which we are unconscious, like the apparent backward motion of a vessel, when we overtake it and pass by it rapidly in a steam-boat.

Such are the real and the apparent motions of the planets. Let us now turn our attention to the laws of the planetary orbits.

There are three great principles, according to which the motions of the earth and all the planets around the sun are regulated, called KEPLER'S LAWS, having been first discovered by the astronomer whose name they bear. They may appear to you, at first, dry and obscure; yet they will be easily understood from the ex planations which follow; and so important have they proved in astronomical inquiries, that they have acquired for their renowned discoverer the appellation of the Legislator of the Skies.' We will consider each of these laws separately; and, for the sake of rendering the explanation clear and intelligible, I shall perhaps repeat some things that have been briefly mentioned before.

FIRST LAW. The orbits of the earth and all the planets are ellipses, having the sun in the common focus. In a circle, all the diameters are equal to one another; but if we take a metallic wire or hoop, and draw it out on opposite sides, we elongate it into an ellipse, of which the different diameters are very unequal. That which connects the points most distant from each other is called the transverse, and that which is at right angles to this is called the conjugate, axis. Thus, A B, Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A B C. By such a process of elongating the circle into an ellipse, the centre of the circle may be conceived of as drawn opposite ways to E and F, each of which becomes a focus, and both together are called the foci of the ellipse. The distance G E, or G F, of the focus from the centre is called the eccentricity of the ellipse; and the ellipse is said to be more or less eccentric, as the distance of the focus from the centre is greater or less. Figure 64.

represents such a collection of ellipses around the common focus F, the innermost, A G D, having a small eccentricity, or varying little from a circle, while the outermost, A C B, is an eccentric ellipse. The orbits of all the bodies that revolve about the sun, both planets and comets, have, in like manner, a common focus, in which the sun is situated, but they differ in eccentricity. Most of the planets have orbits of very little eccentric

ity, differing little from circles, but comets move in very eccentric ellipses. The earth's path around the sun varies so little from a circle, that a diagram representing it truly would scarcely be distinguished from a perfect circle; yet, when the comparative distances of the sun from the earth are taken at different seasons of the year, we find that the difference between their greatest and least distances is no less than three millions of miles.

SECOND LAW.-The radius vector of the earth, or of any planet, describes equal areas in equal times. You will recollect that the radius vector is a line drawn from the centre of the sun to a planet revolving about the sun. This definition I have somewhere given you before, and perhaps it may appear to you like needless repetition to state it again. In a book designed for systematic instruction, where all the articles are distinctly numbered, it is commonly sufficient to make a reference back to the article where the point in question is explained; but I think, in Letters like these, you will bear with a little repetition, rather than be at the trouble of turning to the Index and hunting up a definition long since given.

In Figure 65, Ea, Eb, Ec, &c., are successive representations of the radius vector. Now, if a planet sets

out from a, and travels round the sun in the direction of a b c, it will move faster when nearer the sun, as at a, than when more remote from it, as at m; yet, if a b and m n be arcs described in equal times, then, according to the foregoing law, the space Ea b will be equal to the space Emn; and the same is true of all the other spaces described in equal times. Although the figure É a b is much shorter than Em n, yet its greater breadth exactly counterbalances the greater length of those figures which are described by the radius vector where it is longer.

THIRD LAW.-The squares of the periodical times are as the cubes of the mean distances from the sun. The periodical time of a body is the time it takes to complete its orbit, in its revolution about the sun. Thus the earth's periodic time is one year, and that of the planet Jupiter about twelve years. As Jupiter takes so much longer time to travel round the sun than the earth does, we might suspect that his orbit is larger than that of the earth, and of course, that he is at a greater distance from the sun; and our first thought might be, that he is probably twelve times as far off; but Kepler discovered that the distance does not increase as fast as the times increase, but that the planets which are more distant from the sun actually move slower than those which are nearer. After trying a great many proportions, he at length found that, if we take the squares of the periodic times of two planets, the greater square contains the less, just as often as the cube of the distance of the greater contains that of the less. This fact is expressed by saying, that the squares of the periodic times are to one another as the cubes of the distances.

This law is of great use in determining the distance of the planets from the sun. Suppose, for example, that we wish to find the distance of Jupiter. We can easily determine, from observation, what is Jupiter's periodical time, for we can actually see how long it takes for Jupiter, after leaving a certain part of the heavens

to come round to the same part again. Let this period be twelve years. The earth's period is of course one year; and the distance of the earth, as determined from the sun's horizontal parallax, as already explained, is about ninety-five millions of miles. Now, we have here three terms of a proportion to find the fourth, and therefore the solution is merely a simple case of the rule of three. Thus :-the square of 1 year: square of 12 years cube of 95,000,000 cube of Jupiter's distance. The three first terms being known, we have only to multiply together the second and third and divide by the first, to obtain the fourth term, which will give us the cube of Jupiter's distance from the sun; and by extracting the cube root of this sum, we obtain the distance itself. In the same manner we may obtain the respective distances of all the other planets.

So truly is this a law of the solar system, that it holds good in respect to the new planets, which have been discovered since Kepler's time, as well as in the case of the old planets. It also holds good in respect to comets, and to all bodies belonging to the solar system, which revolve around the sun as their centre of motion. Hence, it is justly regarded as one of the most interesting and important principles yet developed in astronomy.

But who was this Kepler, that gained such an extraordinary insight into the laws of the planetary system, as to be called the Legislator of the Skies?' John Kepler was one of the most remarkable of the human race, and I think I cannot gratify or instruct you more, than by occupying the remainder of this Letter with some particulars of his history.

Kepler was a native of Germany. He was born in the Duchy of Wurtemberg, in 1571. As Copernicus, Tycho Brahe, Galileo, Kepler, and Newton, are names that are much associated in the history of astronomy, let us see how they stood related to each other in point of time. Copernicus was born in 1473; Tycho, in 1546; Galileo, in 1564; Kepler, in 1571; and Newton,