A History of the Theories of Aether and Electricity (1910) — part 8 of 29

Young then proceeds to show the superior power of the^ wave-theory to explain reflexion and refraction. In the corpuscular theory it is difficult to see why part of the light should be reflected and another part of the same beam reflected ; but in the undulatory theory there is no trouble, as is shown by analogy with the partial reflexion of sound from a cloud or _, denser stratum of air : " Nothing more is necessary than to

• Phil. Tni™., 1800, p. 106.

106 The JLuminiferous Medium,

suppose all refracting media to retain, by their attraction, a, greater or less quantity of the luminous ether, so as to make its- density greater than that which it possesses in a vacuum, without increasing its elasticity." This is precisely the hypothesis adopted later by Fresnel and Green.

In 1801 Young made a discovery of the first magnitude* when attempting to explain Newton's rings on the principles of the wave-theory. Eejecting Euler's hypothesis of induced vibrations, he assumed that the colours observed all exist in the incident light, and showed that they could be derived from it by a process which was now for the first time recognized in optical science.

The idea of this process was not altogether new, for it had been used by Newton in his theory of the tides. " It may happen," he wrote, f " that the tide may be propagated from the ocean through different channels towards the same port, and may pass in less time through some channels than through others, in which case the same generating tide, being thus divided into two or more succeeding one another, may produce by composition new types of tide." Newton applied this- principle to explain the anomalous tides at Batsha in Tonkin, which had previously been described by Halley.J

Young's own illustration of the principle is evidently suggested by Newton's. " Suppose," he says,§ " a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake ; suppose then another similar cause to have excited another equal series of waves, which arrive at the same channel, with the same velocity, and at the same time with the first. Neither series of waves will destroy the other, but their effects will be combined ; if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations ; but if the elevations of one

• Phil. Trans., 1802, pp. 12, 387. t Principia, Book in, Prop. 24.

% Phil. Trans, xiv (1684), p. 681. § Young's Works, i, p. 202.

from Bradley to Fremel. 107

series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions, and the surface of the water must remain smooth. Now I maintain that similar effects take place whenever two portions of light are thus mixed ; and this I call the general law of the interference of light."

Thus, " whenever two portions of the same light arrive to the eye by different routes, either exactly or very nearly in the same direction, the light becomes most intense when the difference of the routes is any multiple of a certain length, and least intense in the intermediate state of the interfering portions ; and this length is different for light of different colours."

Young's explanation of the colours of thin plates as seen by reflexion was, then, that the incident light gives rise to two beams which reach the eye : one of these beams has been reflected at the first surface of the plate, and the other at the second surface ; and these two beams produce the colours by their interference.

One difficulty encountered in reconciling this theory with observation arose from the fact that the central spot in Newton's rings (where the thickness of the thin Him of air is zero) is black and not white, as it would be if the interfering beams were similar to each other in all respects. To account for this Young ' showed, by analogy with the impact of elastic bodies, that when -> light is reflected at the surface of a denser medium, its phase is retarded by half an undulation : so that the interfering beams at the centre of Newton's rings destroy each other. The correctness of this assumption he verified by substituting essence of sassafras (whose refractive index is intermediate between those of crown and flint glass) for air in the space between the lenses ; as he anticipated, the centre of the ring-system was now white.

Newton had long before observed that the rings are smaller ~* when the medium producing them is optically more dense. Interpreted by Young's theory, this definitely proved that the wave-length of light is shorter in dense media, and therefore ^ that its velocity is less.

108 The Lumini/erous Medium,

The publication of Young's papers occasioned a fierce attack on him in the Edinburgh Review, from the pen of Henry Brougham, afterwards Lord Chancellor of England. Young replied in a pamphlet, of which it is said* that only a single copy was sold ; and there can be no doubt that Brougham for the time being achieved his object of discrediting the wave- theory, f

Young now turned his attention to the fringes of shadows. In the corpuscular explanation of these, it was supposed that the attractive forces which operate in refraction extend their influence to some distance from the surfaces of bodies, and inflect such rays as pass close by. If this were the case, the amount of inflexion should obviously depend on the strength of the attractive forces, and consequently on the refractive indices of the bodies — a proposition which had been refuted by the experiments of s'Gravesande. The cause of diffraction effects was thus wholly unknown, until Young, in the Bakerian lecture for 1803,J showed that the principle of interference is concerned in their formation ; for when a hair is placed in the cone of rays diverging from a luminous point, the internal fringes (i.e. those within the geometrical shadow) disappear when the light passing on one side of the hair is intercepted. His conjecture as to the origin of the interfering rays was not so fortunate ; for he attri- buted the fringes outside the geometrical shadow to interference between the direct rays and rays reflected at the diffracting edge ; and supposed the internal fringes of the shadow of a narrow object to be due to the interference of rays inflected by the two edges of the object.

The success of so many developments of the wave-theory led Young to inquire more closely into its capacity for solving the chief outstanding problem of optics — that of the behaviour of light in crystals. The beautiful construction for the extra-

• Peacock's Life of Young.

t" Strange fellow," wrote Macaulay, when half a century afterwards he found himself sitting beside Brougham in the House of Lords, " his powers gone : his spite immortal."

I Phil. Trans., 1804; Young's Works, i, p. 179.

from Bradley ( to FresneL 109

ordinary ray given by Huygens had lain neglected for a century ; and the degree of accuracy with which it represented the observations was unknown. At Young's suggestion Wollaston* investigated the matter experimentally, and showed that the agreement between his own measurements and Huygens' rule was remarkably close. " I think," he wrote, " the result must be admitted to be highly favourable to the Huygeniaii theory ; and, although the existence of two refractions at the same time, in the same substance, be not well accounted for, and still less their interchange with each other, when a ray of light is made to pass through a second piece of spar situated transversely to the first, yet the oblique refraction, when considered alone, seems nearly as well explained as any other optical phenomenon."

Meanwhile the advocates of the corpuscular theory were not idle ; and in the next few years a succession of discoveries on their part, both theoretical and experimental, seemed likely to imperil the good position to which Young had advanced the rival hypothesis.

The first of these was a dynamical explanation of the refraction of the extraordinary ray in crystals, which was published in 1808 by Laplace.f His method is an extension of that by which Maupertuis had accounted for the refraction of the ordinary ray, and which since Maupertuis' day had been so developed that it was now possible to apply it to problems of all degrees of complexity. Laplace assumes that the crystalline medium acts on the light-corpuscles of the extraordinary ray so as to modify their velocity, in a ratio which depends on the inclination of the extraordinary ray to the axis of the crystal : so that, in fact, the difference of the squares of the velocities of the ordinary and extraordinary rays is proportional to the square of the sine of the angle which the latter ray makes with the axis. The principle of least action then leads to a law of refraction identical with that found by Huygens' construction

• Phil. Trans., 1802, p. 381.

tMem. de PInst., 1809, p. 300: Journal de Physique, Jan., 1809; Mem. de la Soc. d'Arcueil, ii.

110 The Luminiferous Medium,

with the spheroid ; just as Maupertuis' investigation led to a law of refraction for the ordinary ray identical with that found by Huygens' construction with the sphere.

The law of refraction for the extraordinary ray may also be deduced from Fermat's principle of least time, provided that the velocity is taken inversely proportional to that assumed in the principle of least action ; and the velocity appropriate to Fermat's principle agrees with that found by Huygens, being, in iact, proportional to the radius of the spheroid. These results are obvious extensions of those already obtained for ordinary refraction.

Laplace's theory was promptly attacked by Young,* who pointed out the improbability of such a system of forces as would be required to impress the requisite change of velocity on the light-corpuscles. If the aim of controversial matter is to convince the contemporary world, Young's paper must be counted unsuccessful ; but it permanently enriched science by proposing a dynamical foundation for double refraction on the principles of the wave-theory. " A solution," he says, " might •be deduced upon the Huygenian principles, from the simplest possible supposition, that of a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by a substance somewhat less elastic. Such a structure of the elementary atoms of the crystal may be understood by compar- ing them to a block of wood or of mica. Mr. Chladni found that the mere obliquity of the fibres of a rod of Scotch fir reduced the velocity with which it transmitted sound in the proportion of 4 to 5. It is therefore obvious that a block of such wood -must transmit every impulse in spheroidal — that is, oval — undulations ;• and it may also be demonstrated, as we shall show at the conclusion of this article, that the spheroid will be truly elliptical when the body consists either of plane and parallel strata, or of equidistant fibres, supposing both to be ^extremely thin, and to be connected by a less highly elastic

• Quarterly Eeview, Nov., 1809 ; Young's Works, i, p. 220.

from Bradley to FremeL 111

substance ; the spheroid being in the former case oblate and in the latter oblong." Young then proceeds to a formal proof that "an impulse is propagated through every perpendicular section of a lamellar elastic substance in the form of an elliptic undulation." This must be regarded as the beginning of the dynamical theory of light in crystals. It was confirmed in a striking way not long afterwards by Brewster,* who found that compression in one direction causes an isotropic transparent solid to become doubly-refracting.

Meanwhile, in January, 1808, the French Academy had proposed as the subject for the physical prize in 1810, " To furnish a mathematical theory of double refraction, and to confirm it by experiment." Among those who resolved to compete was Etienne Louis Malus (b. 1775, d. 1812), a colonel of engineers who had seen service with Napoleon's expedition to Egypt. While conducting experiments towards the end of 1808 in a house in the Kue des Enfers in Paris, Malus happened to analyse with a rhomb of Iceland spar the light of the setting sun reflected from the window of the Luxembourg, and was surprised to notice that the two images were of very different intensities. Following up this observation, he found that light which had been reflected from glass acquires thereby a modifi- cation similar to that which Huygens had noticed in rays which have experienced double refraction, and which Newton had explained by supposing rays of light to have " sides." This discovery appeared so important that without waiting for the prize competition he communicated it to the Academy in December, 1808, and published it in the following month.f " I have found," he said, " that this singular disposition, which has hitherto been regarded as one of the peculiar effects of double refraction, can be completely impressed on the luminous molecules by all transparent solids and liquids." " For example, light reflected by the surface of water at an

• Phil. Trans., 1815, p. 60.

tNouveau Bulletin des Sciences, par la Soc. Philomatique. i (1809), p. 266; Memoires de la Soc. d'Arcueil, ii (1809).

112 The Luminiferous Medium,

angle of 52°45' has all the characteristics of one of the beams produced by the double refraction of Iceland spar, whose principal section is parallel to the plane which passes through the incident ray and the reflected ray. If we receive this reflected ray on any doubly- refracting crystal, whose principal section is parallel to the plane of reflexion, it will not be divided into two beams as a ray of ordinary light would be, but will be refracted according to the ordinary law."

After this Malus found that light which has been refracted at the surface of any transparent substance likewise possesses in some degree this property, to which he gave the name polarization. The memoir* which he finally submitted to the Academy, and which contains a rich store of experimental and analytical work on double refraction, obtained the prize in 1810 ; its immediate effect as regards the rival theories of the ultimate nature of light was to encourage the adherents of the corpuscular doctrine ; for it brought into greater prominence the phenomena of polarization, of which the wave-theorists, still misled by the analogy of light with sound, were unable to give any account.

The successful discoverer was elected to the Academy of Sciences, and became a member of the celebrated club of Arcueil.f But his health, which had been undermined by the Egyptian campaign, now broke down completely : and he died, at the age of thirty-six, in the following year.

The polarization of a reflected ray is in general incomplete — i.e. the ray displays only imperfectly the properties of light which has been polarized by double refraction ; but for one particular angle of incidence, which depends on the reflecting body, the polarization of the reflected ray is complete. Malus measured with considerable accuracy the polarizing angles for glass and water, and attempted to connect them with the other optical constants of these substances, the refractive indices and dispersive powers, but without success. The matter was

• Mem. presentes a 1'Inst. par divers Savans, ii (1811), p. 303.

t So called from the village near Paris where Laplace and Berthollet had their country-houses, and where the meetings took place. The club consisted of a dozen of the most celebrated scientific men in France.

from Bradley to Fresnel. 113

afterwards taken up by David Brewster (b. 1781, d. 1868), who in 1815* showed that there is complete polarization by reflexion when the reflected and refracted rays satisfy the condition of being at right angles to each other.

Almost at the same time Brewster made another discovery which profoundly affected the theory of double refraction. It had till then been believed that double refraction is always of the type occurring in Iceland spar, to which Huygens' construction is applicable. Brewster now found this belief to be erroneous, and showed that in a large class of crystals there are two axes, instead of one, along which there is no double refraction. Such crystals are called Uaxal, the simpler type to which Iceland spar belongs being called uniaxal.

The wave-theory at this time was still encumbered with difficulties. Diffraction was not satisfactorily explained ; for polarization no explanation of any kind was forthcoming ; the Huygenian construction appeared to require two different luminiferous media within doubly refracting bodies ; and the universality of that construction had been impugned by Brewster's discovery of biaxal crystals.

The upholders of the emission theory, emboldened by the success of Laplace's theory of double refraction, thought the time ripe for their final triumph ; and as a step to this, in March, 1817, they proposed Diffraction as the subject of the Academy's prize for 1818. Their expectation was disappointed ; and the successful memoir afforded the first of a series of reverses by which, in the short space of seven years, the corpuscular theory was completely overthrown.

The author was Augustin Fresnel (b. 1788, d. 1827), the son of an architect, and himself a civil engineer in the Government service in Normandy. During the brief dominance of Napoleon after his escape from Elba in 1815, Fresnel fell into trouble for having enlisted in the small army which attempted to bar the exile's return ; and it was during a period of enforced idleness following on his arrest that he commenced to study

•Phil. Trans., 1815, p. 125. I

114 The Lumini/erous Medium,

diffraction. In his earliest memoir* he propounded a theory similar to that of Young, which was spoiled like Young's theory by the assumption that the fringes depend on light reflected by the diffracting edge. Observing, however, that the blunt and sharp edges of a knife produce exactly the same fringes, he became dissatisfied with this attempt, and on July 15th, 1816, presented to the Academy a supplement to his paper,f in which, for the first time, diffraction-effects are referred to their true cause — namely, the mutual interference of the secondary waves emitted by those portions of the original wave-front which have not been obstructed by the diffracting screen. Fresnel's method of calculation utilized the principles of both Huygens and Young ; he summed the effects due to different portions of the same primary wave-front, with due regard to the differences of phase engendered in propagation.

The sketch presented to the Academy in 1816 was during the next two years developed into an exhaustive memoir, J which was submitted for the Academy's prize.

It so happened that the earliest memoir, which had been presented to the Academy in the autumn of 1815, had been referred to a Commission of which the reporter was Francois Arago (&. 1786, d. 1853) ; Arago was so much impressed that he sought the friendship of the author, of whom he was later a strenuous champion.

A champion was indeed needed when the larger memoir was submitted ; for Laplace, Poisson, and Biot, who constituted a majority of the Commission to which it was referred, were all zealous supporters of the corpuscular theory. During the examination, however, Fresnel was vindicated in a somewhat curious way. He had calculated in the memoir the diffraction- patterns of a straight edge, of a narrow opaque body bounded by parallel sides, and of a narrow opening bounded by parallel edges, and had shown that the results agreed excellently with

• Annales de Chimie (2), i (1816), p 239 ; (Euvres, i, p. 89.

t (Euvres, i, p. 129.

I Mem. de 1'Acad., v (1826), p. 339 ; (Euvres, i, p. 247.

from Bradley to FresneL 115

his experimental measures. Poisson, when reading the manu- script, happened to notice that the analysis could be extended to other cases, and in particular that it would indicate the existence of a bright spot at the centre of the shadow of a circular screen. He suggested to Fresnel that this and some further consequences should be tested experimentally ; this was done, and the results were found to confirm the new theory. The concordance of observation and calculation was so admirable in all cases where a comparison was possible that the prize was awarded to Fresnel without further hesitation.

In the same year in which the memoir on diffraction was submitted, Fresnel published an investigation* of the influence of the earth's motion on light. We have already seen that aberration was explained by its discoverer in terms of the corpuscular theory ; and it was Young who first showedf how it may be explained on the wave-hypothesis. " Upon con- sidering the phenomena of the aberration of the stars," he wrote, " I am disposed to believe that the luminiferous aether pervades the substance of all material bodies with little or no resistance, as freely perhaps as the wind passes through a grove of trees." In fact, if we suppose the aether surrounding the earth to be at rest and unaffected by the earth's motion, the light- waves will not partake of the motion of the telescope , which we may suppose directed to the true place of the star, and the image of the star will therefore be displaced from the central spider-line at the focus by a distance equal to that which the earth describes while the light is travelling through the telescope. This agrees with what is actually observed.

But a host of further questions now suggest themselves. Suppose, for instance, that a slab of glass with a plane face is carried along by the motion of the earth, and it is desired to adjust it so that a ray of light coming from a certain star shall not be bent when it enters the glass : must the .surface be placed at right angles to the true direction of the

• Annales de Chimie, ix, p. 57 (1818) ; CEnvres, ii, p. 627. t Phil. Trans., 1804, p. 12; Young's Works, i, p. 188. I 2

116 The L uminiferous Medium,

star as freed from aberration, or to its apparent direction as affected by aberration ? The question whether rays coming from the stars are refracted differently from rays origi- nating in terrestrial sources had been raised originally by Michell* ; and Kobison and Wilsonf had asserted that the focal length of an achromatic telescope should be increased when it is directed to a star towards which the earth is moving, owing to the change in the relative velocity of light. AragoJ sub- mitted the matter to the test of experiment, and concluded that the light coming from any star behaves in all cases of reflexion and refraction precisely as it would if the star were situated in the place which it appears to occupy in consequence of aber- ration, and the earth were at rest ; so that the apparent refraction in a moving prism is equal to the absolute refraction in a fixed prism.

Fresnel now set out to provide a theory capable of explaining Arago's result. To this end he adopted Young's suggestion, that the refractive powers of transparent bodies depend on the concentration of aether within them ; and made it more precise by assuming that the aethereal density in any body is pro- portional to the square of the refractive index. Thus, if c denote the velocity of light in vacuo, and if c, denote its velocity in a given material body at rest, so that /u = c/o{ is the refractive index, then the densities p and pl of the aether in interplanetary space and in the body respectively will be connected by the relation

pi = n*P-

Fresnel further assumed that, when a body is in motion, part of the aether within it is carried along — namely, that part which constitutes tne excess of its density over the density of aether in vacuo ; while the rest of the aether within the space occupied by the body is stationary. Thus the density of aether carried

• Phil. Trans., 1784, p. 35.

t Trans. E. S. Edin., i, Hist., p. 30.

J Biot, Astron. Phys., 3rd ed., v, p. 364. The accuracy of Arago's experiment can scarcely have been such as to demonstrate absolutely his result.

ft,

from Bradley to FresneL 117

along is (pi - p) or (^ - l)/o, while a quantity of aether of density p remains at rest. The velocity with which the centre of gravity of the aether within the body moves forward in the direction of propagation is therefore

where w denotes the component of the velocity of the body in this direction. This is to be added to the velocity of propaga- tion of the light- waves within the body ; so that in the moving body the absolute velocity of light is

Many years afterwards Stokes* put the same supposition in a slightly different form. Suppose the whole of the aether within the body to move together, the aether entering the body in front, and being immediately condensed, and issuing from it behind, where it is immediately rarefied. On this assumption a mass pw of aether must pass in unit time across a plane of area unity, drawn anywhere within the body in a direction at right angles to the body's motion; and therefore the aether within the body has a drift- velocity - wp/pl relative to the body : so the velocity of light relative to the body will be Ci - wplp, and the absolute velocity of light in the moving body will be

v*

v* k

or ci + £^i w, as before.

P

This formula was experimentally confirmed in 1851 by H. Fizeau,f who measured the displacement of interference- fringes formed by light which had passed through a column of moving water.

• Phil. Mag. xxviii (1846) p. 76.

t Annales de Chimie, Ivii (1859), p. 385. Also by A. A. Michelson and E. W. Morley, Am. Journ. Science, xxxi (1886), p. 377.

118 The Luminiferous Medium,

The same result may easily be deduced from an experiment performed by Hoek.* In this a beam of light was divided into two portions, one of which was made to pass through a tube of water AB and was then reflected at a mirror C, the light being afterwards allowed to return to A without passing through the water : while the other portion of the bifurcated beam was made to describe the same path in the reverse order, i.e. passing through the water on its return

,. journey from C instead of on the outward journey,

On causing the two portions of the beam to inter- fere, Hoek found that no difference of phase was produced between them when the apparatus was oriented in the direction of the terrestrial motion.

Let w denote the velocity of the earth, supposed to be directed from the tube towards the mirror. Let c/n denote the velocity of light in the water at rest, and C/A* + <l> the velocity of light in the water when moving. Let I denote the length of the tube. The magnitude of the distance BC does not affect the experiment, so we may suppose it zero.

The time taken by the first portion of the beam to perform its journey is evidently

If i

C/fi + ^ — W C + W '

while the time for the second portion of the beam is I I

• —.

C - W C/fJL - 0 + W

The equality of these expressions gives at once, when terms of higher orders than the first in w/c are neglected,

0 = Ou2 - 1) w^\ which is FresneFs expression.!

• Archives Neerl. iii, 180 (1868).

t Fresnel's law may also be deduced from the principle that the amount of light transmitted by a slab of transparent matter must be the same whether the slab is at rest or in motion : otherwise the equilibrium of exchanges of radiation would be tiated. Cf. Larmor, Phil. Trans, clxxxv (1893), p, 775.

from Bradley to Fresnel.

119

On the basis of this formula, Fresnel proceeded to solve the problem of refraction in moving bodies. Suppose that a prism AQ (70 B0 is carried along by the earth's motion in vacuo, its face A(, C0 being at right angles to the direction of motion ; and

that light from a star is incident normally on this face. The rays experience no refraction at incidence ; and we have only to consider the effect produced by the second surface A<>I>0. Sup- pose that during an interval T of time the prism travels from the position AQ C0 Bo to the position A± Ci B^ while the luminous disturbance at C0 travels to £h and the luminous disturbance at A0 travels to D, so that Bv D is the emergent wave-front. Then we have

-1

10

A0D

TC,

If we write CiA\B\ = i, and denote the total deviation of the wave-front by 81, we have

AiD = AJ) - A±AQ cos Si = TC - rw cos 81,

TIC,

120 The Lumniiferous Medium,

and therefore (neglecting second-order terms in w/c]

A

sin A^B^D c - w cos 81 _ c w w ^

-— — • : ~ — ~ — "f- — •*" COo Ol«

sin ^ Ci ct c Ci

Ct-W-

Denoting by 8 the value of 81 when w is zero, we have

sin (i -8) c sin i d

Subtracting this equation from the preceding, we have

8 -Si _ w sin § c

Now the telescope by which the emergent wave-front B\ D is received is itself being carried forward by the earth's motion; and we must therefore apply the usual correction for aberration in order to find the apparent direction of the emergent ray. But this correction is w sin 8/c, and precisely counteracts the effect which has been calculated as due to the motion of the prism. So finally we see that the motion of the earth has no first-order influence on the refraction of light from the stars.

Fresnel inferred from his formula that if observations were made with a telescope filled with water, the aberration would be unaffected by the presence of the water — a result which was verified by Airy* in 1871. He showed, moreover, that the apparent positions of terrestrial objects, carried along with the observer, are not displaced by the earth's motion ; that experi- ments in refraction and interference are not influenced by any motion which is common to the source, apparatus, and observer ; and that light travels between given points of a moving material system by the path of least time. These predictions have also been confirmed by observation: Kespighif in 1861, and Hoek+ in 1868, experimenting with a telescope filled with water and a terrestrial source of light, found that no effect was produced on the phenomena of reflexion and refraction by altering the orienta-

• Proc. Roy. Soc., xx, p. 35. t Mem. Accad. Sci. Bologna, ii, p. 279.

I Ast. Nach., Ixxiii, p. 193.

from Bradtey to Fresnel. 121

tion of the apparatus relative to the direction of the earth's motion. E. Mascart* in 1872 discussed experimentally the question of the effect of motion of the source or recipient of light in all its bearings, and showed that the light of the sun and that derived from artificial sources are alike incapable of revealing by diffraction-phenomena the translatory motion of the earth.

The greatest problem now confronting the investigators of light was to reconcile the facts of polarization with the principles of the wave-theory. Young had long been pondering over this, but had hitherto been baffled by it. In 1816 he received a visit from Arago, who told him of a new experimental result which he and Fresnel had lately obtained! — namely, that two pencils of light, polarized in planes at right angles, do not interfere with each other under circumstances in which ordinary light shows interference-phenomena, but always give by their reunion the same intensity of light, whatever be their difference of path.

Arago had not long left him when Young, reflecting on the new experiment, discovered the long-sought key to the mystery : it consisted in the very alternative which Bernoulli had rejected eighty years before, of supposing that the vibrations of light are executed at right angles to the direction of propagation.

Young's ideas were first embodied in a letter to Arago,J dated Jan. 12, 1817. "I have been reflecting," he wrote, " on the possibility of giving an imperfect explanation of the affection of light which constitutes polarization, without departing from the genuine doctrine of undulations. It is a principle in this theory, that all undulations are simply propagated through homogeneous mediums in concentric spherical surfaces like the

•Ann. de 1'Ecole Noemale, (2) i, p. 157.

t It was not published until 1819, in Annales de Chimie, x ; Fresnel's (Euvres, i, p. 509. By means of this result, Fresnel was able to give a complete explana- tion of a class of phenomena which Arago had discovered in 1811, viz. that when polarized light is transmitted through thin plates of sulphate of lime or mica, and afterwards analysed by a prism of Iceland spar, beautiful complementary colours are displayed. Young had shown that these effects are due essentially to inter- ference, hut had not made clear the part played by polarization.

J Young's JTorks, i., p. 380.

122 The Lumini/erous Medium,

undulations of sound, consisting simply in the direct and retro- grade motions of the particles in the direction of the radius,, with their concomitant condensation and rarefactions. And yet it is possible to explain in this theory a transverse vibration,, propagated also in the direction of the radius, and with equal velocity, the motions of the particles being in a certain constant direction with respect to that radius ; and this is a polarization"

In an article on " Chromatics," which was written in September of the same year* for the supplement to the Encyclopaedia Britannica, he says :f " If we assume as a mathe- matical postulate, on the undulating theory, without attempting to demonstrate its physical foundation, that a transverse motion may be propagated in a direct line, we may derive from this assumption a tolerable illustration of the subdivision of polarized light by reflexion in an oblique plane," by " supposing the polar motion to be resolved " into two constituents, which fare differently at reflexion.