Chapter 1c

# Hooke's Theory

by Edmund Taylor Whittaker

Hooke’s next effort was to produce a mechanical theory of refraction, to replace that given by Descartes.

Hooke says:

“Because 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.

According to the most acute and excellent Philosopher Descartes, 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 history of the theories of aether and electricity. Whittacker E.T. (1910).pdf 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

A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf 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.

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