one place to another. The particles along the line of each wave assume a certain arrangement, and this arrangement passes from one part to another, the particles changing their places only within narrow limits, so as to lend themselves successively to the arrangements by which the successive waves, and the intervals between the waves, are formed.

When such an Undulation is propagated through air, the wave is composed, not, as in water, of particles which are higher than the rest, but of particles which are closer to each other than the rest. The wave is not a ridge of elevation, but a line of condensation; and as in water we have alternately elevated and depressed lines, we have in air lines alternately condensed and rarefied. And the motion of the particles is not, as in water, up and down, in a direction transverse to that of the wave which runs forwards; in the motion of an undulation through air the motion of each particle is alternately forwards and backwards, while the motion of the undulation is constantly forwards.

This precise and detailed account of the Undulatory Motion of air by which sound is transmitted was first given by Newton. He further attempted to determine Che motions of the separate particles, and to point out the force by which each particle affects the next, so as so continue the progress of the undulation once begun. The motions of each particle must be oscillatory; he ssumed the oscillations to be governed by the simplest aw of oscillation which had come under the notice of nathematicians, (that of small vibrations of a penduum;) and he proved that in this manner the forces which are called into play by the contraction and xpansion of the parts of the elastic fluid are such as he continuance of the motion requires.

Newton's proof of the exact law of Oscillatory Motion f the aërial particles was not considered satisfactory y succeeding mathematicians; for it was found that he same result, the development of forces adequate to ontinue the motion, would follow if any other law of he motion were assumed. Cramer proved this by a ort of parody on Newton's proof, in which, by the

alteration of a few phrases in this formula of demonstration, it was made to establish an entirely different conclusion.

But the general conception of an Undulation as presented by Newton was, as from its manifest mechanical truth it could not fail to be, accepted by all mathematicians; and in proportion as the methods of calculating the motions of fluids were further improved, the necessary consequences of this conception, in the communication of sound through air, were traced by unexceptionable reasoning. This was especially done by Euler and Lagrange, whose memoirs on such motions of fluids are some of the most admirable examples which exist, of refined mathematical methods applied to the solution of difficult mechanical problems.

But the great step in the formation of the theory of sound was undoubtedly that which we have noticed, the introduction of the Conception of an Undulation such as we have attempted to describe it:—a state, condition, or arrangement of the particles of a fluid, which is transferred from one part of space to another by means of small motions of the particles, altogether distinct from the movement of the Undulation itself. This is a conception which is not obvious to common apprehension. It appears paradoxical at first sight to speak of a large wave (as the tide-wave) running up a river at the rate of twenty miles an hour, while the stream of the river is all the while flowing downwards. Yet this is a very common fact. And the conception of such a motion must be fully mastered by all who would reason rightly concerning the mechanical transmission of impressions through a medium.

We have described the motion of sound as produced by small motions of the particle forwards and backwards, while the waves, or condensed and rarefied lines, move constantly forwards. It may be asked what right we have to suppose the motion to be of this kind, since when sound is heard, no such motions of the particles of air can be observed, even by refined methods of observation. Thus Bacon declares himself against the hypothesis of such a vibration, since, as he remarks, it

cannot be perceived in any visible impression upon the flame of a candle. And to this we reply, that the supposition of this Vibration is made in virtue of a principle which is involved in the original assumption of a medium; namely, That a Medium, in conveying Secondary qualities, operates by means of its Primary qualities, the bulk, figure, motion, and other mechanical properties of its parts. This is an Axiom belonging to the Idea of a Medium. In virtue of this axiom it is demonstrable that the motion of the air, when any how disturbed, must be such as is supposed in our acoustical reasonings. For the elasticity of the parts of the air, called into play by its expansion and contraction, lead, by a mechanical necessity, to such a motion as we have described. We may add that, by proper contrivances, this motion may be made perceptible in its visible effects. Thus the theory of sound, as an impression conveyed through air, is established upon evident general principles, although the mathematical calculations which are requisite to investigate its consequences are, some of them, of a very recondite kind.

3. Light. The early attempts to explain Vision represented it as performed by means of material rays proceeding from the eye, by the help of which the eye felt out the form and other visible qualities of an object, as a blind man might do with his staff. But Ehis opinion could not keep its ground long: for it did not even explain the fact that light is necessary to vision. Light, as a peculiar medium, was next assumed as the machinery of vision; but the mode in which he impression was conveyed through the medium was eft undetermined, and no advance was made towards sound theory, on that subject, by the ancients.

In modern times, when the prevalent philosophy Degan to assume a mechanical turn (as in the theories of Descartes), light was conceived to be a material subtance which is emitted from luminous bodies, and vhich is also conveyed from all bodies to the eye, so as o render them visible. The various changes of direcion by which the rays of light are affected, (reflection,

refraction, &c.,) Descartes explained, by considering the particles of light as small globules, which change their direction when they impinge upon other bodies, according to the laws of Mechanics. Newton, with a much more profound knowledge of Mechanics than Descartes possessed, adopted, in the most mature of his speculations, nearly the same view of the nature of light; and endeavoured to show that reflection, refraction, and other properties of light, might be explained as the effects which certain forces, emanating from the particles of bodies, produce upon the luminiferous globules.

But though some of the properties of light could thus be accounted for by the assumption of particles emitted from luminous bodies, and reflected or refracted by forces, other properties came into view which would not admit of the same explanation. The phenomena of diffraction (the fringes which accompany shadows) could never be truly represented by such an hypothesis, in spite of many attempts which were made. And the colours of thin plates, which show the rays of light to be affected by an alternation of two different conditions at small intervals along their length, led Newton himself to incline, often and strongly, to some hypothesis of undulation. The double refraction of Iceland spar, a phenomenon in itself very complex, could, it was found by Huyghens, be expressed with great simplicity by a certain hypothesis of undulations.

Two hypotheses of the nature of the luminiferous medium were thus brought under consideration; the one representing Light as Matter emitted from the luminous object, the other, as Undulations propagated through a fluid. These two hypotheses remained in presence of each other during the whole of the last century, neither of them gaining any material advantage over the other, though the greater part of mathematicians, following Newton, embraced the emission theory. But at the beginning of the present century, an additional class of phenomena, those of the interference of two rays of light, were brought under con

sideration by Dr Young; and these phenomena were strongly in favour of the undulatory theory, while they were irreconcilable with the hypothesis of emission. If it had not been for the original bias of Newton and his school to the other side, there can be little doubt that from this period light as well as sound would have been supposed to be propagated by undulations; although in this case it was necessary to assume as the vehicle of such undulations a special medium or ether. Several points of the phenomena of vision no doubt remained unexplained by the undulatory theory, as absorption, and the natural colours of bodies; but such facts, though they did not confirm, did not evidently contradict the theory of a Luminiferous Ether; and the facts which such a theory did explain, it explained with singular happiness and accuracy.

But before this Undulatory Theory could be generally accepted, it was presented in an entirely new point of view by being combined with the facts of polarization. The general idea of polarization must be llustrated hereafter; but we may here remark that Young and Fresnel, who had adopted the undulatory heory, after being embarrassed for some time by the new facts which were thus presented to their notice, t last saw that these facts might be explained by coneiving the vibrations to be transverse to the ray, the notions of the particles being not backwards and forwards in the line in which the impulse travels, but to he right and left of that line. This conception of ransverse vibrations, though quite unforeseen, had othing in it which was at all difficult to reconcile ith the general notion of an undulation. We have escribed an undulation, or wave, as a certain condion or arrangement of the particles of the fluid succesvely transferred from one part of space to another : nd it is easily conceivable that this arrangement or ave may be produced by a lateral transfer of the parles from their quiescent positions. This conception transverse vibrations being accepted, it was found at the explanation of the phenomena of polarization d of those of interference led to the same theory