A Preliminary Discourse on the Study of Natural Philosophy/Part 3, chap. 2
(269.) The propagation of motion through all substances, whether of a single impulse, as a blow or thrust, or of one frequently and regularly repeated, such as a jarring or vibratory movement, depends wholly on these molecular forces; and it is on such propagation that sound and very probably light depend. To conceive the manner in which a motion may be conveyed from one part of a substance to another, whether solid or fluid, we may attend to what takes place when a wave is made to run along a stretched string, or the surface of still water. Every part of the string, or water, is in succession moved from its place, and agitated with a motion similar to that of the original impulse, leaving its place and returning to it, and when one part ceases to move the next receives as it were the impression, and forwards it onward. This may seem a slow and circuitous process in description; but when sound, for example, is conveyed through the air, we are to consider, 1st, that the air, the substance actually in motion, is extremely light and acted upon by a very powerful elasticity, so that the force which propagates the motion, or by which the particles adjacent act on, and urge forward, each other, is very great, compared with the quantity of materials set in motion by it: and the same is true, even in a greater degree, in liquids and solids; for in these the elastic forces are even greater, in proportion to the weight, than in air.
(270.) A general notion of the mode in which sounds are conveyed through the air was not altogether deficient among the ancients; but it is to Newton that we owe the first attempt to analyze the process, and show correctly what takes place in the communication of motion from particle to particle. Reasoning on the properties of the air as an elastic body, he showed the effect of an impulse on any portion of it to consist in a condensation of the air immediately adjacent in the direction of the impulse, which then, re-acting by its spring, drives back the portion which had advanced to its original place, and at the same time urges forward the portion before it, in the direction of the impulse, so that every particle alternately advances and retreats. But, in pursuing this idea into its details, Newton fell into some errors which were pointed out by Cramer, though their origin was not traced, nor the reasoning corrected, till the subject was resumed by Lagrange and Euler; nor is this any impeachment of the penetration of our immortal countryman. The mathematical theory of the propagation of sound, and of vibratory and undulatory motions in general, is one of the utmost intricacy; and, in spite of every exertion on the part of the most expert geometers, continues to this day to give continual occasion for fresh researches; while phenomena are constantly presenting themselves, which show how far we are from being able to deduce all the particulars, even of cases comparatively simple, by any direct reasoning from first principles.
(271.) Whenever an impulse of any kind is conveyed by the air, to our ears, it produces the impression of sound; but when such an impulse is regularly and uniformly repeated in extremely rapid succession, it gives us that of a musical note, the pitch of the note depending on the rapidity of the succession (see art. 153.). The sense of harmony, too, depends on the periodical recurrence of coincident impulses on the ear, and affords, perhaps, the only instance of a sensation for whose pleasing impression a distinct and intelligible reason can be assigned.
(272.) Acoustics, then, or the science of sound, is a very considerable branch of physics, and one which has been cultivated from the earliest ages. Even Pythagoras and Aristotle were not ignorant of the general mode of its transmission through the air, and of the nature of harmony; but as a branch of science, independent of its delightful application in the art of music, it could be hardly said to exist, till its nature and laws became a matter of experimental enquiry to Bacon and Galileo, Mersenne and Wallis; and of mathematical investigation to Newton, and his illustrious successors, Lagrange and Euler. From that time its progress, as a branch both of mathematical and experimental science, has been constant and accelerated. A curious and beautiful method of observation, due to Chladni, consists in the happy device of strewing sand over the surfaces of bodies in a state of sonorous vibration, and marking the figures it assumes. This has made their motions susceptible of ocular examination, and has been lately much improved on, and varied in its application, by M. Savart, to whom we also owe a succession of instructive researches on every point connected with the subject of sound, which may rank among the finest specimens of modern experimental enquiry. But the subject is far from being exhausted; and, indeed, there are few branches of physics which promise at once so much amusing interest, and such important consequences, in its bearings on other subjects, and especially, through the medium of strong analogies, on that of light.
Light and Vision.
(273.) The nature of light has always been involved in considerable doubt and mystery. The ancients could scarcely be said to have any opinion on the subject, unless, indeed, it could be considered such to affirm that distant bodies could not be put into communication without an intermedium; and that, therefore, there must be something between the eye and the thing seen. What that something is, however, they could only form crude and vague conjectures. One supposed that the eyes themselves emit rays or emanations of some unknown kind, by which distant objects are as it were felt; a singularly unfortunate idea, since it gives no reason why objects should not be equally well seen in the dark—no account, in short, of the part performed by light in vision. Others imagined that all visible objects are constantly throwing out from them, in all directions, some sort of resemblances or spectral forms of themselves, which, when received by the eyes, produce an impression of the objects. Vague and clumsy as this hypothesis obviously is, it assigns to the object a power, and to light a diffusive propagation in all directions, which are, the one and the other, independent of our eyes, and therefore goes to separate the phenomena of light from those of vision.
(274.) The hypothesis of Newton is a refinement and improvement on this idea. Instead of spectra or resemblances, he supposes luminous objects actually to dart out from them in all directions, particles of inconceivable minuteness (as indeed they must be, having such an enormous velocity (see 17.), not to dash in pieces every thing they strike upon). These particles he supposes to be acted upon by attractive and repulsive forces, residing in all material bodies, the latter extending to some very small distance beyond their surfaces; and by the action of these forces to be turned aside from their natural straight-lined course, without ever coming in actual contact with the particles themselves of the bodies on which they fall, but either being turned back and reflected by the repulsive forces before they reach them, or penetrating between their intervals, as a bird may be supposed to fly through the branches of a forest, and undergoing all their actions, to take at quitting them a direction finally determined by the position of the surface at which they emerge with respect to their course.
(275.) This hypothesis, which was discussed and reasoned upon by Newton in a manner worthy of himself, affords, by the application of the same dynamical laws which he had applied with so much success to the explanation of the planetary motions, not merely a plausible, but a perfectly reasonable and fair explanation of all the usual phenomena of light known in his time. His own beautiful discoveries, too, of the different refrangibilities of the differently coloured rays, were perfectly well represented in this theory, by simply admitting a difference of velocity in the particles, which produce in the eye the sensations of different colours. And had the properties of light remained confined to these, there would have been no occasion to have resorted to any other mode of conceiving it.
(276.) A very different hypothesis had, however, been suggested about the same period by Huyghens, who supposed light to be produced in the same manner with sound, by the communication of a vibratory motion from the luminous body to a highly elastic fluid, which he imagined as filling all space, and as being less condensed within the limits of space occupied by matter, and that to a greater or less extent, according to the nature of the occupying substance. Thus, in place of any thing actually thrown off, he substituted waves, or vibrations, propagated in all directions from luminous bodies, through this medium, or ether, as he called it. Huyghens, being himself a consummate mathematician, was enabled to trace many of the consequences of this hypothesis, and to show that the ordinary laws of reflection and refraction were represented or accounted for by it, as well as by Newton's. But the hypothesis of Huyghens has not been fully successful in accounting for what may be considered the chief of all optical facts, the production of colours in the ordinary refraction of light by a prism, of which the theory of Newton gives a complete and elegant explanation; and the discovery of which by him marks one of the greatest epochs in the annals of experimental science. This, which has been often urged in objection to it, remains still, if not quite unanswered, at least only imperfectly removed.
(277.) Other phenomena, however, were not wanting to afford a further trial of the explanatory powers of either hypothesis. The diffraction or inflection of light, discovered by Grimaldi, a Jesuit of Bologna, seemed to indicate that the rays of light were turned aside from their straight course by merely passing near bodies of every description. These phenomena, which are very curious and beautiful, were minutely examined by Newton, and referred by him to the action of repulsive forces extending to a sensible distance from the surfaces of bodies; and his explanation, so far as the facts known to him are concerned, appears as satisfactory as could reasonably be then expected; and much more so than any thing which could at that time be produced on the side of the hypothesis of Huyghens, which, in fact, seemed incapable of giving any account whatever of them.
(278.) Another class of delicate and splendid optical phenomena, which had begun to attract attention somewhat previous to Newton's time, seemed to leave both hypotheses equally at a loss. These were the colours exhibited by very thin films, either of a liquid (such as a soap-bubble), or of air, as when two glasses are laid together with only air between them. These colours were examined by Newton with a minuteness and care altogether unexampled in experimental philosophy at that time, and with which few researches undertaken since will bear to stand in competition. Their result was a theory of a very singular nature, which he grounded on an hypothesis of what he termed fits of easy transmission and reflection; and which supposed each ray of light to pass in its progress periodically through a succession of states such as would alternately dispose it to penetrate or be reflected back from the surface of a body on which it might fall. The simplest way in which the reader may conceive this hypothesis, is to regard every particle of light as a sort of little magnet revolving rapidly about its own centre while it advances in its course, and thus alternately presenting its attractive and repulsive pole, so that when it arrives at the surface of a body with its repulsive pole foremost, it is repelled and reflected; and when the contrary attracted, so as to enter the surface. Newton, however, very cautiously avoided announcing his theory in this or any similar form, confining himself entirely to general language. In consequence, it has been confidently asserted by all his followers, that the doctrine of fits of easy reflection and transmission, as laid down by him, is substantially nothing more than a statement of facts. Were it so, it is clear that any other theory which should offer a just account of the same phenomena must ultimately involve and coincide with that of Newton. But this, as we shall presently see, is not the case; and this instance ought to serve to make us extremely cautious how we employ, in stating physical laws derived from experiment, language which involves any thing in the slightest degree theoretical, if we would present the laws themselves in a form which no future research shall modify or subvert.
(279.) A third class of optical phenomena, which were likewise discovered while Newton was yet engaged in his optical researches, was that exhibited by doubly refracting crystals. In what the phenomenon of double refraction consists, we have already had occasion to explain. The fact itself was first noticed by Erasmus Bartolin in the crystal called Iceland spar; and was studied with attention by Huyghens, who ascertained its laws, and referred it with remarkable ingenuity and success to his theory of light, by the additional hypothesis of such a constitution of his ethereal medium within the crystal as should enable it to convey an impulse faster in one direction than another: as if, for example's sake, we should suppose a sound conveyed through the air with different degrees of rapidity in a vertical and horizontal direction.
(280.) Some remarkable facts accompanying the double refraction produced by Iceland spar, which Bartolin, Huyghens, and Newton, had observed, led the latter to conceive the singular idea that a ray of light after its emergence from such a crystal acquires sides, that is to say, distinct relations to surrounding space, which it carries with it through its whole subsequent course, and which give rise to all those curious and complicated phenomena which are now known under the name of the polarization of light. These results, however, appeared so extraordinary, and offered so little handle for further enquiry, that their examination dropped, as if by common consent; Newton himself resting content with urging strongly the apparent incompatibility of these properties with the Huyghenian doctrine, but without making any attempt to explain them by his own.
(281.) From the period of Newton's optical discoveries to the commencement of the present century, no great accession to our knowledge of the nature of light was made, if we except one, which, from its invaluable practical application, must ever hold a prominent place in the annals both of art and science: we mean, the discovery of the principle of the achromatic telescope, which originated in a discussion between the celebrated geometer Euler, Klingenstierna, an eminent Swedish philosopher, and our own countryman, the admirable optician Dollond, on the occasion of certain abstract theoretical investigations of the former, which led him to speculate on its possibility, and which ultimately terminated in its complete and happy execution by the latter; a memorable case in science, though not a singular one, where the speculative geometer in his chamber, apart from the world, and existing among abstractions, has originated views of the noblest practical application.[1]
(282.) The explanation which our knowledge of optical laws affords of the mechanism of the eye, and the process by which vision is performed, is as complete and satisfactory as that of hearing by the propagation of motion through the air. The camera obscura, invented by Baptista Porta in 1560, gave the first idea how the actual images of external objects might be conveyed into the eye, but it was not till after a considerable interval that Kepler, the immortal discoverer of those great laws which regulate the periods and motions of the planets, pointed out distinctly the offices performed by the several parts of the eye in the act of vision. From this to the invention of the telescope and microscope there would seem but a small step, but it is to accident rather than design that it is due; and its reinvention by Galileo, on a mere description of its effects, may serve, among a thousand similar instances, to show that inestimable practical applications lie open to us, if we can only once bring ourselves to conceive their possibility, a lesson which the invention of the achromatic telescope itself, as we have above related it, not less strongly exemplifies.
(283.) The little instrument with which Galileo's splendid discoveries were made was hardly superior in power to an ordinary finder of the present day; but it was rapidly improved on, and in the hands of Huyghens attained to gigantic dimensions and very great power. It was to obviate the necessity of the enormous length required for these telescopes, and yet secure the same power, that Gregory and Newton devised the reflecting telescope, which has since become a much more powerful instrument than its original inventors probably ever contemplated.
(284.) The telescope, as it exists at present, with the improvements in its structure and execution which modern artists have effected, must assuredly be ranked among the highest and most refined productions of human art; that in which man has been able to approximate more closely to the workmanship of nature, and which has conferred upon him, if not another sense, at least an exaltation of one already possessed by him that merits almost to be regarded as a new one. Nor does it appear yet to have reached its ultimate perfection, to which indeed it is difficult to assign any bounds, when we take into consideration the wonderful progress which workmanship of every kind is making, and the delicacy, far superior to that of former times, with which materials may now be wrought, as well as the ingenious inventions and combinations which every year is bringing forth for accomplishing the same ends by means hitherto unattempted.[2]
(285.) After a long torpor, the knowledge of the properties of light began to make fresh progress about the end of the last century, advancing with an accelerated rapidity, which has continued unabated to the present time. The example was set by our late admirable and lamented countryman, Dr. Wollaston, who re-examined and verified the laws of double refraction in Iceland spar announced by Huyghens. Attention being thus drawn to the subject, the geometry of Laplace soon found a means of explaining at least one portion of the mystery of this singular phenomenon, by the Newtonian theory of light, applied under certain supposed conditions; and the reasoning which led him to the result (at that time quite unexpected), may justly be regarded as one of his happiest efforts. The prosecution of the subject, which had now acquired a high degree of interest, was encouraged by the offer of a prize on the part of the French Academy of Sciences; and it was in a memoir which received this honourable reward on that occasion, in 1810, that Malus, a retired officer of engineers in the French army, announced the great discovery of the polarization of light by ordinary reflection at the surface of a transparent body.
(286.) Malus found that when a beam of light is reflected from the surface of such a body at a certain angle, it acquires precisely the same singular property which is impressed upon it in the act of double refraction, and which Newton had before expressed by saying that it possessed sides. This was the first circumstance which pointed out a connection between that hitherto mysterious phenomenon and any of the ordinary modifications of light; and it proved ultimately the means of bringing the whole within the limits, if not of a complete explanation, at least of a highly plausible theoretical representation. So true is, in science, the remark of Bacon, that no natural phenomenon can be adequately studied in itself alone, but, to be understood, must be considered as it stands connected with all nature.
(287.) The new class of phenomena thus disclosed were immediately studied with diligence and success, both abroad by Malus and Arago, and at home by our countryman Dr. Brewster, and their laws investigated with a care proportioned to their importance; when another and apparently still more extraordinary class of phenomena presented itself in the production of the most vivid and beautiful colours (every way resembling those observed by Newton in thin films of air or liquids, only infinitely more developed and striking,) in certain transparent crystallized substances, when divided into flat plates in particular directions, and exposed in a beam of polarized light. The attentive examination of these colours by Wollaston, Biot, and Arago, but more especially by Brewster, speedily led to the disclosure of a series of optical phenomena so various, so brilliant, and evidently so closely connected with the most important points relating to the intimate structure of crystallized bodies, as to excite the highest interest,—that sort of interest which is raised when we feel we are on the eve of some extraordinary discovery, and expect every moment that some leading fact will turn up, which will throw light on all that appears obscure, and reduce into order all that seems anomalous.
(288.) This expectation was not disappointed. So long before the time we are speaking of as the first year of the present century, our illustrious countryman, the late Dr. Thomas Young, had established a principle in optics, which, regarded as a physical law, has hardly its equal for beauty, simplicity, and extent of application, in the whole circle of science. Considering the manner in which the vibrations of two musical sounds arriving at once at the ear affect the sense with an impression of sound or silence according as they conspire or oppose each other's effects, he was led to the idea that the same ought to hold good with light as with sound, if the theory which makes light analogous to sound be the true one; and that, therefore, two rays of light, setting off from the same origin, at the same instant, and arriving at the same place by different routes, ought to strengthen or wholly or partially destroy each other's effects according to the difference in length of the routes described by them. That two lights should in any circumstances combine to produce darkness may be considered strange, but is literally true; and it had even been noticed long ago as a singular and unaccountable fact by Grimaldi, in his experiments on the inflection of light. The experimental means by which Dr. Young confirmed this principle, which is known in optics by the name of the interference of the rays of light, were as simple and satisfactory as the principle itself is beautiful; but the verifications of it, drawn from the explanation it affords of phenomena apparently the most remote, are still more so. Newton's colours of thin films were the first phenomena to which its author applied it with full success. Its next remarkable application was to those of diffraction, of which, in the hands of M. Fresnel, a late eminent French geometer, it also furnished a complete explanation, and that, too, in cases to which Newton's hypothesis could not apparently be made to apply, and through a complication of circumstances which might afford a very severe test of any hypothesis.
(289.) A simple and beautiful experiment on the interferences of polarized light due to Fresnel and Arago enabled them to bring Dr. Young's law to bear on the colours produced by crystallized plates in a polarized beam, and by so doing afforded a key to all the intricacies of these magnificent but complex phenomena. Nothing now was wanting to a rational theory of double refraction but to frame an hypothesis of some mode in which light might be conceived to be propagated through the elastic medium supposed to convey it in such a way as not to be contradictory to any of the facts, nor to the general laws of dynamics. This essential idea, without which every thing that had been before done would have been incomplete, was also furnished by Dr. Young, who, with a sagacity which would have done honour to Newton himself, had declared, that to accommodate the doctrine of Huyghens to the phenomena of polarized light it is necessary to conceive the mode of propagation of a luminous impulse through the ether, differently from that of a sonorous one through the air. In the latter, the particles of the air advance and recede; in the former, those of the ether must be supposed to tremble laterally.
(290.) Taking this as the groundwork of his reasoning, Fresnel succeeded in erecting on it a theory of polarization and double refraction, so happy in its adaptation to facts, and in the coincidence with experience of results deduced from it by the most intricate analysis, that it is difficult to conceive it unfounded. If it be so, it is at least the most curiously artificial system that science has yet witnessed; and whether it be so or not, so long as it serves to group together in one comprehensive point of view a mass of facts almost infinite in number and variety, to reason from one to another, and to establish analogies and relations between them; on whatever hypothesis it may be founded, or whatever arbitrary assumptions it may make respecting structures and modes of action, it can never be regarded as other than a most real and important accession to our knowledge.
(291.) Still, it is by no means impossible that the Newtonian theory of light, if cultivated with equal diligence with the Huyghenian, might lead to an equally plausible explanation of phenomena now regarded as beyond its reach. M. Biot is the author of the hypothesis we have already mentioned of a rotatory motion of the particles of light about their axes. He has employed it only for a very limited purpose; but it might doubtless be carried much farther; and by admitting only the regular emission of the luminous particles at equal intervals of time, and in similar states of motion from the shining body, which does not seem a very forced supposition, all the phenomena of interference at least would be readily enough explained without the admission of an ether.
(292.) The optical examination of crystallized substances affords one among many fine examples of the elucidation which every branch of science is capable of affording to every other. The indefatigable researches of Dr. Brewster and others have shown that the phenomena exhibited by polarized light in its transmission through crystals afford a certain indication of the most important points relating to the structure of the crystals themselves, and thus become most valuable characters by which to recognise their internal constitution. It was Newton who first showed of what importance as a physical character,—as the indication of other properties,—the action of a body on light might become; but the characters afforded by the use of polarized light as an instrument of experimental enquiry are so marked and intimate, that they may almost be said to have furnished us with a kind of intellectual sense, by which we are enabled to scrutinize the internal arrangement of those wonderful structures which Nature builds up by her refined and invisible architecture, with a delicacy eluding our conception, yet with a symmetry and beauty which we are never weary of admiring. In this point of view the science of optics has rendered to mineralogy and crystallography services not less important than to astronomy by the invention of the telescope, or to natural history by that of the microscope; while the relations which have been discovered to exist between the optical properties of bodies and their crystalline forms, and even their chemical habitudes, have afforded numerous and beautiful instances of general laws concluded from laborious and painful induction, and curiously exemplifying the simplicity of nature as it emerges slowly from an entangled mass of particulars in which, at first, neither order nor connection can be traced.
- ↑ There seems no doubt, however, that an achromatic telescope had been constructed by a private amateur, a Mr. Hall, some time before either Euler or Dollond ever thought of it.
- ↑ We allude to the recently invented achromatic combinations of Messrs. Barlow and Rogers, and the dense glasses of which Mr. Faraday has recently explained the manufacture in a memoir full of the most beautiful examples of delicate and successful chemical manipulation, and which promise to give rise to a new era in optical practice, by which the next generation at least may benefit. See Phil. Trans. 1830.