motion for ever; for, according to the laws of motion, mutter has no more power to stop of itself when once put in motion, than it has, if at rest, to move of itself in any way. In the following diagram, let A represent the earth and S the sun,

D

and let us suppose that the earth, having been projected forward, is moving in a straight line with a velocity that would carry it on to B in the space of a month, while the attraction of the sun, under whose influence it has now come, would bring it to C in the same time. Now, as the earth is impelled by two forces acting perpendicularly to each other, it is certain that it will obey neither the one nor the other, but like a ball struck at the same instant by opposite forces, it will move in a direction between them. It will not however, like the ball, move in a straight line, or, as it is said, describe the diagonal of a parallelogram; because as the power of attraction continues to act upon the earth, without speedily retarded and soon stopped; if along a smoother surface, it continues longer in motion; if upon ice, longer still; and the like with regard to wheels, &c., in proportion as we gradually lessen the friction of the machinery. If we remove the resistance of the air, by setting a wheel or pendulum in motion under an air-pump, the motion is still longer continued. Finding, then, that the effect of the original impulse is more and more protracted, in proportion as we more and more remove the impediments to motion from friction and the resistance of the air, we reasonably conclude that if this could be completely done (which is out of our power), the motion would never cease, since what appear to be the only causes of its cessation, would be absent."

ceasing, it continually draws it out of the straight line, and thus converts its course into a curve. This is exemplified in the parallelogram A B D C, in the foregoing diagram. AD is the line described by the earth, in the same time in which it would have described either the line A B, or A C, that is, according to our supposition, in the space of a month. A D is of course a curved line, but as every point of it may be considered as constituting the diagonal of an infinitely small parallelogram, the earth may be said to move as a ball would under similar circumstances. The earth is now at D, and its tendency is to move in a straight line to F in the space of a month, while the attraction of the sun would bring it to E in the same period of time. But, as before, the earth will follow neither the one impulse nor the other, but will move between them in the line D G, which it will describe in the same time in which it would have described either the line D F or D E, that is, in the space of a month. We have now the earth at the point G, and its tendency is to move in a straight line to H, in the space of a month, while the sun's attraction would carry it to K, in the same time. But the combined action of these two forces will, as in the foregoing cases, cause the earth to move between them in a curved line; that is, it will describe the line G I, in the parallelogram G HIK, in the same time in which it would have described either GH or G K.

We have now followed the earth from the point A to the point I, that is, through one-fourth of its orbit, which it has described in the space of three months; and it may be easily shown, by drawing lines at right angles, to represent the forces of projection and attraction, and by completing the parallelograms, that it will describe the entire circle in the course of twelve months.

We have now seen that the earth's motion round the sun in an orbit or circle, is caused by the combination of the forces of projection and attraction. The former of these forces is called the tangential force, because it impels the earth to fly from the sun in a tangent or straight line, touching its orbit; and the latter, the centripetal, because it causes the earth to seek or move towards the sun, or the centre around which it revolves.

What proofs of the Divine power and goodness these

magnificent motions display! If the earth had been at the creation projected in the direction of, or too near the sun, its destruction would have been inevitable; or if it had been projected too remote, or in a line beyond the influence of the sun's attraction, the consequences would have been equally disastrous. And even now, if either of these motions were to prevail over the other, the result to our globe would be fatal. In the one case, it would be burned up and destroyed by falling to the sun; and in the other, it would fly off into infinite space, never more to be warmed or enlightened by his rays.

And, strictly speaking, the tangential and centripetal forces do not in every part of the earth's orbit counterbalance each other symmetrically; and the consequence is, that the earth deviates from an exact circle, and describes what is called an ELLIPSE or oval. The annexed diagram, in which S represents the sun and A the earth, is an ellipse.

At A the earth is in APHELION,* that is, in that part of its orbit most remote from the sun, and its motion or velocity will in consequence be slower. In this case, the force of attraction will begin to prevail, and the earth, instead of describing the circular arc, A C, as in the former diagram, will move nearer the sun in the elliptical line A B. At B the projectile or tangential force impels the earth in the

a Aphelion.-From the Greek words APO, from, and HELIOS, the sun Perihelion is from the same root, and PERI, about or near.

direction B D, but the centripetal force continues to draw it nearer and nearer to the sun till it arrives at E. As the centripetal force increases as the earth approaches the sun, there appears to be some danger of the earth's being drawn into it, particularly as the direction of the force of projection is no longer perpendicular to that of attraction, but inclines more nearly to it, and therefore counteracts it less. The earth, however, with a motion constantly increasing, arrives in safety at E, and all appearance of danger is over. For though the earth will be attracted most powerfully at E, being in PERIHELION, or in that part of its orbit which is nearest to the sun, the velocity which it has acquired in approaching the sun will increase its tangential force, so as to make it prevail over the power of attraction; and the earth will consequently move from the sun in the direction E G. In motion round a centre, the tangential force increases with the velocity of the moving body; or in other words, the quicker it moves, the stronger is its tendency to fly off in a straight line. When a stone is whirled round in a sling, for instance, its tendency is to fly off in a tangent to the circle it describes, and the quicker it is whirled round, the stronger, of course, is its tendency to fly off.

Thus at E in the diagram, the tangential force of the earth is at its maximum, in consequence of the increased velocity which it has acquired in approaching the sun, and its tendency, therefore, will be to fly off with accelerated speed in the direction E F-that is, away from the dangerous proximity of the sun. But this equally dangerous tendency is kept in check by the centripetal force which at this point is also at its maximum; and the consequence is, that the earth moves in the curved line E G. As at the point E the two forces act perpendicularly to each other, we might expect that the earth, as in the preceding diagram, would move in the arc of a circle; but, notwithstanding the proximity of the sun, the tangential force predominates here, and the earth is, in consequence, dragged away in the elliptical line E G. At G the tangential power impels the earth in the direction G H, while the centripetal force draws it towards S, and the consequence is, that it moves between them in the line G A; and in describing this line, the earth will travel slower and slower till it arrives at A; because its motion is always retarded in proportion as it recedes

from the sun. When the earth arrives at A its velocity is so diminished that the centripetal force, though it also is at its minimum here, begins to predominate over the tangential, and the earth will, in consequence, continue to move in the course already described.

But great care should be taken to inform the pupils that the orbit of the earth, though an ellipse, differs little in reality from a circle. The representation of it in this diagram has been purposely given in excess, in order that a clearer view might be had of the causes which retard or accelerate the motion of the earth in receding from, or approaching to the

sun.

The longer diameter or axis of the earth's orbit exceeds its shorter axis by a very small fraction, from which it follows that the orbit itself differs very little from a circle. The aphelion distance of the earth exceeds its perihelion distance by three million miles, about one-sixtieth of the greater diameter of the orbit. But even this immense distance amounts to almost nothing when compared to the entire distance of the earth from the sun-namely, ninety-five millions of miles. That this is so, follows from the fact that the earth is actually nearer the sun in the winter of our year than it is in the summer. This may appear surprising and even incredible, but it is easily explained. The longer the sun is above the horizon, and the more direct his rays are, the more heat he communicates, and the reverse of this is equally evident. Now the days are longer in summer than in winter, and the rays of the sun, in consequence of his higher elevation in the heavens, shine upon our part of the earth more directly; which two causes more than counterbalance the proximity of our hemisphere to the sun during our winter half-year.

b

In further illustration of this, it may be observed, that during the polar summer the sun is for months above the horizon, and yet the temperature is never great, because the rays of the sun strike the earth very obliquely, in consequence of his low elevation in the heavens. Again, the sun is at nearly the same distance from us when rising or setting, as he is when on our meridian, and yet we all know that it is

The centripetal force is, of course, least powerful when the earth is in aphelion. See note, page 41.

b That is, if we are in the northern hemisphere.