NEWTON'S THEORY OF PLANETARY MOTIONS 73 



the fact could be attested. It is said that the * flattest 

 piece of metal in existence, though fashioned with great 

 care, is not flatter than the rotundity of the moon. The 

 curvature of the ocean, level as it may seem to us when 

 looking directly down upon it, slopes away from its tan- 

 gent about eight inches in the first mile. Compare this 

 now with the curvature of the moon's orbit, which, ac- 

 cording to mathematical calculation, swerves from its 

 tangent only 1/10 of an inch in a mile, or .0535 inches in 

 one second of time, during which it travels 3350 feet. 



The mean distance of the moon from the earth is 

 238,840 miles, according to Young. Astronomers have 

 attempted to explain how it got there, saying it was 

 originally a part of the earth and by their mutual attrac- 

 tion has faeen gradually forced out to its present posi- 

 tion ; others, that it came from a distance, and when it 

 approached near enough, was lassoed by the earth's at- 

 traction ; and Newton himself, that the Creator placed it 

 in position. 



Now, considered merely as an isolated fact, it would 

 make very little difference to us whether the moon were a 

 few miles further in or further out; but it makes all the 

 difference in the world when this distance is taken in con- 

 nection with the velocity of the moon in her orbit. For 

 the feasibility of the Newtonian hypothesis presupposes 

 the precisest, undeviating correspondence between the 

 length of the space fallen through by the moon in one sec- 

 ond of time and the rate of her tangential velocity per 

 second, else must she fall to, or escape from, the earth. 

 This point may be made clearer by a reference to Figure 

 1, copied from Sir Oliver Lodge's book, Pioneers of 

 Science (p. 171), with the text accompanying it: 



Now consider circular motion in the same way, say a ball 

 whirled round by a string. 



Attending to the body at O, it is for an instant moving to- 

 wards A, and if no force acted it would get to A in a time which, 

 for brevity, we may call a second. But a force, the pull of the 

 string, is continually drawing it towards S, and so it really finds 

 itself at P, having described the circular arc OP, which may be 

 considered to be compounded of, and analyzable into the rectilin- 



