number of square feet to be 160. Having the length of the diameter of the circle, H I, we find that there are likewise 160 square feet contained within its circumference; and therefore the conclusion is evident, that the space contained within the triangle C is equal to that contained in the circle E. This example, reduced to the form of a syllogism, would stand thus: Any two figures which contain the same number of square feet are equal to one another; but the triangle C contains the same number of square feet as the circle E; therefore the space contained in the triangle C is equal to the space contained within the circle E.

Again, the sun appears to be only a few inches in diameter, and as flat as the face of a clock or a plate of silver. Suppose it were inquired how we may determine that the sun is much larger than he appears to be, and whether his surface be flat or convex, or of any other figure, the pupil may be requested to search for intermediate ideas, by which these points may be determined. One idea or principle, which experience proves, requires to be recognized, that all objects appear less in size, in proportion to their distance from the observer. A large building, at the distance of twenty miles, appears to the naked eye only like a visible point; and dog, a horse, or a man, are, at such a distance, altogether invisible. We find, by experience, that when the sun has just risen above the horizon in the morning, he appears as large as he does, when on our meridian at noon. day; but it can be proved, that he is then nearly 4000 miles (or the half diameter of the earth) nearer to us than when he arose in the morning; therefore, the sun must be at a great distance from us, at least several thousands of miles, otherwise he would appear much larger in the one case than in the other, just as a house or a town appears much larger than when we approach within a mile of it than it does at the distance of eight or ten miles. It is known that the inhabitants of Great Britain, and those who live about the Cape of Good Hope, can see the sun at the same moment; and that he appears no larger to the one than to the other, though they are distant in a straight line more than 5000 miles from each other. We also know, from experience, that when we remove 50 or a hundred miles to the west of our usual place of residence, the sun appears, at his rising, just as large as he did before; and though we are removed from our friends several hundreds or even thousands of miles, they will tell us that the sun uniformly appears of the same size, at the same moment as he does to us. From these and similar considerations, it appears, that the sun must be at a very considerable distance from the earth, and consequently his real magnitude must be much greater

than his apparent, since all bodies appear less in size in propor tion to their distance. If the distance of the sun were only 4000 miles from the earth, he would appear twice as large when he came to the meridian, as he did at his rising in the east; if his distance were only 100,000 miles, he would appear part broader when on the meridian than at his rising-but this is not found to be the case; consequently, the sun is more than 100,000 miles distant, and therefore must be of a very large size. Supposing him no farther distant than 100,000 miles, he behoved to be nearly a thousand miles in diameter, or about the size of Arabia or the United States of America.

To determine whether the sun be flat or convex, we must call in to our assistance the following ideas. Every round body which revolves around an axis, perpendicular to the line of vision, without altering its figure or apparent dimensions, is of a convex or globular shape;—and, Every object which appears of a circular shape near the centre of such a body, will assume an oval or elliptical form when it approaches near its margin. This might be illustrated by fixing a circular patch on a terrestrial globe, and turning it round till it appear near the margin. By means of the telescope, it is found that there are occasionally spots upon the sun, which appear first at the eastern limb, and, in the course of about 13 days, approach the western limb, where they disappear, and, in the course of another 13 days, reappear on the eastern limb; which shows that the sun revolves round an axis without altering his shape. It is also observed that a spot, which appears nearly circular at his centre, presents an oval figure when near his margin. Consequently, the sun is not a flat surface, as he appears at first sight, but a globular body. Again, suppose it was required to determine whether the sun or the moon be nearest the earth. The intermediate idea which requires to be recognised in this case is the following. Every body which throws a shadow on another is nearer the body on which the shadow falls than the luminous body which is the cause of the shadow. In an eclipse of the sun, the body of the moon projects a shadow upon the earth, by which either the whole or a portion of the sun's body is hid from our view. Consequently, the moon is interposed between us and the sun, and therefore is nearer to the earth than that luminary. This might be illustrated to the young by a candle, and two balls, the one representing the moon and the other the earth, placed in a direct line from the candle. -In like manner, were it required, when the moon is eclipsed, to ascertain whether at that time the earth or the moon be nearest to the sun, it might be determined by the same process of reason.

ing; and, on the same principle, it is determined that the planets Mercury and Venus, when they transit the sun's disk, are, in that part of their orbits, nearer the earth than the sun is.

Such reasonings as the above might be familiarly explained, and, in some cases, illustrated by experiments; and the pupil occasionally requested to put the arguments into the form of a syllogism. The reasoning respecting the bulk of the sun may be put into the following syllogistic form:

All objects appear diminished in size in proportion to their dis

tances.

The sun is proved to be many thousands of miles distant, and consequently, diminished in apparent size.

Therefore the sun is much larger in reality than what he appears.

The two first propositions are generally denominated the premises. The first is called the major proposition, the second the minor proposition. If the major proposition be doubtful, it requires to be proved by separate arguments or considerations. In the above example, it may be proved, or rather illustrated, to the young, by experiment-such as placing a 12-inch globe, or any similar body, at the distance of half a mile, when it will appear reduced almost to a point. If the minor, or second proposition be doubtful, it must likewise be proved, by such considerations as suggested above; or by a strictly mathematical demonstration, if the pupils are capable of understanding it. But, in the present case, the arguments above stated are quite sufficient to prove the point intended. When the premises are clearly proved, the conclusion follows as a matter of course. Similar examples of reasoning may be multiplied to an almost indefinite extent, and, in the exercise of instructing the young, they should always be taken from sensible objects with which they are acquainted.

As it would be quite preposterous to attempt instructing young persons, under the age of twelve or thirteen, in the abstract systems of logic generally taught in our universities-it is quite sufficient. for all the practical purposes of human life and of science, that they be daily accustomed to employ their reasoning powers on the various physical, intellectual, and moral objects and circumstances which may be presented before them; and an enlightened and judicious teacher will seldom be at a loss to direct their attention to exercises of this kind. The objects of nature around them, the processes of art, the circumstances and exercises connected with their scholastic instruction, their games and amusements, the manner in which they conduct themselves towards each other, their practices in the streets or on the highways, and the general

tenor of their moral conduct, will never fail to supply topics for the exercise of their rational faculties, and for the improvement of their moral powers. In particular, they should be accustomed, on all occasions, to assign a reason for every fact they admit, and every truth they profess to believe. If, for example, they assert, on the ground of what they read in books, or on the authority of their teachers, that "the earth is round like an artificial globe," they should be required to bring forward the proofs by which this position is supported, so that their knowledge may be the result, not of authority, but of conviction. In like manner, when they profess to believe that the earth moves round its axis and round the sun-that the atmosphere presses with a weight of fifteen pounds on every square inch of the earth's surface-that a magnet will stand in a direction nearly north and south-that water presses upwards as well as downwards-that it is our duty and interest to obey the laws of God-that we ought to exercise justice between man and man-and that children should obey their parents and teachers,-they should be taught to bring for ward, when required, those experiments, arguments, and reasonings, by which such truths are proved and supported.

As an illustration of some of the modes of reasoning to which I allude, the following story respecting the celebrated French philosopher, Gassendi, may be here introduced. From his earliest years he was particularly attentive to all that he heard in conversation, and was fond of contemplating the scenes of nature, particularly the magnificence of a starry sky. When only seven years old, he felt a secret charm in the contemplation of the stars, and, without the knowledge of his parents, he sacrificed his sleep to this pleasure. One evening a dispute arose between him and his young companions, about the motion of the moon, and that of the clouds when they happened to be impelled by a brisk wind. His friends insisted that the clouds were still, and that it was the moon which moved. He maintained, on the contrary, that the moon had no sensible motion, such as they imagined, and that it was the clouds which appeared to pass so swiftly. His reasons produced no effect on the minds of the children, who trusted to their own eyes rather than to anything that could be said on the subject. It was, therefore, necessary to undeceive them by means of their eyes. For this purpose Gassendi took them under a tree, and made them observe that the moon still appeared between the same leaves and branches, while the clouds sailed far away out of sight. This exhibition, of course, was convincing, and at once settled the dispute.

The principle, or "intermediate idea," which Gassendi recog.

nized, in this case, for proving his position, was the following, although he could not at that time express it in words :- When

Gassendi demonstrating the motion of the clouds.

motion appears in the case of two bodies, we ascertain which is the moving body, by causing one of them to appear in a straight line with an object which is known to be fixed. This principle is of considerable practical utility. By means of it we ascertain, when we see a number of ships in a river, or narrow arm of the sea, which of them are in motion or at rest, by comparing their positions or motions with a fixed point on the opposite shore. When looking at the wheels, pinions, and other parts of a piece of machinery, we can, on the same principle, perceive which parts are in motion and which are at rest, which the eye at first view cannot determine; and, in the same way, the real and apparent motions of the planets in the heavens are ascertained, by