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30° 4' *, and quite within reasonable limits of resemblance. But how does this agree with the longer period of 175 years before assigned? To reconcile this we must suppose that these 175 years comprise at least eight returns of the comet, and that in effect a mean period of 2F-875 must be allowed for its return. Now it is worth remarking that this period calculated backwards from 1843*156 will bring us upon a series of years remarkable for the appearance of great comets, many of which, as well as the imperfect descriptions we have of their appearance and situation in the heavens, offer at least no obvious contradiction to the supposition of their identity with this. Besides those already mentioned as indicated by the period of 175 years, we may specify as probable or possible intermediate returns, those of the comets of 1733 ?f, 1689 above-mentioned, 1559?, 1537fc 1515§, 1471, 1426, 1405-6, 1383, 1361, 13401|, 1296, 1274, 1230 f, 1208, 1098, 1056, 1034,1012',*,990?tt,925?,858??,684tt. 552, 530 §§, 421, 245 or 2471|||, 180Iff, 158. Should this view of the subject be the true one, we may expect its return about the end of 1864 or beginning of 1865, in which event it will be observable in the Southern Hemisphere both before and after its perihelion passage.*

• United States Gazette, May 29. 1843. Considering that all the observations lie near the descending node of the orbit, the proximity of the comet at that time to the sun, and the loose nature of the recorded observations, no doubt almost any given inclination might be deduced from them. The true test in such cases is not to ascend from the old incorrect data to elements, but to descend from known and certain elements to the older data, and ascertain whether the recorded phenomena can be represented by them (perturbations included) within fair limits of interpretation. Such is the course pursued by Clausen.

t P. Passage 1733-781. The great southern comet of May 17th seems too early in the year.

t P. P. 1536906. In January 15S7, a comet was seen in Pisces.

§ P. P. 1515-031. A comet predicted the death of Ferdinand the Catholic He died Jan. 23. 1515.

|| P.P. 1.14 0-031. Evidently a southern comet, and a very probable appearance.

1 P. P. 1230-656, was perhaps a return of Halley's.

** P. P. 1011-906. In 1012, a very great comet in the southern pnrt of the heavens. "Son eclat blessait les yeui." (Pingre Com£tographie, from whom all these recorded appearances are taken.)

ff P. P. 990031. "Comete fort epouvantable," tome year between 989 and 998.

}J P. P. 683 781. In 684, appeared two or three comets. Dates begin to be obscure.

§§ Two distinct comets (one probably the comet of Cassar and 1680) appeared in 530 and 531, the former observed in China, the latter in Europe.

HII P. P. 246-281; both southern comets of the Chinese annals. The year of one or other may be wrong.

«,«, P. P. 180-656. Nov6. *.o. 180. A southern comet of the Chinese annals.

(596.) M. Clausen, from the assemblage of all the observations of this comet known to him, has calculated elliptic elements which give the extraordinarily short period of 6*38 years. And in effect it has been suggested that a still further subdivision of the period of 21 "875 into three of 7'292 years would reconcile this with other remarkable comets. This seems going too far, but at all events the possibility of representing its motions by so short an ellipse will easily reconcile us to the admission of a period of 21 years. That it should only be visible in certain apparitions, and not in others, is sufficiently explained by the situation of its orbit.

(597.) We have been somewhat diffuse on the subject of this comet, for the sake of showing the degree and kind of interest which attaches to cometic astronomy in the present state of the science. In fact, there is no branch of astronomy more replete with interest, and we may add more eagerly pursued at present, inasmuch as the hold which exact calculation gives us on it may be regarded as completely established; so that whatever may be concluded as to the motions of any comet which shall henceforward come to be observed, will be concluded on sure grounds and with numerical precision ; while the improvements which have been introduced into the calculation of cometary perturbation, and the daily increasing familiarity of numerous astronomers with computations of this nature, enable us to trace their past and future history with a certainty, which at the commencement of the present century could hardly have been looked upon as attainable. Every comet newly discovered is at once subjected to the ordeal of a most rigorous enquiry. Its elements, roughly calculated within a few days of its appearance, are gradually approximated to as observations accumulate, by a multitude of ardent and expert computists. On the least indication of a deviation from a parabolic orbit, its elliptic

• Clausen, Astron. Nachr. No. 485.
n ■ 3

elements become a subject of universal and lively interest and discussion. Old records are ransacked, and old observations reduced, with all the advantage of improved data and methods, so as to rescue from oblivion the orbits of ancient comets which present any similarity to that of the new visitor. The disturbances undergone in the interval by the action of the planets are investigated, and the past, thus brought into unbroken connexion with the present, is made to afford substantial ground for prediction of the future. A great impulse meanwhile has been given of late years to the discovery of comets by the establishment in 1840*, by his late Majesty the King of Denmark, of a prize medal to be awarded for every such discovery, to the first observer, (the influence of which may be most unequivocally traced in the great number of these bodies which every successive year sees added to our list,) and by the circulation of notices, by special letter f, of every such discovery (accompanied, when possible, by an cphemeris), to all observers who have shown that they take an interest in the enquiry, so as to ensure the full and complete observation of the new comet so long as it remains within the reach of our telescopes.

(598.) It is by no means merely as a subject of antiquarian interest, or on account of the brilliant spectacle which comets occasionally afford, that astronomers attach a high degree of importance to all that regards them. Apart even from the singularity and mystery which appertains to their physical constitution, they have become, through the medium of exact calculation, unexpected instruments of enquiry into points connected with the planetary system itself, of no small importance. We have seen that the movements of the comet of Encke, thus minutely and perseveringly traced by the eminent astronomer whose name is used to distinguish it, has afforded ground for believing in the presence of a resisting medium filling the whole of our system. Similar enquiries, prosecuted in the cases of other periodical comets, will extend, confirm, or modify our conclusions on this head. The per

* Sep the announcement or this institution in Astron. Nachr. No. 400.
t By Prof. Schumacher, Director of the Royal OlKcrTatory of Altona.

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turbations, too, which comets experience in passing near any of the planets, may afford, and have afforded, information as to the magnitude of the disturbing masses, which could not well be otherwise obtained. Thus the approach of this comet to the planet Mercury in 1838 afforded an estimation of the mass of that planet the more precious, by reason of the great uncertainty under which all previous determinations of that element laboured. Its approach to the same planet in the present year (1848) will be still nearer. On the 22d of November their mutual distance will be only fifteen times the moon's distance from the earth.

(599.) It is, however, in a physical point of view that these bodies offer the greatest stimulus to our curiosity. There is, beyond question, some profound secret and mystery of nature concerned in the phenomenon of their tails. Perhaps it is not too much to hope that future observation, borrowing every aid from rational speculation, grounded on the progress of physical science generally, (especially those branches of it which relate to the ajtherial or imponderable elements), may ere long enable us to penetrate this mystery, and to declare whether it is really matter in the ordinary acceptation of the term which is projected from their heads with such extravagant velocity, and if not impelled, at least directed in its course by a reference to the sun, as its point of avoidance. In no respect is the question as to the materiality of the tail more forcibly pressed on us for consideration, than in that of the enormous sweep which it makes round the sun in perihelio, in the manner of a straight and rigid rod, in defiance of the law of gravitation, nay, even of the received laws of motion, extending (as we have seen in the comets of 1680 and 1843) from near the sun's surface to the earth's orbit, yet whirled round unbroken; in the latter case through an angle of 180° in little more than two hours. It seems utterly incredible that in such a case it is one and the same material object which is thus brandished. If there could be conceived such a thing as a negative shadow, a momentary impression made upon the luminiferous octher behind the comet, this would represent in some degree the conception such a phenomenon irresistibly calls up. But this is not all. Even such an extraordinary excitement of the aether, conceive it as we will, will afford no account of the projection of lateral streamers; of the effusion of light from the nucleus of a comet towards the sun; and its subsequent rejection; of the irregular and capricious mode in which that effusion bas been seen to take place; none, of the clear indications of alternate evaporation and condensation going on in the immense regions of space occupied by the tail and coma, — none, in short, of innumerable other facts which link themselves with almost equally irresistible cogency to our ordinary notions of matter and force.

(600.) The great number of comets which appear to move in parabolic orbits, or orbits at least undistinguishable from parabolas during their description of that comparatively small part within the range of their visibility to us, has given rise to an impression that they are bodies extraneous to our system, wandering through space, and merely yielding a local and temporary obedience to its laws during their sojourn. What truth there may be in this view, we may never have satisfactory grounds for deciding. On such an hypothesis, our elliptic comets owe their permanent denizenship within the sphere of the sun's predominant attraction to the action of one or other of the planets near which they may have passed, in such a manner as to diminish their velocity, and render it compatible with elliptic motion. * A similar cause acting the other way, might with equal probability, give rise to a hyperbolic motion. But whereas in the former case, the comet would remain in the system, and might make an indefinite number of revolutions, in the latter it would return no more. This may possibly be the cause of the exceedingly rare occurrence of a hyperbolic comet as compared with elliptic ones.

(601.) All the planets without exception, and almost all the satellites, circulate in one direction. Retrograde comets, however, are of very common occurrence, which

* The velocity in an ellipse is always less than in a parabola, at equal distances from the sun ; in an hyperbola always greater.

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