Page:Popular Science Monthly Volume 11.djvu/47

This page has been validated.

no less than 32 on the Erie Canal. The finest of them are two across the Mohawk River, a third at Richmond over the Seneca River, and a fourth across the Genesee at Rochester. The latter is a splendid stone arcade 920 feet long, having six cut-stone arches of 52 feet span. A wire suspension-bridge of seven spans, each 160 feet long, conveys the Pennsylvania Canal across the Alleghany River at Pittsburg.

"The force of gravity acts on bodies directly in proportion to the quantity of matter in each." "The force of gravity decreases in the reciprocal proportion of the square of the distance."—(Orr's "Circle of the Sciences," vol. vi., p. 1.)

AMONG students of natural philosophy no facts are more frequently misunderstood than those pertaining to the laws of gravitation. It is readily admitted that if a body A exerts on B a certain force of attraction, if A's mass be doubled, then will A's attractive influence on B be doubled also, but the fact is not so apparent that any two bodies, whatever their disparity of mass, or however great their distance apart, will attract each other with precisely equal forces; and that if, for instance, the mass of A be doubled, not only will A's attraction for B be doubled, but at the same time B's attraction for A will be doubled also. The pen I hold in my hand attracts the sun with precisely the same amount of force that the sun attracts the pen, and, if either the mass of the pen or sun be doubled, the mutual attraction will be doubled also. The first law of gravitation most certainly teaches that the earth, so insignificantly small as compared with the sun, both in volume and mass, attracts the sun with a force exactly equal to that which, being by the sun exerted on itself, reduces it to obedience, and compels it to make its annual revolution. So, too, the moon and the earth mutually and equally attract each other.

The fact that the forces of attraction between two bodies are equal may be easily explained as follows: Let there be five bodies. A, B, C, D, E, and let A be so situated as to be at equal distances from the other four: then it is evident that the forces which measure the mutual attractions of (A and B), (A and C), (A and D), and (A and E), are equal. Calling the force which A exerts on B, or B exerts on A, one, then will the sum of the forces which B, C, D, and E exert on A be equal to four, but the sum of A's attractions for B, C, D, and E, will also be equal to four, since A's attraction for B is in no way