plane in opposite directions, has been called an entire undulation, and to each of its halves excited by these opposite oscillations, the name of semiundulation has been given; of which the whole may be styled a complete oscillation, since it comprises the return of the vibrating plane to the point of departure, We see that the two demi-undulations which compose the complete undulation, present in the fluid sections which they embrace, velocities absolutely equal as to magnitude, but which are of contrary signs, that is to say, which carry the molecules of the fluid in opposite directions. These velocities are at their maximum in the middle of each of these semi-undulations, and decrease gradually to their extremities, where they fall to zero. Thus the points of repose and of greatest positive or negative velocity, are separated by intervals of a quarter undulation.

The length d of an undulation depends on two things: 1. On the promptitude with which the movement is propagated in the fluid; 2. On the time of the complete oscillation of the vibrating plane; for the longer its duration, and the more rapid the propagation of the motion, the farther will the first disturbance extend from the solid plane at the moment when this returns to its point of departure. If the undulations are performed in the same medium, the promptitude of the propagation remaining the same, the length of the undulations will be proportional to the time of the oscillations of the vibrating particles that give them birth. While the vibrating particles continue subject to

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the same forces, the laws of mechanics demonstrate that each of their small oscillations has always the same duration, whatever may be its amplitude. Thus the correspondent oscillations will have in this case, the same length; they will differ merely by the greater or less energy of the oscillations of the fluid sections, whose amplitude will be proportional to that of the oscillations of the illuminating particles; for we see, from what has been stated, that each section of the fluid repeats all the movements of the vibrating molecule. The greater or less amplitude of the oscillations of the sections of the fluid, determines the degree of absolute velocity with which they move, and of consequence the energy, but not the nature of the sensation, which must depend, according to every analogy, on the time of these oscillations. It is thus that the nature of the sounds which the air transmits to our ear depends solely on the time of each of the oscillations performed by the air, or by the sonorous body, which sets it a vibrating; and that the greater or less amplitude, or energy of these oscillations, does nothing more than augment or diminish the intensity of the sound, without changing its nature, namely, its pitch or tone.

The intensity of light, therefore, will depend on the intensity of the vibrations of the ether; and its nature, that is to say, the sensation of colour which it produces, will depend on the duration of each oscillation, or on the length of the undulation, since the one is proportional to the other.

On this principle, the intensity of light must decrease in the ratio of the square of the distance

from the luminous point. rupted series of luminous system of undulations.

A regular and uninterundulations, is called a

The length of d, or one undulation, for red light, is one forty thousandth of an inch; and for violet light, about one sixty-four thousandth; and proportionally for the intermediate colours. From the prodigious rapidity of the luminous vibrations, it is natural to suppose, that the illuminating particles may execute a very great number of regular oscillations in each of the different mechanical circumstances, in which they are placed, during the combustion or incandescence of the luminous body, although these variable circumstances succeed each other undoubtedly with an extreme promptitude. The millionth part of a second is sufficient for the production of 545 thousand undulations of the yellow light. Hence the mechanical perturbations which derange the regular succession of the vibrations of the illuminating particles, or even change their nature, might be repeated at each thousandth of a second, as it could still perform in the intervals more than 500 millions of regular and consecutive undulations. This observation serves to determine the circumstances in which the interferences of the luminous waves can or cannot exhibit sensible effects to our eyes.

We have seen that every wave produced by an oscillatory movement, was composed of two semiundulations, which impressed on the molecules of the fluid, velocities absolutely equal as to intensity, but opposite as to the sign or direction of the movement. Let us suppose, first of all, that two entire

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waves, moving with the same sign, and in the same direction, differ by a semi-undulation in their march. They will now apply to each other only over the half of their length, or half the interval between the first and last point of the fluid set in motion. There will be an interference only between the second half of the wave furthest in advance, and the first half of the other. If these two half waves are of equal intensity, as they bring to the same points of the ether, directly opposite impulsions, they will be mutually neutralised, and the movement will be destroyed throughout this portion of the fluid; but the movement will subsist without alteration in the two other semi-undulations. Hence, only one half of the movement will be destroyed.

Let us now suppose that every one of these two waves which differ in their route by a semi-undulation, is preceded and followed by a great number of other similar waves; then instead of the interference of two insulated waves, we shall have to consider the interference of two systems of waves. Suppose them equal, both in the number of waves that they contain, and in their intensity. Since, by hypothesis, they differ by a semi-undulation in their pace, the half waves of the one which tend to propel the molecules of the ether forwards, coincide with the half waves of the other which tend to - propel them backwards, and they are in equilibrium of force. Hence the movement will be destroyed through the whole extent of the two systems of waves, excepting the two extreme half waves, which escape from the interference. But as these form a very small portion of the systems of waves, we per

ceive that almost the whole of the movement must be annihilated.

It is extremely probable that the single impulse of a luminous semi-undulation, or even of an entire undulation, is not sufficient to irritate the fibres of the optic nerves, just as a single sonorous wave cannot put in vibration the bodies which might vibrate to its unison. It is the succession of these waves, which, by the continual addition of their minute partial effects, causes the sonorous body finally to oscillate in a perceptible manner, just as the regular succession of very inconsiderable impulses eventually sets the heaviest bell a vibrating. On applying to vision this admitted principle, which is most natural, and most conformable to every analogy, we see that the two residuary half waves mentioned above cannot affect the retina in a sensible manner, and that the combination of these two systems of luminous waves, must therefore realise the state of complete darkness.

If we retard, by a semi-undulation, the one system of waves, which is already that quantity in arrear, the difference of pace being thus an entire undulation, the coincidence between the movements of the two groupes of waves will be restored, and the velocities of oscillation will become additive throughout all the points of their mutual superposition. The intensity of the light is now at its maximum, or is doubled.

If we still retard by a semi-undulation the same system of waves, the difference of route being now an undulation and a half, we perceive that the super-position takes place between the half waves