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.[1]
[Footnote 1: Certain persons, as well known, undergo an optical
impression under the action of certain sounds.]
[Illustration: I]
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.
[Illustration: II]
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.
[Illustration: III]
III.--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.
[Illustration: IV]
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 [gamma] (Fig. 5) that the tangent to the orbit makes
with the sun at a given point, and the angle [delta] 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: