(902.) Now this is precisely what actually happens. The meteors of the 12th-14th of November, or at least the vast majority of them, describe apparently arcs of great circles, passing through or near y Leonis. No matter what the situation of that star with respect to the horizon or to its east and west points may be at the time of observation, the paths of the meteors all appear to diverge from that star. On the 9th-11th of August the geometrical fact is the same, the apex only differing; B Camelopardali being for that epoch the point of divergence. As we need not suppose the meteoric ring coincident in its plane with the ecliptic, and as for a ring of meteors we may substitute an elliptic annulus of any reasonable excentricity, so that both the velocity and direction of each meteor may differ to any extent from the earth's, there is nothing in the great and obvious difference in latitude of these apices at all militating against the conclusion.

(903.) If the meteors be uniformly distributed in such a ring or elliptic annulus, the earth's encounter with them in every revolution will be certain, if it occur once. But if the ring be broken, if it be a succession of groupes revolving in an ellipse in a period not identical with that of the earth, years may pass without a rencontre; and when such happen, they may differ to any extent in their intensity of character, according as richer or poorer groupes have been encountered.

(904.) No other plausible explanation of these highly characteristic features (the annual periodicity, and divergence from a common apex, always alike for each respective epoch) has been even attempted, and accordingly the opinion is generally gaining ground among astronomers that shooting stars belong to their department of science, and great interest is excited in their observation and the further development of their laws. The most connected and systematic series of observations of them, having for their object to trace out their relative paths with respect to the earth, are those of Benzenberg and Brandes, who, by noting the instants and apparent places of appearance and extinction, as well as the precise

apparent paths among the stars, of individual meteors, from the extremities of a measured base line nearly 50,000 feet in length, were led to conclude that their heights at the instant of their appearance and disappearance vary from 16 miles to 140, and their relative velocities from 18 to 36 miles per second, velocities so great as clearly to indicate an independent planetary circulation round the sun. [A very remarkable meteor or bolide, which appeared on the 19th August, 1847, was observed at Dieppe and at Paris, with sufficient precision to admit of calculation of the elements of its orbit in absolute space. This calculation has been performed by M. Petit, director of the observatory of Toulouse, and the following hyperbolic elements of its orbit round the sun are stated by him (Astr. Nachr. 701.) as its result; viz., Semimajor axis = -0.3240083; excentricity=3.95130; perihelion distance = 0·95626; inclination to plane of the earth's equator, 18° 20′ 18′′; ascending node on the same plane, 10° 34′ 48′′; motion direct. According to this calculation, the body would have occupied no less than 37340 years in travelling from the distance of the nearest fixed star supposed to have a parallax of 1′′].

(905.) It is by no means inconceivable that the earth approaching to such as differ but little from it in direction and velocity, may have attached many of them to it as permanent satellites, and of these there may be some so large, and of such texture and solidity, as to shine by reflected light, and become visible (such, at least, as are very near the earth) for a brief moment, suffering extinction by plunging into the earth's shadow; in other words, undergoing total eclipse. Sir John Lubbock is of opinion that such is the case, and has given geometrical formulæ for calculating their distances from observations of this nature.* The observations of M. Petit would lead us to believe in the existence of at least one such body, revolving round the earth, as a satellite, in about 3 hours 20 minutes, and therefore at a distance equal to 2.513 radii of the earth from its center, or 5000 miles above its surface.†

Phil. Mag., Lond. Ed. Dub. 1848, p. 80.

FOR CALCULATING THE DAYS ELAPSED BETWEEN GIVEN DATES. EQUINOCTIAL TIME.

(906). TIME, like distance, may be measured by comparison with standards of any length, and all that is requisite for ascertaining correctly the length of any interval, is to be able to apply the standard to the interval throughout its whole extent, without overlapping on the one hand, or leaving unmeasured vacancies on the other; to determine, without the possible error of a unit, the number of integer standards which the interval admits of being interposed between its beginning and end; and to estimate precisely the fraction, over and above an integer, which remains when all the possible integers are subtracted.

(907). But though all standard units of time are equally possible, theoretically speaking, yet all are not, practically, equally convenient. The solar day is a natural interval which the wants and occupations of man in every state of society force upon him, and compel him to adopt as his fundamental unit of time. Its length as estimated from the departure of the sun from a given meridian, and its next return to the same, is subject, it is true, to an annual fluctuation in excess and defect of its mean value, amounting at its

maximum to full half a minute. But except for astronomical purposes, this is too small a change to interfere in the slightest degree with its use, or to attract any attention, and the tacit substitution of its mean for its true (or variable) value may be considered as having been made from the earliest ages, by the ignorance of mankind that any such fluctuation existed.

*

(908). The time occupied by one complete rotation of the earth on its axis, or the mean sidereal day, may be shewn, on dynamical principles, to be subject to no variation from any external cause, and although its duration would be shortened by contraction in the dimensions of the globe itself, such as might arise from the gradual escape of its internal heat, and consequent refrigeration and shrinking of the whole mass, yet theory, on the one hand, has rendered it almost certain that this cause cannot have effected any perceptible amount of change during the history of the human race; and, on the other, the comparison of ancient and modern observations affords every corroboration to this conclusion. From such comparisons, Laplace has concluded that the sidereal day has not changed by so much as one hundredth of a second since the time of Hipparchus. The mean sidereal day therefore possesses in perfection the essential quality of a standard unit, that of complete invariability. The same is true of the mean sidereal year, if estimated upon an average sufficiently large to compensate the minute fluctuations arising from the periodical variations of the major axis of the earth's orbit due to planetary perturbation (Art. 668.).

(909.) The mean solar day is an immediate derivative of the sidereal day and year, being connected with them by the same relation which determines the synodic from the sidereal revolutions of any two planets or other revolving bodies (Art. 418.). The exact determination of the ratio of the sidereal to the solar day, which is a point of the utmost importance in astronomy, is however, in some degree, complicated by the effect of precession, which renders it necessary

The true sidereal day is variable by the effect of nutation; but the variation (an excessively minute fraction of the whole) compensates itself in a re

to distinguish between the absolute time of the earth's rotation on its axis, (the real natural and invariable standard of comparison,) and the mean interval between two successive returns of a given star to the same meridian, or rather of a given meridian to the same star, which not only differs by a minute quantity from the sidereal day, but is actually not the same for all stars. As this is a point to which a little difficulty of conception is apt to attach, it will be necessary to explain it in some detail. Suppose then the

pole of the ecliptic, and P that of the equinoctial, ABCD the solstitial and equinoctial colures at any given epoch, and Ppqr the small circle described by P about in one revolution of the equinoxes, i. e. in 25870 years, or 9448300 solar days, all projected on the plane of the ecliptic A B C D. Let S be a star anywhere situated on the ecliptic, or between it and the small circle Pqr. Then if the pole P were at

rest, a meridian of the earth setting out from PSC, and revolving in the direction CD, will come again to the star after the exact lapse of one sidereal day, or one rotation of the earth on its axis. But P is not at rest. After the lapse of one such day it will have come into the situation (suppose) p, the vernal equinox B having retreated to b, and the colure PC having taken up the new position pc. Now a conical movement impressed on the axis of rotation of a globe already rotating is equivalent to a rotation impressed