TUTOR. Having at our last meeting explained to you the nature of the attractive and projectile forces, I shall proceed to shew you that it is by the joint action or combination of these two forces that the planets are retained in their orbits. PUPIL. I am all anxiety, as I wish to be informed how, or in what manner they can act against each other, to produce that effect. TUTOR. Answer me a few questions, and you will soon know. PUPIL. As many as you please, Sir. TUTOR. If you whirl a stone in a sling, what will be its motion? PUPIL. Circular. TUTOR. Is you let it suddenly slip out of the sling, will it continue its circular motion? PUPIL. No, Sir, but fly off in a strait line. TUTOR. This line you must remember is what mathematicians call the tangent of a circle, as A _a_, B _b_, &c. (Plate II. fig. 5.) for all bodies moving in a circle have a natural tendency to fly off in that direction. Thus a body at A will tend towards _a_; at B towards _b_, and so on; but the central force acting against it preserves its circular motion. PUPIL. By the central force here you mean the action of the hand, do you not? TUTOR. Yes. For, as soon as the stone is released and that power is lost, it assumes its natural, that is, its rectilineal motion.—Again. If you are left at liberty, cannot you run strait forward? PUPIL. Yes, Sir. TUTOR. Now, suppose one of your companions were to fasten a rope round your body, and at the extent of it were to stand still and hold it tight, with a force equal to that with which you run, could you, do you think, move in a strait line, that is, in a tangent of a circle? PUPIL. No, Sir. I must run in a circle. TUTOR. Why? PUPIL. Because, whilst the rope is extended I am prevented running in any other direction. TUTOR. Just so it is with the planets: the attractive or centripetal force of the sun being equal to that of the projectile or centrifugal force of the planets, they are by attraction prevented moving on in a strait line, and, as it were, drawn towards the sun; and by the projectile force from being overcome by attraction. They must therefore revolve in circular orbits. PUPIL. What I have so long wished is now accomplished. I understand it perfectly. TUTOR. What I have now explained relates not only to the primary planets which have the sun for their center of motion; but, you must remember that the secondary planets are governed by the same laws, in revolving about their respective primaries; for, as by the attractive power of the sun combined with the projectile force of the primary planets they are retained in their orbits; so also the action of the primaries upon their respective secondaries together with their projectile force, will preserve them in their orbits. PUPIL. Pray, Sir, what have you else to observe? TUTOR. Have I not told you that the orbits of the planets are not true circles, but a little elliptical?