quarter of a pound, and fall through only four feet in a second.

*

Emma. How is that known, papa, for nobody ever was there?

Father. You are right, my dear, for Garnerin, who last summer astonished all the people of the metropolis and its neighbourhood, by his flight in a balloon, ascended but a little way in comparison of the distance that we are speaking of. However, I will try to explain in what manner philosophers have come by their knowledge on this subject.

The moon is a heavy body, connected with the earth by this bond of attraction, and by the most accurate observations, it is known to be obedient to the same laws as other heavy bodies are its distance is also clearly ascertained, being about 240,000 miles, or equal to about sixty semi-diameters of the earth, and of course the earth's attraction upon the moon ought to diminish in the proportion of the square of this distance, that is, it ought to be 60 times 60, or

* Ex. Suppose it were required to find the weight of a leaden ball, at the top of a mountain three miles high, which on the surface of the earth weighs 201b.

If the semi-diameter of the earth be taken at 4000; then add to this the height of the mountain, and say as the square of 4003 is to the square of 4000, so is 20lb. to a fourth proportional or as 16024009: 16000000 : : 20:19.97 or something more than 19lb. 15 oz. which is the weight of the leaden ball at the top of the mountain.

3600 times less at the moon than it is at the surface of the earth. This is found to be the case.

Again, the earth is not a perfect sphere, but a spheroid, that is, of the shape of an orange, rather flat at the two ends called the poles, and the distance from the centre to the poles is about eighteen or nineteen miles less than its distance from the centre to the equator, consequently, bodies ought to be something heavier at, and near the poles, than they are at the equator, which is also found to be the case. Hence it is inferred that the attraction of gravitation varies at all distances from the centre of the earth, in proportion as the squares of those distances increase.

*

Charles. It seems very surprising that philosophers, who have discovered so many things, have not been able to find out the cause of gravity. Had Sir Isaac Newton been asked why a marble, dropped from the hand, falls to the ground, could he not have assigned a reason?

Father. That great man, probably the greatest man that ever adorned this world, was as modest as he was great, and he would have told you he knew not the cause.

The excellent and learned Dr. Price, in a work which he published twenty-five years ago, asks, "who does not remember a time when he

See Vol. I. Conver. XXVI.

would have wondered at the question, why does water run down hill? What ignorant man is there who is not persuaded that he understands this perfectly? But every improved man knows it to be a question he cannot answer." For the descent of water, like that of other heavy bodies, depends upon the attraction of gravitation, the cause of which is still involved in darkness..

Emma. You just now said that heavy bodies by the force of gravity fall sixteen feet in a second of time, is that always the case?

Father. Yes, all bodies near the surface of the earth fall at that rate in the first second of time, but as the attraction of gravitation is continually acting, so the velocity of falling bodies is an increasing, or, as it is usually called, an accelerating velocity. It is found by very accurate experiments, that a body, descending from a considerable height by the force of gravity, falls 16 feet in the first second of time; 3 times 16 feet in the next; 5 times 16 feet in the third; 7 times 16 feet in the fourth second of time; and so on, continually increasing according to the odd numbers, 1, 3, 5, 7, 9, 11, &c.

B 2

CONVERSATION VIII.

Of the Attraction of Gravitation.

Emma. And would a ball of twenty pounds weight here, weigh half an ounce less on the top of the mountain?

Father. Certainly: but you would not be able to ascertain it by means of a pair of scales, and another weight, because both weights being in similar situations would lose equal portions of their gravity.

Emma. How, then, would you make the experiment?

Father. By means of one of those steel spiralspring instruments, which you have seen occasionally used, the fact might be ascertained.

Charles. I think, from what you told us yesterday, that with the assistance of your stopwatch, I could tell the height of any place, by observing the number of seconds, that a marble or other heavy body would take in falling from that height.

Father. How would you perform the calculation?

Charles. I should go through the multiplications according to the number of seconds, and then add them together.

Father. Explain yourself more particularly: supposing you were to let a marble or pennypiece fall down that deep well which we saw last summer in the brick field near Ramsgate, and that it was exactly five seconds in the descent, what would be the depth of the well?

Charles. In the first second it would fall 16 feet; in the next 3 times 16 or 48 feet; in the third 5 times 16 or 80 feet; in the fourth 7 times 16 or 112 feet; and in the fifth second 9 times 16 or 144 feet; now if I add 16, 48, 80, 112, and 144 together, the sum will be 400 feet, which, according to your rule, is the depth of the well. But was the well so deep?

Father. I do not think it was, but we did not make the experiment; should we ever go to that place again, you may satisfy your curiosity. You recollect that at Dover Castle we were told of a well there 360 feet deep.

Though your calculation was accurate, yet it was not done as nature effects her operations, it was not performed in the shortest way.

Charles. I should be pleased to know an easier method; this, however, is very simple, it required nothing but multiplication and addition.

Father. True, but suppose I had given you an example in which the number of seconds had been fifty instead of five, the work would have taken you an hour or more to have performed it: whereas, by the rule which I am going to give, it might have been done in half a minute.