Father. It is nothing more than some truth clearly deducible from some other truth before demonstrated or admitted. Thus by the first law of motion, every body must endeavour to continue in the state into which it is put, whether it be of rest, or uniform motion in a straight line: from which it follows as a corollary, "that when we see a body move in a curve line, it must be acted upon by at least two forces."

Charles. When I whirl a stone round in a sling, what are the two forces which act upon the stone?

Father. There is the force, by which, if you let go the string, the stone will fly off in a right line; and there is the force of the hand, which keeps it in a circular motion.

Emma. Are there any of these circular motions in nature?

Father. The moon, and all the planets move by this law; to take the moon as an instance. It has a constant tendency to the earth, by the attraction of gravitation, and it has also a tendency to proceed in a right line, by that projectile force impressed upon it by the Creator, in the same manner as the stone flies from your hand; now, by the joint action of these two forces it describes a circular motion.

Emma. And what would be the consequence, supposing the projectile force to cease?

Father. The moon must fall to the earth; and if the force of gravity were to cease acting upon

the moon, it would fly off into infinite space. Now the projectile force, when applied to the planets, is called the centrifugal foree, as having a tendency to recede or fly from the centre; and the other force is termed the centripetal force, from its tendency to some point as a centre.

Charles. And all this is in consequence of the inactivity of matter, by which bodies have a tendency to continue in the same state they are in, whether of rest or motion?

Father. You are right; and this principle, which Sir Isaac Newton assumed to be in all bodies, he called their vis inertiæ.

Charles. A few mornings ago, you showed us that the attraction of the earth upon the moon* is 3600 times less than it is upon heavy bodies near the earth's surface. Now as this attraction is measured by the space fallen through in a given time, I have endeavoured to calculate the space which the moon would fall through in a minute, were the projectile force to cease.

Eather. Well, and how have you brought it out?

Charles. A body falls 16 feet in the first second, consequently in a minute, or 60 seconds it would fall 60 times 60 feet, multiplied by 16, that is 3600 feet, which is to be multiplied by 16; and as the moon would fall through 3600 times less space in a given time than a body here, it would fall only 16 feet in the first minute.

*See Conversation IV.

Father. Your calculation is accurate. I will recall to your mind the second law, by which it appears, that every motion or change of motion produced in a body, must be proportional to, and in the direction of, the force impressed. Therefore, if a moving body receives an impulse in the direction of its motion, its velocity will be increased; if in the contrary direction, its velocity will be diminished ;-but if the force be impressed in a direction oblique to that in which it moves, then its direction will be between that of its former motion, and that of the new force impressed.

Charles. This I know from the observations I have made with my cricket-ball.

Father. By this second law of motion, you will easily understand, that if a body at rest receives two impulses, at the same time, from forces whose directions do not coincide, it will, by their joint action, be made to move in a line that lies between the direction of the forces impressed.

Emma. Have you any machine to prove this satisfactorily to the senses?

Father. There are many such invented by different persons, descriptions of which you will hereafter find in various books on these subjects. But it is easily understood by a figure. If on the ball A, (Plate 11. Fig. 14.) a force be impressed, sufficient to make it move with a uniform velocity to the point в, in a second of

time; and if another force be also impressed on the ball, which alone would make it move to the point c, in the same time; the ball, by means of the two forces, will describe the line A D, which is a diagonal of the figure, whose sides are AC and A B.

Charles. How then is motion produced in the direction of the force; according to the second law, it ought to be in one case, in the direction A c, and in the other, in that of A B, whereas, it is in that of A D?

Father. Examine the figure a little attentively, carrying this in your mind, that for a body to move in the same direction, it is not necessary that it should move in the same straight line; but that it is sufficient to move either in that line, or in any one parallel to it.

Charles. I perceive then that the ball when arrived at D, has moved in the direction A c, because B D is parallel to A c; and also in the direction AB, because C D is parallel to it.

Father. And in no other possible situation but at the point D could this experiment be conformable to the second law of motion.

CONVERSATION XIII.

On the Laws of Motion.

Father. If you reflect a little upon what we said yesterday on the second law of motion, you will readily deduce the following corollaries: (Plat 11. Fig 14.)

1. That if the forces be equal, and act at right angles to one another, the line described by the ball will be the diagonal of a square. But in all other cases, it will be the diagonal of a parallelogram of some kind.

2. By varying the angle, and the forces, you vary the form of your parallelogram.

Charles. Yes, papa; and I see another consequence, viz. that the motions of two forces acting conjointly in this way, are not so great as when they act separately.

Father. That is true, and you are led to the conclusion, I suppose, from the recollection,. that in every triangle any two sides taken together are greater than the remaining side; and therefore you infer, and justly too, that the motions which the ball A must have received, had the forces been applied separately, would have been equal to a c and a в, or, which is the