosophers constructed those more valid theories which have endured to our own time.

Descartes regarded the world as an immense machine, operating by the motion and pressure of matter. “Give me matter and motion," he cried, "and I will construct the universe." A peculiarity which distinguished his system from that which afterwards sprang from its decay was the rejection of all forms of action at a distance; he assumed that force cannot be communicated except by actual pressure or impact. By this assumption he was compelled to provide an explicit mechanism in order to account for each of the known forces of nature—a task evidently much more difficult than that which lies before those who are willing to admit action at a distance as an ultimate property of matter.

Since the sun interacts with the planets, in sending them light and heat and influencing their motions, it followed from Descartes' principle that interplanetary space must be a plenum, occupied by matter imperceptible to the touch but capable of serving as the vehicle of force and light. This conclusion in turn determined the view which he adopted on the all-important question of the nature of matter.

Matter, in the Cartesian philosophy, is characterized not by 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, transparence, and opacity, in order to distinguish the three elements of the visible world.^[3]

According to Descartes' theory, the sun is the centre of an immense vortex formed of the first or subtlest kind of matter.^[4] 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;^[5] so that the globules are pressed in contact with each other, and tend to move outwards, although they do not actually so move.^[6] 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.^[7] In the Dioptrique,^[8] 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.^[9] In the Météores,^[10] 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.^[11] 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."^[12] 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^[11]:—

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

ray. So if i and r denote the angles of incidence and refraction, we have

$\sin {r}={\frac {BE}{BI}}=k.{\frac {BC}{BA}}=k\sin {i}$,

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,^[13] 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.^[14] 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^[15] (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^[16] 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^[17] 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;^[18] and in the middle of the eighteenth century Euler and two of the Bernoullis based the explanation of magnetism on the hypothesis of vortices.^[19]

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),^[20] 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^[21] 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.^[22] 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.^[23] “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^[24] 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^[25] 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^[26] Hooke's second experimental discovery^[27] 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^[28] 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,^[29] "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.

Hooke's next effort was to produce a mechanical theory of refraction, to replace that given by Descartes. "Because," he says, "all transparent mediums are not Homogeneous to one another, therefore we will next examine how this pulse or motion will be propagated through differingly transparent mediums. And here, according to the most acute and excellent Philosopher Des Cartes, I suppose the sine of the angle of inclination in the first medium to be to the sine of refraction in the second, as the density of the first to the density of the second. By density, I mean not the density in respect of gravity (with which the refractions or transparency of mediums hold no proportion), but in respect only to the trajection of the Rays of light, in which respect they only differ in this, that the one propagates the pulse more easily and weakly, the other more slowly, but more strongly. But as for the pulses themselves, they will by the refraction acquire another property, which we shall now endeavour to explicate.

"We will suppose, therefore, in the first Figure, ACFD to be

a physical Ray, or ABC and DEF to be two mathematical Rays, trajected from a very remote point of a luminous body through an Homogeneous transparent medium LL, and DA, EB, FC, to be small portions of the orbicular impulses which must therefore cut the Rays at right angles: these Hays meeting with the plain surface NO of a medium that yields an easier transitus to the propagation of light, and falling obliquely' on it, they will in the medium MM be refracted towards the perpendicular of the surface. And because this medium is more easily trajected than the former by a third, therefore the point U of the orbicular pulse FC will be moved to H four spaces in the same time that F, the other end of it, is inoved to three spaces, therefore the whole refracted pulse to H shall be oblique to the refracted Rays CHK and GI."

Although this is not in all respects successful, it represents a decided advance on the treatment of the same problem by Descartes, which rested on a mere analogy. Hooke tries to determine what happens to the wave-front when it meets the interface between two media, and for this end he introduces the correct principle that the side of the wave-front which first meets the interface will go forward in the second medium with the velocity proper to that medium, while the other side of the wave-front which is still in the first medium is still moving with the old velocity: so that the wave-front will be deflected in the transition from one medium to the other.

This deflection of the wave-front was supposed by Hooke to be the origin of the prismatic colours. He regarded natural or white light as the simplest type of disturbance, being constituted by a simple and uniform pulse at right angles to the direction of propagation, and inferred that colour is generated by the distortion to which this disturbance is subjected in the process of refraction, "The Ray,"^[30] he says, "is dispersed, split, and opened by its Refraction at the Superficies of a second medium, and from a line is opened into a diverging Superficies, and so obliquated, whereby the appearances of Colours are produced." "Colour," he says in another place,^[31] "is nothing but the disturbance of light by the communication of the pulse to other transparent mediums, that is by the refraction thereof." His precise hypothesis regarding the different colours was^[32] "that Blue is an impression on the Retina of an oblique and confus'd pulse of light, whose weakest part precedes, and whose strongest follows. And, that red is an impression on the Retina of an oblique and confus'd pulse of light, whose strongest part precedes, and whose weakest follows."

Hooke's theory of colour was completely overthrown, within a few years of its publication, by one of the earliest discoveries of Isaac Newton (b. 1642, d. 1727). Newton, who was elected a Fellow of Trinity College, Cambridge, in 1667, had in the beginning of 1666 obtained a triangular prism, "to try therewith the celebrated Phaenomena of Colours." For this purpose, "having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Sun's light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form, which, according to the received laws of Refraction, I expected should have been circular." The length of the coloured spectrum was in fact about five times as great as its breadth.

This puzzling fact he set himself to study; and after more experiments the true explanation was discovered---namely, that ordinary white light is really a mixture of rays of every variety of colour, and that the elongation of the spectrum is due to the differences in the refractive power of the glass for these different rays.

“Amidst these thoughts," he tells us,^[33] "I was forced from Cambridge by the intervening Plague"; this was in 1666, and his memoir on the subject was not presented to the Royal Society until five years later, In it he propounds a theory of colour directly opposed to that of Hooke. "Colours," he says, "are not Qualifications of light derived from Refractions, or Reflections of natural Bodies (as 'tis generally believed), but Original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other: some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.

"To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility:"

“The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from natural bodies, nor by any other cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it."

The publication of the new theory gave rise to an acute controversy. As might have been expected, Hooke was foremost among the opponents, and led the attack with some degree of asperity. When it is remembered that at this time Newton was at the outset of his career, while Hooke was an older man, with an established reputation, such harshness appears particularly ungenerous; and it is likely that the unpleasant consequences which followed the announcement of his first great discovery had much to do with the reluctance which Newton ever afterwards showed to publish his results to the world.

In the course of the discussion Newton found occasion to explain more fully the views which he entertained regarding the nature of light. Hooke charged him with holding the doctrine that light is a material substance. Now Newton had, as a matter of fact, a great dislike of the more imaginative kind of hypotheses; he altogether renounced the attempt to construct the universe from its foundations after the fashion of Descartes, and aspired to nothing more than a formulation of the laws which directly govern the actual phenomena. His theory of gravitation, for example, is strictly an expression of the results of observation, and involves no hypothesis as to the cause of the attraction which subsists between ponderable bodies; and his own desire in regard to optics was to present a theory free from speculation as to the hidden mechanism of light. Accordingly, in reply to Hooke's criticism, he protested^[34] that his views on colour were in no way bound up with any particular conception of the ultimate nature of optical processes.

Newton was, however, unable to carry out his plan of connecting together the phenomena of light into a coherent and reasoned whole without having recourse to hypotheses. The hypothesis of Hooke, that light consists in vibrations of an aether, he rejected for reasons which at that time were perfectly cogent, and which indeed were not successfully refuted for over a century. One of these was the incompetence of the wave-theory to account for the rectilinear propagation of light, and another was its inability to embrace the facts--discovered, as we shall presently see, by Huygens, and first interpreted correctly by Newton himself-of polarization. On the whole, he seems to have favoured a scheme of which the following may be taken as a summary^[35]:—

All space is permeated by an elastic medium or aether, which is capable of propagating vibrations in the same way as the air propagates the vibrations of sound, but with far greater velocity.

This aether pervades the pores of all material bodies, and is the cause of their cohesion; its density varies from one body to another, being greatest in the free interplanetary spaces. It is not necessarily a single uniform substance: but just as air contains aqueous vapour, so the aether may contain various "aethereal spirits," adapted to produce the phenomena of electricity, magnetism, and gravitation.

The vibrations of the aether cannot, for the reasons already mentioned, be supposed in themselves to constitute light. Light is therefore taken to be "something of a different kind, propagated from lucid bodies. They, that will, may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes, springing from shining bodies at great distances one after another, but yet without any sensible interval of time, and continually urged forward by a principle of motion, which in the beginning accelerates them, till the resistance of the aethereal medium equals the force of that principle, much after the manner that bodies let fall in water are accelerated till the resistance of the water equals the force of gravity. But they, that like not this, may suppose light any other corporeal emanation, or any impulse or motion of any other medium or aethereal spirit diffused through the main body of aether, or what else they can imagine proper for this purpose. To avoid dispute, and make this hypothesis general, let every man here take his fancy; only whatever light be, I suppose it consists of rays differing from one another in contingent circumstances, as bigness, form, or vigour."^[36]

In any case, light and aether are capable of mutual interaction; aether is in fact the intermediary between light and ponderable matter. When ray of light meets a stratum of aether denser or rarer than that through which it has lately been passing, it is, in general, deflected from its rectilinear course; and differences of density of the aether between one material medium and another account on these principles for the reflexion and refraction of light. The condensation or rarefaction of the aether due to a material body extends to some little distance from the surface of the body, so that the inflexion due to it is really continuous, and not abrupt; and this further explains diffraction, which Newton took to be "only a new kind of refraction, caused, perhaps, by the external aether's beginning to grow rarer a little before it came at the opake body, than it was in free spaces."

Although the regular vibrations of Newton's aether were not supposed to constitute light, its irregular turbulence seems to have represented fairly closely his conception of heat. He supposed that when light is absorbed by a material body, vibrations are set up in the aether, and are recognizable as the heat which is always generated in such cases. The conduction of heat from hot bodies to contiguous cold ones he conceived to be effected by vibrations of the aether propagated between them; and he supposed that it is the violent agitation of aethereal motions which excites incandescent substances to emit light.

Assuming with Newton that light is not actually constituted by the vibrations of an aether, even though such vibrations may exist in close connexion with it, the most definite and easily conceived supposition is that rays of light arc streams of corpuscles emitted by luminous bodies. Although this was not the hypothesis of Descartes himself, it was so thoroughly akin to his general scheme that the scientific men of Newton's generation, who were for the most part deeply imbued with the Cartesian philosophy, instinctively selected it from the wide choice of hypotheses which Newton had offered them, and by later writers it was generally associated with Newton's name. A curious argument in its favour was drawn from a phenomenon which had then been known for nearly half a century: Vincenzo Cascariolo, a shoemaker of Bologna, had discovered, about 1630, that a substance, which afterwards received the name of Bologna stone or Bologna phosphorus, has the property of shining in the dark after it has been exposed for some time to sunlight; and the storage of light which seemed to be here involved was more easily explicable on the corpuscular theory than on any other. The evidence in this quarter, however, pointed the other way when it was found that phosphorescent substances do not necessarily emit the same kind of light as that which was used to stimulate them.

In accordance with his earliest discovery, Newton considered colour to be an inherent characteristic of light, and inferred that it must be associated with some definite quality of the corpuscles or aether-vibrations. The corpuscles corresponding to different colours would, he remarked, like sonorous bodies of different pitch, excite vibrations of different types in the aether; and “if by any means those [aether-vibrations] of unequal bignesses be separated from one another, the largest beget a Sensation of a Red colour, the least or shortest of a deep Violet, and the intermediate ones, of intermediate colours; much after the manner that bodies, according to their several sizes, shapes, and motions, excite vibrations in the Air of various bignesses, which, according to those bignesses, make several Tones in Sound."^[37]

This sentence is the first enunciation of the great principle that homogeneous light is essentially periodic in its nature, and that differences of period correspond to differences of colour. The analogy with Sound is obvious; and it may be remarked in passing that Newton's theory of periodic vibrations in an elastic medium, which he developed^[38] in connexion with the explanation of Sound, would alone entitle him to a place among those who have exercised the greatest influence on the theory of light, even if he had made no direct contribution to the latter subject.

Newton devoted considerable attention to the colours of thin. plates, and determined the empirical laws of the phenomena with great accuracy. In order to explain them, he supposed that "every ray of light, in its passage through any refracting surface, is put into a certain transient constitution or state, which, in the progress of the ray, returns at equal intervals, and disposes the ray, at every return, to be easily transmitted through the next refracting surface, and, between the returns, to be easily reflected by it."^[39] The interval between two consecutive dispositions to easy transmission, or "length of fit," he supposed to depend on the colour, being greatest for red light and least for violet. If then a ray of homogeneous light falls on a thin plate, its fortunes as regards transmission and reflexion at the two surfaces will depend on the relation which the length of fit bears to the thickness of the plate; and on this basis he built up a theory of the colours of thin plates. It is evident that Newton's "length of fit" corresponds in some measure to the quantity which in the undulatory theory is called the wave-length of the light; but the suppositions of easy transmission and reflexion were soon found inadequate to explain all Newton's experimental results, at least without making other and more complicated additional assumptions.

At the time of the publication of Hooke's Micrographia, and Newton's theory of colours, it was not known whether light is propagated instantaneously or not. An attempt to settle the question experimentally had been made many years previously by Galileo,^[40] who had stationed two men with lanterns at a considerable distance from each other, one of them was directed to observe when the other uncovered his light, and exhibit his own the moment he perceived it. But the interval of time required by the light for its journey was too small to be perceived in this way; and the discovery was ultimately made by an astronomer. It was observed in 1675 by Olof Roemer^[41] (b. 1644, d. 1710) that the eclipses of the first satellites of Jupiter were apparently affected by an unknown disturbing cause; the time of the occurrence of the phenomenon was retarded when the earth and Jupiter, in the course of their orbital motions, happened to be most remote from each other, and accelerated in the contrary case. Roemer explained this by supposing that light requires a finite time for its propagation from the satellite to the earth; and by observations of eclipses, he calculated the interval required for its passage from the sun to the earth (the light-equation, as it is called) to be 11 minutes.^[42]

Shortly after Roemer's discovery, the wave-theory of light was greatly improved and extended by Christiaan Huygens (b. 1629, d. 1695). Huygens, who at the time was living in Paris, communicated his results in 1678 to Cassini, Roemer, De la Hire, and the other physicists of the French Academy, and prepared a manuscript of considerable length on the subject. This he proposed to translate into Latin, and to publish in that language together with a treatise on the Optics of Telescopes; but the work of translation making little progress, after a delay of twelve years, he decided to print the work on wave-theory in its original form. In 1690 it appeared at Leyden,^[43] under the title Traité de la lumière où sont expliquées les causes de ce qui luy arrice dans la réflexion et dans la réfraction. Et parti- culièrement dans l'étrange réfraction du cristal d'Islande, Par C.H.D.Z^[44]

The truth of Hooke's hypothesis, that light is essentially a form of motion, seemed to Huygens to be proved by the effects observed with burning-glasses; for in the combustion induced at the focus of the glass, the molecules of bodies are dissociated; which, as he remarked, must be taken as a certain sign of motion, if, in conformity to the Cartesian philosophy, we seek the cause of all natural phenomena in purely mechanical actions.

The question then arises as to whether the motion is that of a medium, as is supposed in Hooke's theory, or whether it may be compared rather to that of a flight of arrows, as in the corpuscular theory. Huygens decided that the former alternative is the only tenable one, since beams of light proceeding in directions inclined to each other do not interfere with each other in any way.

Moreover, it had previously been shown by Torricelli that light is transmitted as readily through a vacuum as through air; and from this Huygens inferred that the medium or aether in which the propagation takes place must penetrate all matter, and be present even in all so-called vacua.

The process of wave-propagation he discussed by aid of a principle which was now^[45] introduced for the first time, and has since been generally known by his name. It may be stated thus: Consider a wave-front,^[46] or locus of disturbance, as it exists at a definite instant t₀: then each surface-element of the wave-front may be regarded as the source of a secondary wave, which in a homogeneous isotropic medium will be propagated outwards from the surface-element in the form of a sphere whose radius at any subsequent instant t is proportional to (t-t₀); and the wave-front which represents the whole disturbance at the instant t is simply the envelope of the secondary waves which arise from the various surface elements of the original wave-front.^[47] The introduction of this principle enabled Huygens to succeed where Hooke and other contemporary wave-theorists^[48] had failed, in achieving the explanation of refraction and reflexion. His method was to combine his own principle with Hooke's device of following separately the fortunes of the right-hand and left-hand sides of a wave-front when it reaches the interface between two media. The actual explanation for the case of reflexion is as follows:—

Let AB represent the interface at which reflexion takes place, AHC the incident wave-front at an instant t₀, GMB the position which the wave-front would occupy at a later instant t if the propagation were not interrupted by reflexion. Then by

Huygens' principle the secondary wave from A is at the instant t a sphere RNS of radius equal to AG: the disturbance from H, after meeting the interface at K, will generate a secondary wave TV of radius equal to KM, and similarly the secondary wave corresponding to any other element of the original wavefront can be found. It is obvious that the envelope of these secondary waves, which constitutes the final wave-front, will be a plane BN, which will be inclined to AB at the same angle as AC. This gives the law of reflexion.

The law of refraction is established by similar reasoning, on the supposition that the velocity of light depends on the medium in which it is propagated. Since a ray which passes from air to glass is bent inwards towards the normal, it may be inferred that light travels more slowly in glass than in air.

Huygens offered a physical explanation of the variation in velocity of light from one medium to another, by supposing that transparent bodies consist of hard particles which interact with the aethereal matter, modifying its elasticity. The opacity of metals he explained by an extension of the same idea, supposing that some of the particles of metals are hard (these account for reflexion) and the rest soft: the latter destroy the luminous motion by damping it.

The second half of the Théorie de la lumière is concerned with a phenomenon which had been discovered a few years previously by a Danish philosopher, Erasmus Bartholin (b. 1625, d. 1698). A sailor had brought from Iceland to Copenhagen a number of beautiful crystals which he had collected in the Bay of Röerford. Bartholin, into whose hands they passed, noticed^[49] that any small object viewed through one of these crystals appeared double, and found the immediate cause of this in the fact that a ray of light entering the crystal gave rise in general to two refracted rays. One of these rays was subject to the ordinary law of refraction, while the other, which was called the extraordinary ray, obeyed a different law, which Bartholin did not succeed in determining.

The matter had arrived at this stage when it was taken up by Huygens. Since in his conception each ray of light corresponds to the propagation of a wave-front, the two rays in Iceland spar must correspond to two different wave-fronts propagated simultaneously. In this idea he found no difficulty; as he says: “It is certain that a space occupied more than one kind of matter may permit the propagation of several kinds of waves, different in velocity; for this actually happens in air mixed with aethereal matter, where sound-waves and light-waves are propagated together."

Accordingly he supposed that a light-disturbance generated at any spot within a crystal of Iceland spar spreads out in the form of a wave-surface, composed of a sphere and a spheroid having the origin of disturbance as centre. The spherical wave-front corresponds to the ordinary ray, and the spheroid to the extraordinary ray: and the direction in which the extraordinary ray is refracted may be determined by a geometrical construction, in which the spheroid takes the place which in the ordinary construction is taken by the sphere.

Thus, let the plane of the figure be at right angles to the intersection of the wave-front with the surface of the crystal; let AB represent the trace of the incident wave-front; and suppose that in unit time the disturbance from B reaches the interface at T. In this unit-interval of time the disturbance from A will have spread out within the crystal into a sphere and spheroid: so the wave-front corresponding to the

ordinary ray will be the tangent-plane to the sphere through the line whose trace is T, while the wave-front corresponding to the extraordinary ray will be the tangent-plane to the spheroid through the same line. The points of contact N and M will determine the directions AN and AN of the two refracted rays^[50] within the crystal.

Huygens did not in the Théorie de la lumière attempt a detailed physical explanation of the spheroidal wave, but communicated one later in a letter to Papin,^[51] written in December, 1690, “As to the kinds of matter contained in Iceland crystal," he says, "I suppose one composed of small spheroids, and another which occupies the interspaces around these spheroids, and which serves to bind them together. Besides these, there is the matter of aether permeating all the crystal, both between and within the parcels of the two kinds of matter just mentioned; for I suppose both the little spheroids, and the matter which occupies the intervals around them, to be composed of small fixed particles, amongst which are diffused in perpetual motion the still finer particles of the aether. There is now no reason why the ordinary ray in the crystal should not be due to waves propagated in this aethereal matter. To account for the extraordinary refraction, I conceive another kind of waves, which have for vehicle both the aethereal matter and the two other kinds of matter constituting the crystal. Of these latter, I suppose that the matter of the small spheroids transmits the waves a little more quickly than the aethereal matter, while that around the spheroids transmits these waves a little more slowly than the same aethereal matter, ... These same waves, when they travel in the direction of the breadth of the spheroids, meet with more of the matter of the spheroids, or at least pass with less obstruction, and so are propagated a little more quickly in this sense than in the other ; thus the light-disturbance is propagated as a spheroidal sheet."

Huygens made another discovery^[52] of capital importance when experimenting with the Iceland crystal. He observed that the two rays which are obtained by the double refraction of a single ray afterwards behave in a way different from ordinary light which has not experienced double refraction, and in particular, if one of these rays is incident on a second crystal of Iceland spar, it gives rise in some circumstances to two, and in others to only one, refracted ray. The behaviour of the ray at this second refraction can be altered by simply rotating the second crystal about the direction of the ray as axis; the ray undergoing the ordinary or extraordinary refraction according as the principal section of the crystal is in a certain direction or in the direction at right angles to this.

The first stage in the explanation of Huygens' observation was reached by Newton, who in 1717 showed^[53] that a ray obtained by double refraction differs from a ray of ordinary light in the same way that a long rod whose cross-section is a rectangle differs from a long rod whose cross-section is a circle: in other words, the properties of a ray of ordinary light are the same with respect to all directions at right angles to its direction of propagation, whereas a ray obtained by double refraction must be supposed to have sides, or properties related to special directions at right angles to its own direction. The refraction of such a ray at the surface of a crystal depends on the relation of its sides to the principal plane of the crystal.

That a ray of light should possess such properties seemed to Newton^[54] an insuperable objection to the hypothesis which regarded waves of light as analogous to waves of sound. On this point he was in the right: his objections are perfectly valid against the wave-theory as it was understood by his contemporaries,^[55] although not against the theory^[56] which was put forward a century later by Young and Fresnel.

Notes

1. Of the works which bear on our present subject, the Dioptrique and the Météores were published at Leyden in 1638, and the Principia Philosophiae at Amsterdam in 1644, six years before the death of its author.
2. The principal philosophical works of Bacon were written about eighteen years before those of Descartes.
3. Principia, Part iii, §52.
4. It is curious to speculate on the impression which would have been produced had the spirality of nebulæ been discovered before the overthrow of the Cartesian theory of vortices.
5. Principia, Part iii, §§55-59.
6. Principia, Part iii, §63.
7. Principia, Part iii, §64.
8. Discours premier.
9. Principia, Part iv, §195.
10. Discours Huitième.
11. Dioptrique, Discours second.
12. Dioptrique, Discours premier.
13. His Epistola was written in 1269.
14. "Proeul dubio omnes lincae hujusznodi in duo puncta concurrent sicut omnes orbes meridiani in duo concurrunt polos mundi oppositos."
15. The form in the Colchester records is Gilberd.
16. Culielmi Gilberti De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure: London, 1600. An English translation by P. F. Mottelay was published in 1893.
17. Principia, Part iv, § 133 sqq.
18. Whiston has recorded that, having returned to Cambridge after his ordination in 1693, he resumed his studies there, "particularly the Mathematicks, and the Cartesian Philosophy: which was alone in Vogue with us at that Time. But it was not long before I, with immense Pains, but 19 Assistance, set myself with the utmost Zeal to the study of Sir Isaac Newton's wonderful Discoveries." - Whiston's Memoirs (1749), i, p. 36.
19. Their memoirs shared a prize of the French Academy in 1713, and were printed in 1762 in the Recueil des pièces qui ont remporté les prix de l'Acad., tome v.
20. Renati Descartes Epistolae, Pars tertia; Amstelodamni, 1983. The Fermat correspondence is comprised in letters xxix to xlvi.
21. Epist. xlii, written at Toulouse in August, 1657, to Monsieur de la Chambre; reprinted in Œuvres de Fermat (ed. 1891), ii, p. 354.
22. That reflected light follows the shortest path was no new result, for it had been affirmed (and attributed to Hero of Alexandria) in the Κεφάλαια τών οπτικών of Heliodorus of Larissa, a work of which several editions were published in the seventeenth century.
23. Epist. xliii, written at Toulouse on Jan. 1, 1662; reprinted in Œuvres de Fermat, ii, p. 467; i, pp. 170, 173.
24. The imprimatur of Viscount Brouneker, p.r.s., is dated Nov. 23, 1664.
25. Micrographia, p. 47.
26. Boyle's Works (ed. 1772), i, p. 742.
27. Hooke's Posthuanows Works, p. 186.
28. Physico-Mathesis de bemine, coloribus, et iride. Bologna, 1665; book i, prop. i.
29. Micrographia, p. 55.
30. Hooke, Posthumous Works, p. 82.
31. To the Royal Society, February lá, 1671-2.
32. Micographia, p. 64.
33. Phil. Trans., No. 80, February 19, 1671-2.
34. Phil. Trans. vi, 1672, p. 5086.
35. Cf. Newton's memoir in Phil. Trans. vii, 1672; his memoir presented to the Royal Society in December, 1675, which is printed in Birch, iii, p. 247; his Opticks, especially Queries 18, 19, 20, 21, 23, 29; the Scholium at the end of the Principia; and a letter to Boyle, written in February, 1678-9, which is printed in Horsley's Nextoni Opera, p. 385.
    

    In the Principia, Book I., section xiv, the analogy between rays of light and streams of corpuscles is indicated; but Newton does not commit himself to any theory of light based on this.

36. Royal Society, Dec. 9, 1675.
37. Phil. Trans, vii (1672), p. 5088.
38. Newton's Principia, Book ii., Props. xliii.-l.
39. Opticks, Book ii., Prop. 12.
40. Discorsi e dimostrazioni malemaliche, p. 43 of the Elzevir edition of 1638.
41. Mént, de l'Acad. 1. (1666-1699), p. 575.
42. It was soon recognized that Roemer's value was too large; and the astronomers of the succeeding half-century reduced it to 7 minutes. Delambre, by an investigation whose details appear to have been completely destroyed, published in 1817 the value 498·2^s, from a discussion of eclipses of Jupiter's satellites during the previous 150 years. Glasenapp, in an inaugural dissertation published in 1875, discussed the eclipses of the first satellite between 1848 and 1870, and derived, by different assumptions, values between 496^s and 501^s, the most probable value being 600·8^s. Sampson, in 1909, derived 498·64^s from his. own readings of the Harvard Observations, and 498·79^s from the Harvard readings, with probable errors of about ±0·02^s. The inequalities of Jupiter's surface give rise to some difficulty in exact determinations.
43. Huygens Lad by this time returned to Holland.
44. i.e. Christiaan Huygens de Zugliehem. The custom of indicating names by initials was not unusual in that age.
45. Traité de la lun., p. 17.
46. It may be remarked that Huygens' "waves" are really what modern writers, following Hooke, call "pulses"; Huygens never considered true wave-trains having the property of periodicity.
47. The justification for this was given long afterwards by Fresnel, Annales de chimie, xxi.
48. e.g. Ignace Gaston Pardies and Pierre Ango, the latter of whom published a work on Optics at Paris in 1682.
49. Experimenta cristalli Islandici disdiaclastici: 1669.
50. The word ray in the wave-theory is always applied to the line which goes from the centre of a wave (i.e. the origin of the disturbance) to a point on its surface, whatever may be the inclination of this line to the surface-element on which it abuts; for this line has the optical properties of the "rays" of the emission theory.
51. Huygens' Œuvres, ed. 1905, x., p. 177.
52. Théorie de la lumière, p. 89.
53. The second edition of Newton's Opticks, Query 26.
54. Opticks, Query 28.
55. In which the oscillations are performed in the direction in which the wave advances.
56. In which the oscillations are performed in a direction at right angles to that in which the wave advances.