If a ball a (Plate 1. Fig. 6.) lean against the obstacle b, it will not be able to overturn it, but if it be taken up to c and suffered to roll down the inclined piane AB against b, it will certainly overthrow it;-in the former case, b would only have to resist the weight of the ball a, in the latter it has to resist the weight multiplied into its motion or velocity.

Charles. Then the momentum of a small body whose velocity is very great, may be equal to that of a very large body with a slow velocity.

Father. It may, and hence you see the reason why immense battering rams, used by the ancients, in the art of war, have given place to cannon balls of but a few pounds weight.

Charles. I do for what is wanting in weight, is made up by velocity.

Father. Can you tell me what velocity a cannon ball of 28 pounds must have to effect the same purposes, as would be produced by a battering ram of 15,000 pounds weight, and which, by manual strength, could be moved at the rate of only two feet in a second of time?

Charles. I think I can ;-the momentum of the battering ram must be estimated by its weight, multiplied into the space passed over in a second, which is 15,000 multiplied by two feet, equal to 30,000; now if this momentum, which must also be that of the cannon ball, be divided by the weight of the ball, it will give the velocity required; and 30,000 divided by 28, will

give for the quotient 1072 nearly, which is the number of feet which the cannon ball must pass over in a second of time, in order that the momenta of the battering ram and the ball may be equal, or in other words, that they may have the same effect in beating down an enemy's wall.

Emma. I now fully comprehend what the mo mentum of a body is, for if I let a common trapball accidentally fall from my hand, upon my foot, it occasions more pain than the pressure of a weight several times heavier.

Charles. If the attraction of gravitation be a power by which bodies in general tend towards each other, why do all bodies tend to the earth as a centre?

Father. I have already told you that by the great law of gravitation, the attraction of all bodies is in proportion to the quantity of matter which they contain. Now the earth, being so immensely large in comparison of all other substances in its vicinity, destroys the effect of this attraction between smaller bodies, by bringing them all to itself. If two balls are let fall from a high tower at a small distance apart; though they have an attraction for one another, yet it will be as nothing when compared with the attraction by which they are both impelled to the earth, and consequently the tendency which they mutually have of approaching one another will not be perceived in the fall. If, however, any two bodies were placed in free space, and

came nearer.

out of the sphere of the earth's attraction, they would, in that case, assuredly fall towards each other, and that with increased velocity as they If the bodies were equal, they would meet in the middle point between the two; but if they were unequal, they would then meet as much nearer the larger one, as that contained a greater quantity of matter than the other.

Charles. According to this, the earth ought to move towards falling bodies, as well as they move to it.

Father. It ought, and, in just theory, it does; but when you calculate how many million of times larger the earth is than any thing belonging to it, and if you reckon at the same time, the small distances from which bodies can fall, you will know that the point where the falling bodies and earth will meet, is removed only to an indefinitely small distance from its surface, a distance much too small to be conceived by the human imagination.

We will resume the subject of gravity to

morrow.

CONVERSATION VII

Of the Attraction of Gravitation.

Emma. Has the attraction of gravitation, papa, the same effect on all bodies, whatever be their distance from the earth.

Father. No; this, like every power which proceeds from a centre, décreases as the of the distances from that centre increase.

squares

Emma. I fear that I shall not understand this, unless you illustrate it by examples.

Father. Suppose you are reading at the distance of one foot from a candle, and that you receive a certain quantity of light on your book; now if you remove to the distance of two feet from the candle, you will, by this law, receive four times less light than you had before; here then, though you have increased your distance but two-fold, yet the light is diminished fourfold, because four is the square of two, or two multiplied by itself. If, instead of removing two feet from the candle, you take your station at 3, 4, 5, or 6 feet distance, you will then receive at the different distances, 9, 16, 25, 36 times less light than when you were within a single VOL. I.—D

2

foot from the candle, for these, as you know, arc the squares of the numbers, 3, 4, 5, and 6. The same is applicable to the heat imparted by a fire; at the distance of one yard from which, a person will enjoy four times as much heat, as he who sits or stands two yards from it; and nine times as much as one that shall be removed to the distance of three yards.

Charles. Is then the attraction of gravity four times less at a yard distance from the earth, than it is at the surface?

Father. No; whatever be the cause of attraction, which to this day remains undiscovered, it acts from the centre of the earth, and not from its surface, and hence the difference of the power of gravity cannot be discerned at the small distances to which we can have access; for a mile or two, which is much higher than, in general, we have opportunities of making experiments, is nothing in comparison of 4000 miles, the distance of the centre from the surface of the earth. But could we ascend 4000 miles above the earth, and of course be double the distance that we now are from the centre, we should there find that the attractive force would be but onefourth of what it is here; or in other words, that a body, which, at the surface of the earth, weighs one pound, and, by the force of gravity, falls through sixteen feet in a second of time, would at 4000 miles above the earth weigh but a