TUTOR. Having mentioned attraction of magnetism, electricity, and gravitation, it may not be amiss to inform you of another kind, called _attraction of cohesion_. PUPIL. Any thing which tends to my improvement, I shall be obliged to you to communicate. TUTOR. By attraction of cohesion is meant that property in bodies which connects or firmly unites the different particles of matter of which the body is composed. PUPIL. Pray, Sir, inform me what you mean by the _laws_ of attraction? TUTOR. You are to understand, 1st. That _attraction decreases as the squares of the distances between the centers of the attracting bodies increase_. PUPIL. I must beg you, Sir, to explain to me the meaning of the squares of the distances. TUTOR. Any number multiplied into itself is a square number, thus 1 is the square of 1; 4 is the square of 2; 9 is the square of 3, and so on, because 1 multiplied into itself is 1; 2 by 2 is 4; 3 by 3 is 9, &c. Now suppose, that when the planet is at B (Plate II. fig. 4.) it is twice as far from the sun as it is at A: how much more will it be attracted by the sun at A than at B? PUPIL. You say, Sir, that the distance is twice as great at B as at A? TUTOR. I do. PUPIL. Then as the square of the distance 2 is 4, the decrease of attraction at B, the planet at A will be attracted with four times the force it would be at B.—Am I right, Sir? TUTOR. Perfectly so. And if the distance at B were three times as great as at A, it would be attracted with a force nine times as great. PUPIL. I perceive it must be so. TUTOR. I shall now give you the 2d law, namely, That _bodies attract one another with forces proportionable to the quantities of matter they contain_. PUPIL. Do all bodies of the same magnitude contain equal quantities of matter? TUTOR. No, certainly: For a ball of cork may be as large as one of lead, and yet not contain the same quantity of matter, because it is more porous, and not so compact or dense a body as the lead; neither will a ball of lead of the same magnitude as one of gold contain an equal quantity of matter.—So the sun, though a million of times as big as the earth, contains a quantity of matter only 200,000 as great, therefore attracts the earth with a force 200,000 as great as the earth attracts him. PUPIL. I think this is clear. TUTOR. We will now suppose that in the river are two boats of equal bulk, at the distance of twenty yards from each other, and that a man in one boat pulls a rope which is fastened to the other, what effect will be produced, or where do you think the boats will meet? PUPIL. Had you not told me that bodies attract one another with forces which are proportioned to the quantities of matter they contain, I should say the boat to which the rope is fastened would come to that in which the man stands: but as I imagine you mean to apply this to attraction, by the above rule, they will meet at a point which is half way between them.