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: