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tically available. But we should imagine it could not be undeserving of attention; and in the hands of a person of moderate skill would certainly confer new powers of discrimination in such cases.
The undulatory doctrine, however, was long embarrassed by several objections which it required more extended consideration to remove. Thus, it had long since been remarked by Newton that waves spread round an obstacle, and on the same principle the rectilinear propagation of light is a difficulty; light ought to bend round the edges of any intercepting body. But the very principle suggested by Huyghens afforded in some sense an answer; and a fuller examination of the nature and mode of propagation of the waves showed that the oblique and diverging portions will in general interfere with and neutralise each other, so that the main effect will be confined to that part which is in the direct line of the proportion. Young* dwelt much at first on this objection; and afterwards, in a letter to Arago, he renews a similar expression of the difficulties he felt in another point of view: “If light has so great a tendency to diverge into the path of neighbouring rays, and to interfere with them, as Huyghens supposes, I do not see how it escapes being totally extinguished in a very short space, even in the most transparent medium.” But the principle just adverted to shows that the middle portion of the light coming from a point of any physical magnitude is not subject to these mutual interferences, and does not diverge, but is perpetually reinforced by the supply of fresh waves incessantly propagated from the original source. In these explanations Young at length expressed his full concurrence in a letter to Fresnel.
The capital discovery of the polarisation of light by reflection made by Malus in 1810 formed a remarkable epoch in the history of optical research. The same idea of sides or poles imagined by Newton seemed to be involved. The reflected ray acquired the same character and properties as each of the rays in the doubly refracting crystal, though their planes of polarisation are at right angles to each other, and in determinate directions with respect to the crystal. A ray polarised in one plane will neither be transmitted through the crystal nor reflected from glass, when the planes in which they are respectively presented to it are at right angles to its own plane of polarisation. A ray may also be polarised by other methods: by transmission through a number of parallel plates of glass, or through a plate of tourmaline, or certain other substances. Hence any of these methods may be used convertibly to test the polarisation of a ray, and the plates or crystals employed are then termed analysers. A particular angle of incidence is necessary to give the maximum effect; different for each reflecting substance; and this subject to a law whose subsequent disclosure constituted one of the most beautiful discoveries of Sir D. Brewster, viz. that it takes place at that incidence at which the refracted ray is perpendicular to the reflected; or, which is mathematically the same thing otherwise expressed, when the tangent of the angle of incidence is the index of refraction of the substance.
* Life, p. 140.
Such were some of the leading points successively disclosed; and they soon engaged the attention of Young, as well as Fresnel, who afterwards so largely contributed to the development and extension of them in connection with the doctrine of undulations, of which they were destined to form one of the strongest supports. Yet so little was the value and tendency of Malus' discovery at first perceived, that it was regarded as quite at variance with the wave theory. Young himself went so far as to predict that it was a problem which “would probably long remain to mortify the vanity of an ambitious philosophy, completely unresolved by any theory.” Again, in a review of Malus paper (in 1811), he considers it “conclusive with respect to the insufficiency of the undulatory theory in its present state for explaining all the phenomena of light. And, again, in a letter to Sir D. Brewster, five years later, he expresses himself thus: “With respect to my fundamental hypotheses respecting the nature of light (i.e. the wave theory), I become less and less fond of dwelling on them, as I learn more and more facts like those which M. Malus discovered ; because though they may not be incompatible with those facts, they certainly give no assistance in explaining them.” Even Malus himself was at first of opinion that the phenomena of polarisation were equally irreconcilable with both the undulatory and molecular theories; an opinion which he distinctly expressed in a letter to Young. *
Somewhat later, however, we find Young beginning to entertain a more satisfactory view of the case, as appears by the following passage from a letter addressed by him to Arago in 1817:
“ I have been reflecting upon the possibility of giving an imperfect explanation of the affection of light, which constitutes polarisation, without departing from the genuine doctrine of undulations. It is a principle of this theory that all undulations are simply propagated through homogeneous mediums in concentric spherical surfaces, like the undulations of sound, consisting simply of the direct and retrograde motions of their particles in the direction of the radius, with their concomitant condensations 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
* Works, vol. i. p. 248, note.
the particles bearing a certain constant direction with respect to that radius; and this is polarisation."
The conception of transverse vibrations, now that the idea has become familiarised, seems to present little difficulty; yet it was at first opposed to the prepossessions even of the most zealous undulationists. Fresnel long hesitated fully to adopt the idea, although admitting it to be the only mode of representing polarisation,-on the ground of being unable to reconcile it with mechanical principles; and this more precisely as to the notion of transverse vibrations alone being produced, which constituted this theory in all its simplicity; whereas Young had (as we have just seen) believed both these and longitudinal vibrations to co-exist. To establish this point, he expressly says, was the main difficulty which embarrassed him.*
This idea of vibrations performed in directions at right angles to the line of the ray received at length its decisive proof from the phenomena of the coloured tints developed in polarised light by the interposition of plates of crystals (such as those of mica, selenite, &c.), when examined by an analyser.
Young ascribed these colours generally to interference; but both Fresnel and Arago pointed out that this explanation was incomplete. Why did it only take place in polarised light, and even then not until the analyser had been applied ?
These questions could not be answered until another important law had been established by the joint researches of Fresnel and Arago; and this consisted in the experimental conclusion, that when two rays are, in other respects, in a condition to interfere, but are polarised in planes at right angles to each other, they cannot interfere : they can only do so when polarised in parallel planes. Now this result, of necessity, implies that in rays polarised in different planes the vibrations must be executed in different planes; and this involves the admission that the vibrations must be transverse to the ray.
This principle was at length seen to complete the explanation so long sought of the polarised tints. The light originally polarised in one plane was, in traversing the doubly refracting crystal, divided into two portions in planes at right angles, which, as Young had shown in regard to position, were in a condition to interfere; (the ordinary ray of one such pair coinciding in direction with the extraordinary of some other pair :) were it not that being polarised in these rectangular planes, they could not interfere. It only required, then, the action of the analyser to resolve each portion into two, suppressing those in one plane, and transmitting those in the other, which, having their vibrations now parallel,
* Ann, de Chimie, 1831, tom. xvii. p. 184.
were thus enabled to manifest their interference, and produce the polarised tints, which in homogeneous light are simply alternations of light and darkness.
Such was the beautiful train of reasoning followed out by Arago and Fresnel to explain those polarised colours, originally and independently discovered by Arago and by Sir D. Brewster, and which, when the crystal is cut perpendicular to its axis, are seen in the form of rings round that axis; and of which the varieties in different crystals are now become familiar by means of the little instrument called the polariscope. But the principle of transverse vibrations thus established was the fruitful source of numerous other conclusions.
We have dwelt on the principle involved chiefly as bearing on the difficulties already spoken of, as experienced by Young and Fresnel in the explanation of phenomena with which these last would at first sight not appear to have any connection, but which were now shown to have a direct relation to them. According to the principle of transverse vibrations, as investigated by Fresnel, a number of comprehensive formulas resulted, including the deduction of Brewster's law of the polarising angle, as well as other important consequences.
One of these is the simple consideration, that in reflection, an oblique vibration is resolved into two at right angles, and thus a change of plane, or of angular phase, takes place. This is equivalent to a retardation or acceleration in route by a corresponding portion of a wave length; and if in any case the plane were turned through 180°, the ray would be in an opposite phase, or the change would be equivalent to a difference of one half an undulation. Obvious as now seems the conception, that a change of plane or angular phase is equivalent to retardation or acceleration in length of route, it does not appear to have been distinctly apprehended in the first instance either by Young or Fresnel, or it would have obviated some difficulties which long perplexed them; especially in the remarkable instance before mentioned of the colours of thin plates, the central black spot, and the supposed arbitrary assumption of the loss or gain of the half-undulation necessary to explain it.
Although Young, in the very same paper containing his theory of interference, pointed to a mechanical analogy which involved nearly the principle of its explanation, he did not perceive the application of it. Indeed, it can hardly be said to have been very clearly or happily expounded by any of the elementary writers who have systematised the theory, not excepting the author of the biography before us. It is thus less surprising that it should have long continued to furnish a ground of difficulty and objection. Yet in Fresnel's formula a mere change of algebraical sign, in the sine of an angle, in the expression for the reflections at the first and at the second surface, gives a difference of 180° in phase, which is thus accounted for without any subsidiary assumption whatever.
We have thus far endeavoured briefly to sketch the leading points in the history of the first establishment of those grand principles of the theory of light, which Young has the undivided and unquestioned honour of having been the first to propose and to demonstrate. Every subsequent improvement and enlargement of the theory, which has regularly kept pace with the advance of experimental discovery, has, as it were, grown out of the simple principles at first laid down by a natural sequence, without any new hypotheses or forced and arbitrary changes. It is a theory of which an eminent philosopher, by no means unduly biased in its favour, and at a time when it had not reached its present point of perfection, emphatically said, “It is a series of felicities; and if not true, eminently deserves to be true.” And the increasing proof which it continues to receive by its readiness in meeting nearly every new experimental case as it arises, aug. ments in the same proportion our conviction that it will, sooner or later, be equally successful in the solution of those few phenomena which still appear to stand out as exceptional instances to its application.
The First Cause ; or, a Treatise upon the Being and Attributes of
God. By Rev. J. C. Whish, M.A. Seeley, Jackson, and Hal
liday. 1855. The Burnett Prize-Essays. Principles of Psychology. By Herbert Spencer. Longmans, 1855. George Jacob Holyoake and Modern Atheism. An Essay. By
. S. D. Collet. Trübner. 1855. The Reasoner for 1855. Edited by G. J. Holyoake. Holyoake,
Fleet Street. If ever the dark shadow of Atheism were suddenly to envelop the earth, would the crash of falling churches, the disbanding of ecclesiastical classes, and the vanishing of all conscious individual intercourse with God, be necessarily accompanied by the yielding of all moral ties and the dissolution of every sacred social organisation? Before we can attempt to answer such a question, we must call to mind a very obvious but a strangely-forgotten truth, that