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centre of the earth, and A a body A
without it. Every portion of matter in the earth exerts some force on A, to draw it down to the earth.
But since there is just as much B
matter on one side of the line A B, as on the other side, each half exerts an equal force to draw the
body towards itself; therefore it B
falls in the direction of the diagonal between the two forces. Thus,
if we compare the effects of any two particles of matter at equal distances from the line A B, but on opposite sides of it, as a, b, while the force of the particle at a would tend to draw A in the direction of A a, that of b would draw it in the direction of A b, and it would fall in the line A B, half way between the two. The same would hold true of any other two corresponding particles of matter on different sides of the earth, in respect to a body situated in any place without it.
Secondly, all bodies fall towards the earth, from the same height, with equal velocities. A musket-ball, and the finest particle of down, if let fall from a certain height towards the earth, tend to descend towards it at the same rate, and would proceed with equal speed, were it not for the resistance of the air, which retards the down more than it does the ball, and finally stops it. If, however, the air be removed out of the way, as it may be by means of the air-pump, the two bodies keep side by side in falling from the greatest height at which we can try the experiment.
Thirdly, bodies, in falling towards the earth, have their rate of motion continually accelerated. Suppose we let fall a musket-ball from the top of a high tower, and watch its progress, disregarding the resistance of the air: the first second, it will pass over sixteen feet and one inch, but its speed will be constantly increased, being all the while urged onward by the
same force, and retaining all that it has already acquired; so that the longer it is in falling, the swifter its motion becomes. Consequently, when bodies fall from a great height, they acquire an immense velocity before they reach the earth. Thus, a man falling from a balloon, or from the mast-head of a ship, is broken in pieces; and those meteoric stones, which sometimes fall from the sky, bury themselves deep in the earth. On measuring the spaces through which a body falls, it is found, that it will fall four times as far in two seconds as in one, and one hundred times as far in ten seconds as in one; and universally, the space described by a falling body is proportioned to the time multiplied into itself; that is, to the square of the time.
Fourthly, gravity is proportioned to the quantity of matter. A body which has twice as much matter as another exerts a force of attraction twice as great, and also receives twice as much from the same body as it would do, if it were only just as heavy as that body. Thus the earth, containing, as it does, forty times as much matter as the moon, exerts upon the moon forty times as much force as it would do, were its mass the same with that of the moon; but it is also capable of receiving forty times as much gravity from the moon as it would do, were its mass the same as the moon's; so that the power of attracting and that of being attracted are reciprocal; and it is therefore correct to say, that the moon attracts the earth just as much as the earth attracts the moon; and the same may be said of any two bodies, however different in quantity of matter.
Fifthly, gravity, when acting at a distance from the earth, is not as intense as it is near the earth. At such a distance as we are accustomed to ascend above the general level of the earth, no great difference is observed. On the tops of high mountains, we find bodies falling towards the earth, with nearly the same speed as they do from the smallest elevations. It is found, nevertheless, that there is a real difference; so that, in fact, the weight of a body (which is nothing more than the measure of its force of gravity) is not quite so great on the tops of high mountains as at the general level of the sea. Thus, a thousand pounds' weight, on the top of a mountain half a mile high, would weigh a quarter of a pound less than at the level of the sea; and if elevated four thousand miles above the earth,that is, twice as far from the centre of the earth as the surface is from the centre,—it would weigh only one fourth as much as before ; if three times as far, it would weigh only one ninth as much. So that the force of gravity decreases, as we recede from the earth, in the same proportion as the square of the distance increases. This fact is generalized by saying, that the force of gravity, at different distances from the earth, is inversely as the square of the distance.
Were a body to fall from a great distance,-suppose a thousand times that of the radius of the earth,—the force of gravity being one million times less than that at the surface of the earth, the motion of the body would be exceedingly slow, carrying it over only the sixth part of an inch in a day. It would be a long time, therefore, in making any sensible approaches towards the earth ; but at length, as it drew near to the earth it would acquire a very great velocity, and would finally rush towards it with prodigious violence. Falling so far, and being continually accelerated on the way, we might suppose that it would at length attain a velocity infinitely great; but it can be demonstrated, that, if a body were to fall from an infinite distance, attracted to the earth only by gravity, it could never acquire a velocity greater than about seven miles per second. This, however, is a speed inconceivably great, being about eighteen times the greatest velocity that can be given to a cannon-ball, and more than twenty-five thousand miles per hour.
But the phenomena of falling bodies must have long been observed, and their laws had been fully investigated by Galileo and others, before the cause of their falling was understood, or any such principle as gravity, inherent in the earth and in all bodies, was applied to them. The developement of this great principle was the work of Sir Isaac Newton; and I will give you, in my next Letter, some particulars respecting the life and discoveries of this wonderful man.
SIR ISAAC NEWTON.--UNIVERSAL GRAVITATION.—FIGURE OF
THE EARTH's ORBIT.-PRECESSION OF THE EQUINOXES.
" The heavens are all his own; from the wild rule
Of whirling vortices, and circling spheres,
ŞIR ISAAC NEWTON was born in Lincolnshire, England, in 1642, just one year after the death of Galileo. His father died before he was born, and he was a helpless infant, of a diminutive size, and so feeble a frame, that his attendants hardly expected his life for a single hour. The family dwelling was of humble architecture, situated in a retired but beautiful valley, and was surrounded by a small farm, which afforded but a scanty living to the widowed mother and her precious charge. The cut on page 144, Fig 30, represents the modest mansion, and the emblems of rustic life that first met the eyes of this pride of the British nation, and ornament of human nature. It will probably be found, that genius has oftener emanated from the cottage than from the palace.
The boyhood of Newton was distinguished chiefly for his ingenious mechanical contrivances. Among other pieces of mechanism, he constructed a windmill so curious and complete in its workmanship, as to excite universal admiration. After carrying it a while by the force
of the wind, he resolved to substitute animal power; and for this purpose he inclosed in it a mouse, which he called the miller, and which kept the mill a-going by acting on a tread-wheel. The power of the mouse was brought into action by unavailing attempts to reach a portion of corn placed above the wheel. A water-clock, a four-wheeled carriage propelled by the rider himself, and kites of superior workmanship, were among the productions of the mechanical genius of this gifted boy. At a little later period, he began to turn his attention to the motions of the heavenly bodies, and constructed several sun-dials on the walls of the house where he lived. All this was before he had reached his fifteenth year. At this age, he was sent by his mother, in company with an old family servant, to a neighboring market-town, to dispose of products of their farm, and to buy articles of merchandise for their family use; but the young philosopher left all these negotiations to his worthy partner, occupying himself, mean-while, with a collection of old books, which he had found in a garret. At other times, he stopped on the road, and took shelter with his book under a hedge, until the servant returned. They en