This diagram not only exhibits the course of the comet at its last return, but also denotes its future positions on the first day of every year during its next revolution. It is also apparent that it will return to its perihelion again in the autumn of 1839, but not so immediately in our vicinity as to be the proper cause of alarm. To be able to predict the very day and circumstances of the return of such a bodiless and eccentric wanderer, after the lapse of so many years, evinces a perfection of the astronomical calculus that may justly challenge our admiration.

"The re-appearance of this comet," says Herschel, whose return in 1832 was made the subject of elaborate calculations by mathematicians of the first eminence, did not disappoint the expectation of astronomers. It is hardly possible to imagine any thing more striking than the appearance, after the lapse of nearly seven years, of such an all but imperceptible cloud or wisp of vapour, true, however, to its predicted time and place, and obeying laws like those which regulate the planets."

Herschel, whose Observatory is at Slough, England, observed the daily progress of this comet from the 24th of September, until its disappearance, compared its actual position from day to day with its calculated position, and found them to agree within four or five minutes of time in right ascen sion, and within a few seconds of declination. Its position, then, as repre sented on a planisphere which the author prepared for his pupils, and af terwards published, was true to within a less space than one third of its projected diameter. Like some others that have been observed, this comet has no luminous train by which it can be easily recognized by the naked eye, except when it is very near the Sun. This is the reason why it was not more generally observed at its late return.

Although this comet is usually denominated "Biela's comet," yet it seems that M. Gambart, director of the Observatory at Marseilles, is equally entitled to the honour of identifying it with the comet of 1772, and of 1805. He discovered it only 10 days after Biela, and immediately set about calculating its elements from his own observations, which are thought to equal, if they do not surpass, in point of accuracy, those of every other as

tronomer.

Up to the beginning of the 17th century, no correct no tions had been entertained in respect to the paths of comets. Kepler's first conjecture was that they moved in straight lines; but as that did not agree with observation, he next concluded that they were parabolic curves, having the Sun near the vertex, and running indefinitely into the regions of space at both extremities. There was nothing in the ob servations of the earlier astronomers to fix their identity, or to lead him to suspect that any one of them had ever been seen before; much less that they formed a part of the solar

When will this comet return again? How much did its actual position from day to day, as observed by Herschel, differ from its calculated position? Why was it not more generally observed at its late return? What astronomer besides Biela identi fied it with the comet of 1772 and 1805? What were the opinions of astronomers in regard to the paths of comets, up to the beginning of the 17th century? What were Kepler's pinions on this subject}

system, revolving about the Sun in elliptical orbits that returned into themselves.

This grand discovery was reserved for one of the most industrious and sagacious astronomers that ever lived-this was Dr. Halley, the contemporary and friend of Newton. When the comet of 1682 made its appearance, he set himself about observing it with great care, and found there was a wonderful resemblance between it and three other comets that he found recorded, the comets of 1456, of 1531, and 1607. The times of their appearance had been nearly at equal and regular intervals ; their perihelion distances were nearly the same; and he finally proved them to be one and the same comet, performing its circuit around the Sun in a period varying a little from 76 years. This is therefore called Halley's comet. It is the very same comet that filled the eastern world with so much consternation in 1456, and became an object of such abhorrence to the church of Rome.

Of all the comets which have been observed since the Christian era, only three have had their elements so well determined that astronomers are able to fix the period of their revolution, and to predict the time and circumstances. of their appearance. These three are, Encke's, whose last revolution about the Sun was performed in 1212 days; Biela's, whose period was 2461 days; and Halley's, which is now accomplishing its broad circuit in about 28,000 days. Encke's and Halley's will return to their perihelion the present year (1835), and Biela's in 1839.

Halley's comet, true to its predicted time and place, is now (Oct. 1835, ) visible in the evening sky. But we behold none of those phenomena which threw our ancestors of the middle ages into agonies of superstitious terrour. We see not the cometa horrendo magnitudinis, as it appeared in 1305, nor that tail of enormous length which, in 1456, extended over two thirds of the interval between the horizon and the zenith, nor even a star as brilliant as was the same comet in 1682, with its tail of 30°.

Its mean distance from the Sun is 1,713,700,000 miles; the eccentricity of Its orbit is 1,658,000,000 miles; consequently it is 3,316,000,000 miles farther from the Sun in its aphelion than it is in its perihelion. In the latter case, its distance from himi is only 55,700,000 miles; but in the former, it is 3,371,700,000 miles Therefore, though its aphelion distance be great, its mean distance is less than that of Herschel; and great as is the aphelion distance, it is but a very small fraction less than one five-thousandth part of that distance from the Sun, beyond which the very nearest of the fixed stars must be situated; and, as the determination of their distance is nega

Who first discovered the identity of comets? Relate the manner by which he came to this discovery. How many of all the comets observed since the Christian era, have had their elements so well determined, that astronomers are able to fix the period of their revolutions, and to predict the time and circumstances of their appearance? What comets are these? In what time do they accomplish their revolutions? When will hey, severally, return to their perihelion? What comet is nmo (Oct. 1835) visible? What are the mean, and the aphelion and perihelion distances of Halley's comet from the Sun ? What part of the distance beyond which the nearest of the fixed stars must be pla ced, is its aphelion distance?

tive and not positive, the nearest of them may be at twice or ten times that distance.

The number of comets which have been observed since the Christian era, amounts to 700. Scarcely a year has passed without the observation of one or two. And since multitudes of them must escape observation, by reason of their traversing that part of the heavens which is above the hori zon in the day time, their whole number is probably many thousands. Comets so circumstanced, can only become visible by the rare coincidence of a total eclipse of the Sun-a coincidence which happened, as related by Seneca, 60 years before Christ, when a large comet was actually observed very near the Sun.

But M. Arago reasons in the following manner, with respect to the num ber of comets :-The number of ascertained coinets, which, at their least distances, pass within the orbit of Mercury, is thirty. Assuming that the comets are uniformly distributed throughout the solar system, there will be 117,649 times as many comets included within the orbit of Herschel, as there are within the orbit of Mercury. But as there are 30 within the orbit of Mercury, there must be 3,529,470 within the orbit of Herschel!

Of 97 comets whose elements have been calculated by astronomers, 24 passed between the Sun and the orbit of Mercury; 33 between the orbits of Mercury and Venus; 21 between the orbits of Venus and the Earth; 15 between the orbits of Ceres and Jupiter. Forty-nine of these comets move from east to west, and 48 in the opposite direction.

The total number of distinct comets, whose paths during the visible part of their course had been ascertained, up to the year 1832, was one hundred and thirty-seven.

What regions these bodies visit, when they pass beyond the limits of our view; upon what errands they come, when they again revisit the central parts of our system; what is the difference between their physical constitution and that of the Sun and planets; and what important ends they are destined to accomplish, in the economy of the universe, are inquiries which naturally arise in the mind, but which ́surpass the limited powers of the human understanding at present to determinê.

CHAPTER XX.

OF THE FORCES BY WHICH THE PLANETS ARE
RETAINED IN THEIR ORBITS.

Having described the real and apparent motions of the bodies which compose the solar system, it may be interesting next to show, that these motions, however varied or complex they may seem, all result from one simple principle, or law, namely, the

What is the number of comets which have been observed since the Christian era? Why must some of them escape observation? How great is probably their actual number? In what case alone can comets which traverse the horizon in the day time become visible? Mention an instance of a comet thus becoming visible? What is the reasoning of M. Arago in regard to the number of comets ? _Describe the track among the orbits of the planets, of the 97 comets whose elements have been calculated by astronomers. In what direction do they move? What, up to the year 1832, was the whole number of distinct comets, whose path, during the visible part of their course, has been determined? By what principle. or law, are the planets reained in their orbits }

LAW OF UNIVERSAL GRAVITATION.

It is said, that Sir Isaac Newton, when he was drawing to a close the demonstration of the great truth, that gravity is the cause which keeps the heavenly bodies in their orbits, was so much agitated with the magnitude and importance of the discovery he was about to make, that he was unable to proceed, and desired a friend to finish what the intensity of his feelings did not allow him to do. By gravitation is meant, that universal law of attraction, by which every particle of matter in the system has a tendency to every other particle.

This attraction, or tendency of bodies towards each other, is in proportion to the quantity of matter they contain. The Earth, being immensely large in comparison with all other substances in its vicinity, destroys the effect of this attraction between smaller bodies, by bringing them all to itself. The attraction of gravitation is reciprocal. All bodies not only attract other bodies, but are themselves attracted, and both according to their respective quantities of matter The Sun, the largest body in our system, attracts the Earth and all the other planets, while they in turn attract the Sun. The Earth, also, attracts the Moon, and she in turn attracts the Earth. A ball, thrown upwards from the Earth, is brought again to its surface; the Earth's attraction not only counterbalancing that of the ball, but also producing a motion of the ball towards itself.

This disposition, or tendency towards the Earth, is manifested in whatever falls, whether it be a pebble from the hand, an apple from a tree, or an avalanche from a mountain. All terrestrial bodies, not excepting the waters of the ocean, gravitate towards the centre of the Earth, and it is by the same power that animals on all parts of the globe stand with their feet pointing to its centre.

The power of terrestrial gravitation is greatest at the earth's surface, whence it decreases both upwards and downwards; but not both ways in the same proportion. It decreases upwards as the square of the distance from the Earth's centre ncreases; so that at a distance from the centre equal to twice the semi-diameter of the Earth, the gravitating force would be only one fourth of what it is at the surface. But below the surface, it decreases in the direct ratio of the dis

Who discovered this great truth, and how was he affected in view of it? What is meant by gravitation? To what is it proportioned? Give some example. How is it known that the attraction of gravitation is reciprocal? Give some examples to illustrate this principle. Where is the power of terrestrial gravitation the greatest? From this point, does the power decrease equally, both upwards and downwards? What is the law of decrease upwards? Give an example. What is the law of decreas, downwards? Give an example.

tance from the centre; so that at a distance of half a semi diameter from the centre, the gravitating force is but half what it is at the surface.

Weight and Gravity, in this case, are synonymous terms. We say a piece of lead weighs a pound, or 16 ounces; but if by any means it could be raised 4000 miles above the surface of the Earth, which is about the distance of the surface from the centre, and consequently equal to two semi-diameters of the Earth above its centre, it would weigh only one fourth of a pound, or four ounces; and if the same weight could be raised to an elevation of 12,000 miles above the surface, or four semi-diameters above the centre of the Earth, it would there weigh only one sixteenth of a pound, or one ounce.

The same body, at the centre of the Earth, being equally attracted in every direction, would be without weight; at 1000 miles from the centre it would weigh one fourth of a pound; at 2000 miles, one half of a pound; at 3000 miles, three fourths of a pound; and at 4000 miles, or at the surface, one pound.

It is a universal law of attraction, that its power decreases as the square of the distance increases. The converse of this is also true, viz. The power increases, as the square of the distance decreases. Giving to this law the form of a practical rule, it will stand thus:

The gravity of bodies above the surface of the Earth, decreases in a dupli cate ratio, (or as the squares of their distances) in semi-diameters of the earth, from the earth's centre. That is, when the gravity is increasing, multiply the weight by the square of the distance; but when the gravity is decreasing, divide the weight by the square of the distance.

Suppose a body weighs 40 pounds at 2000 miles above the Earth's surface, what would it weigh at the surface, estimating the Earth's semi-diameter at 4000 miles? From the centre to the given height, is 1 semi-diameters: the square of 14, or 1.5 is 2.25, which, multiplied into the weight, (40,) gives 90 pounds, the answer.

Suppose a body which weighs 256 pounds upon the surface of the Earth, be raised to the distance of the Moon, (240,000 miles,) what would be its weight. Thus, 4000)240,000(60 semi diameters, the square of which is 3600. As the gravity, in this case, is decreasing, divide the weight by the square of the distance, and it will give 3600)256(1-16th of a pound, or 1 ounce.

2. To find to what height a given weight must be raised to lose a certain portion of its weight.

RULE.-Divide the weight at the surface, by the required weight, and extract the square root of the quotient. Ex. A boy weighs 100 pounds, how high must he be carried to weigh but 4 pounds? Thus, 100 divided by 4, gives 25, the square root of which is 5 semi-diameters, or 20,000 miles above the

centre.

Bodies of equal magnitude do not always contain equal

What is the relation between weight and gravity? Illastrate it by some examples. What, then, is the general law in regard to the increase and decrease of attraction? How may this law be expressed, in the form of a practical rule? Suppose, for example, the semi-diameter of the Earth be estimated, in round numbers, at 4000 miles, and that a body, elevated 2000 miles above its surface, should weigh 40 pounds, what would the same body weigh, if brought to the Earth's surface? Suppose a body which weighs 256 pounds upon the surface of the Earth, be raised to the distance of the Moon, what would be its weight at such an elevation? [The pupil should be required to give the calculation, as well as the answer.] By what rule can we determine the height to which a body must be raised, in order to its losing a certain portion of its weight? Give an example. Do bodies of the same magnitude always contain equal quantities of matter?