a bissextile were suppressed every 4000 years, the difference would be only 0.000014 day, and this would fall within the limits of the errors which may exist in the determination of the length of the year.

19

235

233

228

235

The Council of Nice, by supposing the exactness of the Metonic cycle, in which 19 solar tropical years were considered equal to 235 lunations, or synodical revolutions of the moon, must, consequently, have supposed one lunation to be equal to of a solar year; and the lunar year, or twelve such lunations, to be equal to of the former year; the difference between the two is of the solar year, which, as they considered the latter to contain 365 days exactly, would be equal to 10.8798 days, or nearly 11 days: hence, the epact, as it was called, or the moon's age at the end of any given year being known, it would be easy to ascertain that of any subsequent year, by the continual addition of 11 days to the original epact: thus, if a full moon should take place on the last day of any year, the epact for the next year would be 0; of the second following year, 11; of the third, 22; and of the fourth 3, thirty days being rejected: the epact for the succeeding years would be, respectively, 14, 25, 7; rejecting twenty-nine days from the last; and so on, rejecting alternately, 30 days and 29 days, because the lunation was supposed to be equal to 29 days, and taking care to increase the epact by unity in each bissextile year. The error arising from the excess of the solar, above the lunar year not being exactly 11 days, was corrected, at the end of every lunar cycle, on the supposition that the cycle was correct, by making the epact the same as that of the nineteenth precedent year. But nineteen solar years are equal to 6939.603016 days, and 235 lunations are equal to 6939.6881565 days: the difference between these periods is 0.08514 day, which renders the Metonic cycle erroneous to the amount of one day in about 222 years; consequently, to the amount of above 6 days in the time elapsed since the regulation was established; and the computed day of the Paschall full moon, in the sixteenth century, necessarily differed just as much from the true day. In order, therefore, to keep this full moon to its place in the calendar it was necessary to allow the above rule for the epacts, which was

before perpetual, to hold good only for one hundred years; then, on account of the omission of the bissextile in every hundredth year except that which is a complete thousand, the epact at the end of every century except the tenth, was to be diminished by one day; and, again, on account of the anticipation above mentioned, the epact was to be increased, at the end of every two hundred years, by the same quantity. Tables were computed on this system by Luilius of Verona, and were employed for the purpose of determining the time of Easter, till they were superseded by the ephemerides; in these, the times at which the phases of the moon, as well as the other phenomena of the heavens, will occur, are given with superior accuracy by means of computations from the general tables of the celestial movements, which have, since those days, been brought to vast perfection.

CHAPTER XIX.

THE FIRST TELESCOPIC DISCOVERIES IN THE HEAVENS.

The Composition of forces investigated by Galileo.-Telescopic discoveries of that philosopher.-The practice of notifying discoveries in anagrams.— Persecution of Galileo by the Italian clergy.-The system of Tycho Brahe still supported by some astronomers.-Method of determining the distances and magnitudes of the planets.--System of Bullialdus.—Its improvement by Ward.—Transit of Venus observed by Horrox.-Scepticism of Descartes in philosophy. His hypothesis that the planets revolve in vortices.-Weakness of the theory.-Forms of orbits proposed by Cassini and La Hire.Discoveries of Huygens and Maraldi on Saturn's ring.—Discoveries of Cassini on the rotations of the planets.-Changes in the positions of the aphelia and nodes of planets. Variations in the mean motions of Jupiter and Saturn.

AN important change was now to take place in the philosophy of nature in consequence of the discovery, made by Galileo, of the laws by which material bodies act mechanically on each other. To this great mathematician we are indebted for the theory of the composition of forces, by which is determined the resultant, or equivalent, of forces acting upon bodies in the same or different directions; to him, also, we owe the investigation of the spaces described, the times of description, and the acquired velocities of bodies moving by instantaneous impulses or by the continued action of impelling forces; and the application of the theory, to bodies falling towards the earth by that attractive power with which our planet was known to be endowed. By him, also, was discovered the isochronous motion of pendulums, which has since been of so much importance in the construction of machines for measuring time.

The knowledge man had acquired of the visible heavens, also received many important accessions from the discoveries which Galileo was enabled to make by means of the telescope, then recently invented. Except the sun and moon, not one of the

celestial bodies had hitherto been observed to have any visible form or magnitude; and it was to the eye of reason alone that those appeared to be any thing but plane surfaces: the fixed stars and planets were, alike, known only as luminous and undefined points: but, now, the view of the heavens began to excite a new interest; by the telescope the planets were found to have certain magnitudes, and some of them, to undergo variations of form, while the fixed stars appeared unchanged, or only shorn of the radiance with which they seem to be surrounded when seen by the naked eye: and hence it became obvious that the former must constitute a distinct groupe of bodies infinitely nearer the earth than the others. The sun, from the spots observed on his surface, was found to revolve on its axis and, consequently, was ascertained to be globular; and the light and dark spaces on the moon were distinctly perceived to be mountains and valleys nearly resembling those features on the surface of the earth.

That an instrument should have been invented by which objects, even in the remotest depths of space, are rendered accessible to human vision; and by which terrestrial objects, faintly visible in the distance, are brought, as it were, close to the eye, must have at one time appeared miraculous; but such were the effects produced by the telescope; a tube containing a system of glass lenses, in passing through which, the rays of light coming from an object are turned from their previous directions and made to converge towards the axis, so that the rays proceeding from opposite sides of the object, and entering the eye, form there an angle many times greater than that caused merely by the refractive powers of the eye itself, while the interference of rays coming from surrounding objects is almost wholly prevented; thus is produced an augmentation of the visible magnitude of an object with as small a diminution as possible of its brilliancy, and thereby may be obtained a view of the parts of its surface which would be insensible to the unassisted sight; the object being seen in the telescope just as it would appear to a spectator without one, if situated as much nearer, as the power of the telescope exceeds that of the natural eye. This instrument, in the hands of Galileo, was the means of making more disco

veries in the heavens than had been made during three thousand years previously; and it may be added, if we consider their importance, more than have been made since the days of that philosopher. He relates, in the Sidereus Nuncius, that, in the year 1610, he discovered the four moons or satellites of Jupiter, and observed, also, that these revolve about that planet as our moon revolves about the earth: a circumstance which afforded, by analogy, an argument in favour of the earth's motion about the sun; since Jupiter, a planet known to have a similar motion, was found to be attended by secondary planets which, it was easily perceived, would reflect the sun's light on the primary planet as the moon reflects it on the earth. About the same time, as we learn from his letters at the end of the work above mentioned, Galileo observed that Saturn presented a remarkable appearance; at first it was thought to be accompanied by two smaller planets, one on each side, and the discovery was so announced; but, when telescopes were constructed with superior magnifying powers, what appeared to be secondary planets were found to be portions of a vast annulus which surrounds Saturn without any where touching his surface; and this circumstance, also, contributed, though indirectly, to diminish the confidence hitherto placed in the ancient systems of astronomy, by shewing that there was yet much to learn concerning the planets, and that, to obtain a correct knowledge of the universe, there would be required a more attentive study of their visible phenomena. Soon afterwards, the telescope revealed to the assiduous Florentine that Venus had phases similar to those of the moon; that, when near the sun, she was scen either in the crescent form or with a round orb, and when at her greatest elongations, her disc appeared to be semicircular; and it was observed that her change of form took place exactly in that insensible manner by which the face of the moon increases and diminishes: the agreement of these phenomena with those which would be presented by a globular body revolving about, and receiving its light from another body placed at the centre of motion, rendered it impossible to doubt that Venus revolved, periodically, about the sun, and that she was, like the moon, an opaque and globular mass; it was also evi