instances of considerable duration. The same is true of the nebulæ, which are distinguished from comets by the fact of their immobility. Hence comet-seekers have only to pursue a method analogous to that which astronomers follow for the discovery of small planets.

Comets, on the contrary, have a motion of their own, a motion oftentimes of great rapidity; we can see that they perceptibly change their places from day to day, and sometimes hour by hour, amongst the constellations. This move

ment they have in common with the planets, and it is due, as we are about to see, to the same

causes.

In the first place, to confine ourselves to the real movement of a celestial body and its gradual change of place in space. Let us for a moment suppose the earth at rest. The

Fig. 5.-Proper motion of a Comet; dis- observer situated on its surface tinction between a Comet and a Nebula. would in that case see the body in motion gradually overtake and pass the different stars in its course, and describe upon the concave sphere of the heavens a curve whose form, position, and apparent dimensions would depend upon the actual path of the body, and its velocity of motion. For example, the moon, which describes an oval-shaped curve or ellipse around the earth, in about a month would appear to describe a great circle in the heavens from west to east. The planets Mercury and Venus, which revolve about the sun, and describe closed orbits differing more or less from a circle, but enclosed by the earth's orbit, would appear to move from one side to the other of the central luminary of our system, oscillating periodically to the

east and west of it. The superior planets, Mars, Jupiter, and Saturn, as seen from the earth, would make the tour of the heavens in unequal periods of time, because these planets describe orbits exterior to that of the earth, and the actual time of their revolution depends upon the dimensions of their orbits.

But this simplicity of motion does not exist for an observer situated upon the earth, and for the following reasons.

The real and regular motion of the planets becomes combined with the motion of the earth; in the interval of a year our globe itself moves likewise round the sun in a closed curve or orbit differing but slightly from a circle; in fact, our earth moves in an ellipse whose focus is the sun. This displacement of the earth, it will be readily understood, has the effect of complicating the apparent motion of the planets; that is, their change of position upon the starry vault. Sometimes this motion appears accelerated, as will naturally happer. when the planet and the earth are describing arcs in opposite directions; the two velocities are then added together, just as to a traveller in a railway train a second train, moving in the contrary direction, appears to pass with a speed equal to the sum of the velocities. But should the two trains be moving in the same direction, they then separate with a speed equal to the difference only of their velocities; and if the velocities are equal, each appears to the other motionless. This is what occurs in the case of the planets as seen from the earth; for we observe that their velocities sometimes decrease and become nil, in which case the planet is to all appearance stationary among the stars; and at other times it appears to retrograde.

Thus these effects admit of a very simple explanation. They are merely the result of the combination of the respective movements of the planet and of the earth in their orbits. Whatever may be the true orbit of a comet in the heavens, its

apparent path will always be modified by the continual change of position of our earth.

In order, then, to determine the orbit of a comet we must take into account the motion of the earth in its orbit during the time of the comet's apparition. The stationary periods and retrogressions-although, as we have seen, admitting of a most simple explanation-long embarrassed astronomers; but when the true system of the universe was discovered by Copernicus, and more fully developed by Kepler, these apparent complications of the celestial movements, which had always been stumbling-blocks in the way of the erroneous systems, became so many striking confirmations of the true theory.

Difficulties analogous in kind, but much more numerous and grave, long prevented astronomers from discovering the true nature of comets and the laws which regulate their movements. We shall now see why.

SECTION III.

IRREGULARITIES IN THE MOTIONS OF COMETS.

Coniets appear in all regions of the heavens-Effects of parallax-Apparent motion of a comet, in opposition and in perihelion, moving in a direction opposite to the earth-Hypothetical comet of Lacaille; calculations of Lacaille and Olbers concerning the maximum relative movement of this hypothetical comet and the earth.

THE orbits which the planets describe about the sun are not circles, but oval curves, termed ellipses; these ellipses differ but little from circles; that is to say, their eccentricities are small. Moreover, the planes of the orbits in which they move are inclined at small angles to the plane of the ecliptic. Hence it follows that their apparent paths are confined to a comparatively narrow zone of the heavens, which zone is called the zodiac. If we imagine these curves pressed down, as it were, upon the ecliptic they will appear as nearly concentric circles described about the sun, and so disposed as not to intersect each other. The distances of the earth and of each of the planets vary according to the position occupied by these bodies in their respective orbits; but these variations are confined within very narrow limits, and hence it follows that the velocities of the planets change so slightly that the difference is all but imperceptible. The mean diurnal motion of Mercury, which of all the planets moves the most rapidly, amounts to only 4°5'.

With comets the case is very different. These bodies, as we

have seen, are restricted to no region of the starry vault, and traverse the heavens in all directions, and with very different velocities. The third comet of 1739, and the comet of 1472, mentioned by Pingré, described in a single day, the first an arc of 120 degrees that is to say, the third part of the whole celestial circumference-the second, an arc of 41 degrees and a half in longitude and nearly 4 degrees in latitude. Their real movement was, it is true, in a direction contrary to that of the earth, so that their apparent velocities were in both cases made up of the sum of their own and the earth's velocity combined. Here, then, we have an instance of what is called parallax; that is to say, the apparent movement of the object is affected by the observer's own displacement. We might multiply examples of a similar kind, but the following will suffice. The comet of 1729,' says Lalande, 'observed by Cassini during several months, after advancing more than 15 degrees towards the west from the head of Equuleus to the constellation Aquila, suddenly curved round to retrace its path towards the east, thus showing in a very striking manner the effect of the annual parallax.'

These rapid movements are produced by very simple causes, the most important of which are the near proximity of the comet to our globe, and the direction of its movement in relation to that of the earth. The following is a supposititious case, imagined by Lacaille, in which the apparent angular velocity of a comet would be enormous.

This astronomer supposes a comet to be moving in a direction. contrary to that of our globe, and in the plane of the ecliptic; it is in perihelion, or at its least distance from the sun, and consequently at that point of its orbit in which its velocity is at its maximum. At the same time the earth is supposed to be in perihelion, and is also moving in its orbit with its greatest velocity. Lastly, the comet is to be not more distant from the earth than the moon, and it is to be in opposition. It is, of