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: V = v × (sinus [delta] / sinus([gamma] - [delta])) or (Fig. 1), V = da/t'', t'' being the time taken to pass over aa''. [Illustration: V] 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. [Illustration: VI] 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. [Illustration: VII]