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It was the declared opinion of one Bodinus, a learned man of the 16th century, that comets were no other than the souls of illustrious men, who, having remained many ages upon the earth in the capacity of guardian angels, had been called to heaven in the shape of flaming stars. If a comet, instead of being a mere accumulation of nebulous matter, as our philosophy teaches us that it is, were, as Bodinus believed it to be, some bright intelligence interested in the destinies of our race, and commissioned, at stated seasons, to work out the designs of Providence in this nether world, how manifold are the subjects of speculation which we might assign to it, as, after each return, it again and again toiled through the years of its solitary journey.

The comet of 1835, when it came in 1456, was encountered by the anathemas of the whole Catholic Church, headed by the Pope. Dismayed at once by the progress of the Turks and the


of the comet, Calixtus included them both in the same prayer of conjuration ordered to be said in all the churches.

It came again in 1531, and found America discovered, printing invented and in general use, and the Reformation begun*.

1607 again completed its cycle. And now the Copernican system had been published to the world t; the telescope had been discovered; Galileo and Kepler had been born, and had probably laid the foundations of their discoveries, the one in mechanics, and the other in astronomy.

Next came 1682 and the comet, and the laws of motion were ascertained and published to the world; the discoveries of Kepler were made, and Newton had built up upon them the theory of universal gravitation.

1759 was to be the next period of its appearance, and its coming was now, for the first time, foreseen. Halley, afterwards Savilian professor at Oxford, having undertaken to calculate the orbits of the different comets which had, up to that time, been observed, presented, in 1705, to the Royal Society, a work called Comelographia, in which he predicted † the return of the comet of 1682 in 1758, an announcement received in those days with no little surprise and interest. It was, however, immediately foreseen by astronomers, that the path of this comet would be disturbed by the attraction of the planet Jupiter. Lalande and Clairaut undertook to calculate the amount of this disturbance. The work was one of enormous labour, which they would never have undertaken, as Lalande himself admits, had not assistance been rendered to them (strange to say) by a lady. To Madame Lepaute, the wife of a celebrated watch-maker in Paris, was assigned a principal portion of their calculations, and to that lady is due a principal

* This time it was accurately observed by one Apian, a professor of mathematics, at Ingolstadt.

# The great work of Copernicus, De Revolutionibus, was published in 1543.

# His words, translated, are “ Hence I dare venture to foretel that it will return again in 1758.”

share in their success. “During six months we calculated from morning till night, even during meals," says Lalande. They determined the actual perturbations, during 150 years, of Jupiter and Saturn, and they arrived, finally, at the conclusion, that its coming would be delayed no less than 518 days by the attraction of Jupiter, and 100 more days by Saturn. The time of its perihelion passage* was thus brought to 13th April, 1759: it was, nevertheless, stated that errors might have been made amounting to a month either way.

These conclusions Clairaut published to the world in November, 1758, when astronomers had already begun to look for the comet. It was first seen by a farmer of the name of Palitzch, near Dresden, on December 25, 1758, and at Paris, on January 21, 1759. It passed its perihelion on March 13, 1759, just one month after the time predicted.

The comet of 1759 was next to complete its orbit in 1835; and of its appearance in that year an account will shortly be given, when we shall first have answered two questions, which will, no doubt, have suggested themselves to every one who has read so far of this paper. They are these:

How can any prediction of the return of a comet be made? and, supposing such a prediction to be possible, How can it thence be shown that this comet of 1835, is the same with those seen in 1682, in 1607, in 1531, and in 1456?

Before the first of these questions is answered, the reader must be made acquainted with the nature and properties of a certain curve, called by geometers an ellipse. If a fine thread be taken, and its two extremities fastened to two points, s and , fixed on a flat surface, and not so far distant from one another as the thread is long; and if the al thread, which will thus lie loosely between the points, be now stretched by means of a slender pencil to P, and keeping it thus stretched, if the pencil be made to move to q, tracing as it thus moves a line PQ, that line will form part of a curve called an ellipse, the whole of which curve may be described by continuing the motion of the pencil completely round, in the direction PQR. Now the lines sp and pH, added together, are equal to the length of the string; for when the pencil was at p, the string coincided with them, and, for the same reason, the lines sQ and qu are, together, equal to the length of the string, and are, therefore, together equal to sp and Ph added together; and this is the distinguishing property of the ellipse: “ If, from any point in it, lines be drawn to s and 1, the sum of these will always be the same;" thus at R, the sum of the lines Rs and RH is equal to the sum of qs and QH, and Ps and PH.

If now the point u be brought nearer to s than it was before, the length of the string remaining the same, and the curve be then described as before, it will be found to have altered its form, so as more nearly to approach that of a circle, as shown in the second figure, and h may be


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* This terin will be explained in the course of this paper.

brought so near to s, that its form shall scarcely be distinguishable from that of a circle, which figure it would indeed manifestly become, if the point u were made accurately to coincide with s.






Again, if instead of being movei nearer to s the point u be moved further from it, then the ellipse will be found to have assumed a form like that of the third figure, not nearer to, but further from, the form of a circle than it was at first. Ellipses whose foci s and u are near one another, and which, therefore, approximate to circles, are called ellipses of small eccentricity. Ellipses whose foci are further from one another, and which, therefore, deviate more from circles, are called ellipses of greater eccentricity. These curves have been supposed to be described with a piece of thread short enough to be conveniently used for the purpose. But curves may be imagined to be described according to the same law, and having, therefore, the same properties, traversing vast and inaccessible regions of space, and in which dimensions, which we have taken to be inches, are replaced by millions of miles.

The properties of the ellipse have, even from a very remote period *, been the subject of careful study among geometers, and their acquaintance with them is so far perfected, that knowing certain circumstances with regard to any portion of an ellipse, or having certain dala (as it is termed) in respect to that portion of an ellipse, they can tell the form and magnitude of the whole of the ellipse. Having these data of any, the least part, they know certainly what is the whole of the ellipse of which it forms a part.

Now, four observations upon one of the heavenly bodies, describing an ellipset, are sufficient to give an observer at the earth's surface, these data. Thus then four observations tell him what is the ellipse, which, if it describe an ellipse, a comet is describing. Now, knowing the form and magnitude of the ellipse, he can further, by another known process of calculation, tell all the circumstances of the comet's motion in it; and if it really move in an ellipse, he can, therefore, tell beforehand, what place it will occupy in it, after any given time.

Suppose him to have done this, and to wait until that time, and again then to observe it. If his observations agree with the prediction, he will

Apollonius Pergæus, the author of a most learned treatise on the curves, called Conic Sections. of which number is the ellipse, flourished in the second century before Christ.

+ A comet can only be seen by us when it is describing that portion of its elongated orbit which is nearest the sun; now this portion of its orbit coincides very nearly with the corresponding portion of a certain other curve, called a parabola, and three observations are sufficient on the supposition that it is a parabola.


know that he was right in supposing the comet to describe an ellipse-and that particular ellipse. Now, observations of this kind have for the last two centuries been made upon all the comets which have appeared, one hundred and thirty in number, and the observations on each have been repeated so as to verify one another in a great variety of different ways; and the conclusion from all has been the same; viz., that those portions of their orbits, which the comets are describing when within our sight, are ellipses *; ellipses which have all of them the sun for their focus, or rather, for one of their foci,—and that the other focus is infinitely far off, beyond the limits of the orbit of the most distant of the planets. Moreover, that all these ellipses are of the kind which we have described as of great eccentricity, or deviating greatly from circles. Now, similar observations applied to the planets of our system, show them also to describe ellipses, having, too, the sun in one of the foci of each ellipse ; but those ellipses are of exceedingly small eccentricities, or they approximate very nearly to circles.

But the elliptic orbit of a comet may lie in an infinite variety of positions in respect to the sun, and yet in all these have. its focus in the sun. The length of the ellipse may lie one way or another, to the right or the left of a line drawn, for instance, from the sun to a particular star, or at any angular distance from that line, or having its plane inclined, at one angle or another, to the plane of the orbit which our earth describes round the sun; and all these things we are required to know, before we can fix what is the precise path in space along which the comet goes. They are called the elements of its orbit. And on the other hand, knowing these, we do know precisely the curved line which through the years, perhaps centuries, of each of its revolution, the comet is describing through the fields of space. Nay more, we can tell precisely what part of that path it is at any given time describing; the inward eye remains, as it were, fixed upon it, long after it is beyond the reach of the most powerful telescopes. We can tell when it will slowly reach its greatest distance from the sun, or its aphelion, as it is called. Somewhere, perhaps, double or treble the distance of Uranus from us; and we can tell precisely when it will go through its perihelion, or that extremity of its orbit in which it is nearest to the sun and to us. Now these other elements of a comet's orbit may all be determined from the same four observations which ascertained its form and its magnitude.

These things have been calculated in respect to one hundred and thirty-three comets, which have appeared at different periods of the two last centuries, and of one hundred and thirty of these no two are found to describe the same orbit,—no two of them are, then, different returns of the same comet. But if two comets, appearing at different periods, had on examination been found to be describing, one of them at one period the same path in space, which the other did at the other period ; if, moreover, the actual motion of the first comet, known from a previous knowledge of its orbit, ought to bring it precisely to that point of its orbit, where the second comet was, at the time or near about the time when it was seen there, then we should have known that the two comets were, in fact, one and the same comet.

* This observation will in the course of this paper be qualified.

Now, although out of one hundred and thirty, no two have thus been found to be the same; yet in the whole number, one hundred and thirtythree observed, there were three, the identity of which with three others was established. Of these, one is the comet of 1835, or 1759, called Halley's comet, because he first established its identity with the comet of 1682, 1607, and 1531; another is the comet called, for a similar reason, the comet of Encke, and the third is the comet of Biela; the first has a period of about seventy-six years, the second of three years and three-tenths, and the third of seven years and three quarters.

Thus, then, we know that there are at least one hundred and thirty different comets revolving continually about the sun, that number of different comets having been seen during the last two hundred years.

None of these, except three, have as yet had time to return to us; these three have returned severally at their appointed periods. How

many other comets there may be, or what is the whole number of bodies which compose the cometary, as distinguished from the planetary, system of our sun, we know not. Comets have been observed by astronomers only during the two last centuries; one hundred and thirty different ones have during that time been seen, and more are continually discovered, as instruments are perfected and observations multiplied*. Nevertheless, hundreds may, during this period, have escaped observation. Because of their distance, the faintness of their light, or because we cannot observe the heavens in the day, they traverse them so rapidly, that long before the period of the year when that portion of the sky in which they move becomes visible, they are gonet. The comet of Biela could only be found by Sir John Herschel, “ with a reflecting telescope of twenty feet in length, an instrument of enormous power in the collection of light.” What shall we say then of the number and variety of the cometary bodies, which might have been discovered, had we instruments of greater power, were our observations more numerous, and carried back through a greater distance; or what shall we say of the possible number of cometary bodies which may be discovered during the two next centuries? It is quite within the bounds of possibility, that the number of the different comets, revolving continually round the sun, may amount to thousands.

Those which are known to us have their orbits lying in every conceivable position in space, subject all, however, to the condition, that one of their foci is occupied by the sun; they have their planes inclined to one another, and to the plane of the earth's orbit, at every possible angle up to ninety degrees, and the lengths of their orbits are directed towards any and every point in space; moreover, and this is a singular fact, they have the directions of their motion some one way and some another. Thus, one comet revolves in its orbit eastward, and another westward. Moreover, by reason of the elongated forms of their orbits, and their various directions in space, these orbits are made continually to cross one another, and the orbits of the planets, and comets are thus frequently brought into such positions,

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Scarcely a year passes in which one or more new comets are not discovered.

+ It is related by Seneca, that during a great solar eclipse, sixty years B, C., a large comet was seen near the sun.

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