These tables show that the further back we go the more nearly the comets of 1677 and 1683, and the three comets of 1860 III., 1863 I., and 1863 VI., are found respectively to approach each other. Have they started simultaneously on their course, or has each had a separate epoch of departure? M. Hoek gives no opinion in favour of either of these hypotheses. Only, he shows that the extremely small difference of 26 inches per second between the initial velocities of the comets of 1677 and 1860 (supposing them to have started together from a distance so great as to be practically infinite, i.e. to have been originally fragments of the same body) would suffice to produce a difference of 200 years in the times of their arrival into our system; it is, therefore, not impossible that the two comets of 1677 and 1860 may have quitted at the same time the focus from which they emanated.

Let us take another example from M. Hoek-comets III. and V. of 1857 and comet III. of 1867. These three comets, in fact, described orbits with elements so similar, and the intervals separating their apparitions were so short, as to point to the probability of a common origin. At first M. Hoek only regarded the two former comets as forming a system, but the comparison of the third with the other two removed all doubt from his mind.

Speaking of the two comets III. and V., 1857, M. Hoek proceeds, 'I did not hesitate to attribute to these two bodies a common origin, considering the extreme resemblance of all the elements of their orbits, and the short interval between their appearance. The comet 1867 III. has just given an unexpected confirmation to this view. The circle which is the intersection of its orbit with the sphere passes through almost the same point of the sky. The planes of the three orbits intersect therefore in the same line, which is necessarily parallel to the direction of the initial motion of the comets.'

The radiant point of their orbits-that point in which their planes intersect each other—is situated in the southern hemisphere, upon the confines of the constellation of Piscis Australis.

This cometary system is not the only one. In the first place, the three comets mentioned above are not the only members of the group, to which must be added the following comets: 1596, 1781 I., 1790 III., 1825 I., 1843 II., and 1863 III., and even 1785 II., 1818 II., 1845 III. The subjoined table sums up the conclusions of the learned astronomer :

In the preceding section we have already said a few words on the origin of comets, a question still involved in much obscurity. We here merely quote from the Monthly Notices of the Royal Astronomical Society* the following summary of the views to which M. Hoek's researches lead:-'Every star is associated with a cometary system of its own; but owing to the attraction of planetary or other cosmical matter, these bodies continually leave their proper primaries, and revolve either permanently in ellipses, or temporarily in parabolas or hyperbolas, round other suns.'

On studying the distribution throughout the celestial sphere of the aphelia of 190 cometary orbits M. Hoek discovered a somewhat curious fact. If we suppose a circle drawn through three points, the respective longitudes of which are 95°, 169°, and 243°, and the latitudes 0°, 32°, and 0°, the sector comprised between this circle and the ecliptic will be found particularly poor in aphelions. Instead of including fifteen, as it would were the distribution uniform, it contains only one, that of the comet of 1585, situated at a distance of three degrees only from the ecliptic. How is this peculiarity to be explained? To this question M. Hoek replies, 'If we knew that the solar system was removing from the point situated in the middle of that sector, I should be inclined to attribute the phenomenon to a difficulty comets might experience in overtaking the sun. But the direction of the solar motion, such as it was given by Mädler's investigations, does not allow of such

*Vol. xxvi., p. 147 (February 1866).

an explanation.* Therefore we may ask if the phenomenon is a real one, and there is in that direction of the heavens a scarcity of centres of cometary emanations; or rather, if it depends on the circumstances under which comets are ordinarily detected, the sector in question being so near the part of the ecliptic occupied by the sun from July to December.'†

The first of these two hypotheses is not in our opinion at all improbable; the labours of Sir John Herschel on the distribution of nebulæ prove that they are disposed very unequally in the different regions of the sky. A similar inequality in the distribution of the nebulous centres from whence the comets emanate would be a fact of the same kind, and one perhaps not without physical connexion with the first. If future observations should establish this connexion, it would add one more gleam of light to those which astronomy has already thrown on the constitution of the universe.

* See on this subject two interesting letters from M. Hoek to M. Delaunay. Comptes rendus de l'Académie des Sciences, 1868, I.

† Monthly Notices of the Royal Astronomical Society, vol. xxvi., p. 207. M. Hoek's other papers are published in vol. xxv., p. 243 (June 1865), vol. xxvi., p. 1 (November 1865), and vol. xxviii., p. 129 (March 1868).—ED.

SECTION V.

COMETARY STATISTICS.

Comparison of the elements of cometary orbits-Eccentricities; numbers of elliptic, parabolic, and hyperbolic comets-Distribution of comets according to their nodes and perihelion distances-Equality of the numbers of direct and retrograde orbits. If we arrange in the order of date the various apparitions of comets that have been recorded, and note how these bodies appear in different regions of the heavens, and how some pursue a direct and others a retrograde course; or, better, if we study their elements in a catalogue, our attention is at once arrested by the diversity of these elements, which seem connected by no relation.

It may, however, be instructive to examine, by comparing these materials, whether any law presides over the distribution of comets in time and space. We shall, therefore, give a rapid résumé of the analysis we have made with this object. We have taken the catalogue published by Mr. Watson at the end of his work on Theoretical Astronomy as the basis of our investigation.

In this catalogue, which we reproduce at the end of this work, we find 279 comets arranged in the order of their successive apparitions, from the most ancient times to the commencement of the year 1867; we have ourselves completed it for the seven following years, including also the first