I. - If we throw a stone into the water, a wave will be produced that will extend in a circle. The size of this wave and the velocity with which it extends depend upon the size of the stone, that is to say, upon the intensity of the mechanical action that created it. The extent and depth of the water are likewise factors.
If we cause a cord to vibrate in the water, we shall obtain a succession of waves, the velocity and size of which will be derived from the cord's size and the intensity of its action. These waves, which are visible upon the surface, constitute what I shall call mechanical waves. But there will be created at the same time other waves, whose velocity of propagation will be much greater than that of the mechanical ones, and apparently independent of mechanical intensity. These are acoustic waves. Finally, there will doubtless be created optical waves, whose velocity will exceed that of the acoustic ones. That is to say, if a person fell into water from a great height, and all his senses were sufficiently acute, he would first perceive a luminous sensation when the first optical wave reached him, then he would perceive the sound produced, and later still he would feel, through a slight tremor, the mechanical wave.6
Under the action of the same mechanical energy there form, then, in a mass of fluid, waves that vary in nature, intensity, and velocity of propagation; and although but three modes appreciable to our senses have been cited, it does not follow that these are the only ones possible.
We may remark, again, that if we produce a single wave upon water, it will be propagated in a uniform motion, and will form in front of it successive waves whose velocity of propagation is accelerated.
This may explain why sounds perceived at great distances are briefer than at small ones. A detonation that gives a quick dead sound at a few yards is of much longer duration, and softer at a great distance.
The laws that govern the system of wave propagation are, then, very complex.
II. - If an obstacle be in the way of the waves, there will occur in each of them an alteration, a break, which it will carry along with it to a greater or less distance. This succession of alterations forms a trace behind the obstacle, and in opposition to the line of the centers. Finally, if the obstacle itself emits waves in space that are of less intensity then those which meet it, these little waves will extend in the wake of the large ones, and will form a trace of parabolic form situated upon the line of the centers.
Let us admit, then, that the sun, through the peculiar energy that develops upon its surface or in its atmosphere, engenders in ethereal space successive waves of varying nature and intensity, as has been said above, and let us admit that its mechanical waves are traversed obliquely (Fig. 1) by any spherical body - by a comet, for example; then, under the excitation of the waves that it is traversing, and through its velocity, the comet will itself enter into action, and produce mechanical waves in its turn. As the trace produced in the solar waves consists of an agitation of the ether on such trace, it will become apparent, if we admit that every luminous effect is produced by an excitation - a setting of the ether in vibration. The mechanical waves engender of themselves, then, an emission of optical waves that render perceptible the alteration which they create in each other.
Let a be the position of the comet. The altered wave, a, will carry along the mark of such alteration in the direction a b, while at the same time extending transversely the waves emitted by the comet. During this time the comet will advance to a', and the wave will be altered in its turn, and carry such alteration in the direction, a' b'.
The succession of all these alterations will be found, then, upon a curve a'' d' d, whose first elements, on coming from the comet, will be upon the resultant of the comet's velocity, and of the propagation of the solar waves. Consequently, the slower the motion of the comet, with respect to the velocity of the solar waves, the closer will such resultant approach the line of centers, and the more rectilinear will appear the trace or tail of the comet.
IV. - If the comet have satellites, we shall see, according to the relative position of these, several tails appear, and these will seem to form at different epochs. If c and s be the positions of a comet and a satellite, it will be seen that if, while the comet is proceeding to c', the satellite, through its revolution around it, goes to s', the traces formed at c and s will be extended to d and d', and that we shall have two tails, c' d and s' d', which will be separated at d and d' and seem to be confounded toward c' s'.
V. - When the comet recedes from the sun, the same effect will occur - the tail will precede it, and will be so much the more in a line with the sun in proportion as the velocity of the solar waves exceeds that of the comet.
If we draw a complete diagram (Fig. 4), and admit that the alteration of the solar waves persists indefinitely, we shall see (supposing the phenomenon to begin at a) that when the comet is at a 1, the tail will and be at a 1 b; when it is a 2 the tail will be at a 2 b'; and when it is at a 4, the tail will have become an immense spiral, a 4 b'''. As in reality the trace is extinguished in space, we never see but the origin of it, which is the part of it that is constantly new - that is to say, the part represented in the spirals of Fig. 4.
The comet of 1843 crossed the perihelion with a velocity of 50 leagues per second; it would have only required the velocity of the solar waves' propagation to have been 500 leagues per second to have put the tail in a sensibly direct opposition with the sun.
Knowing the angle γ (Fig. 5) that the tangent to the orbit makes with the sun at a given point, and the angle δ of the track upon such tangent, as well as the velocity v of the comet, we can deduce therefrom the velocity V of the solar waves by the simple expression:
V = v × (sinus δ / sinus(γ - δ)) or (Fig. 1),
V = da/t'',
t'' being the time taken to pass over aa''.
VI. - The tail, then, is not a special matter which is transported in space with the comet, but a disturbance in the solar waves, just as sound is an atmospheric disturbance which is propagated with the velocity of the sonorous wave, although the air is not transported. The tail which we see in one position, then, is not that which we see in another; it is constantly renewed. Consequently, it is easy to conceive how, in as brief a time as it took the comet of 1843 to make a half revolution round the sun, the tail which extended to so great a distance appeared to sweep the 180° of space, while at the same time remaining in opposition to the great luminary.
The spiral under consideration may be represented practically. If to a vertical pipe we adapt a horizontal one that revolves with a certain velocity, and throws out water horizontally, it will be understood that, from a bird's eye view, the jet will form a spiral. Each drop of water will recede radially in space, the spiral will keep forming at the jet, and if, through any reason, the latter alone be visible, we shall see a nearly rectilinear jet that will seem to revolve with the pipe.
Finally, if the jet be made to describe a curve, m n (Fig. 4), while it is kept directed toward the opposite of a point, c, the projected water will mark the spiral indicated, and this will continue to widen, and each drop will recede in the direction shown by the arrows.
VII. - It seems to result from this explanation that all the planets and their satellites ought to produce identical effects, and have the appearance of comets. In order to change the conditions, it suffices to admit that the ethereal mass revolves in space around the sun with a velocity which is in each place that of the planets there; and this is very reasonable if, admitting the nebular hypothesis, we draw the deduction that the cause that has communicated the velocity to the successive rings has communicated it to the ethereal mass.
The planets, then, have no appreciable, relative velocity in space, and for this reason do not produce mechanical waves; and, if they become capable of doing so through a peculiar energy developed at their surface, as in the case of the sun, they are still too weak to give very perceptible effects. The satellites, likewise, have relatively too feeble velocities.
The comet, on the contrary, directly penetrates the solar waves, and sometimes has a relatively great velocity in space. If its proper velocity be of directly opposite direction to that of the ethereal mass's rotation, it will then be capable of producing sufficiently intense mechanical effects to affect our vision.
VIII. - Finally, seeing the slight distances at which these stars pass the sun, the attraction upon the comet and its satellites may be very different, and the velocity of rotation of the latter, being added to or deducted from that of the forward motion, there may occur (as in the case shown in Fig. 6) a separation of a satellite from the principal star. The comet then appears to separate into two, and each part follows different routes in space; or, as in Fig. 7, one of the satellites may either fall into the sun or pursue an elliptical orbit and become periodical, while the principal star may preserve a parabolic orbit, and make but one appearance. - A. Goupil.
Certain persons, as well known, undergo an optical impression under the action of certain sounds.