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 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''.
V