692 KANSAS CITY REVIEW OF SCIENCE. 



extract the square root of the product, and we shall have 2,411,631 inches per 

 second, through which the moon must move in orbital flight to make centripetal 

 force equal gravity and keep it from falling. 



But we should have strange times on the earth ; we should be blessed with 

 more than two moons every day, for with this velocity the moon would make a 

 revolution in ten hours fifty-five minutes, giving us new moon in the evening, 

 say at 6 o'clock P. M., and full moon before midnight. We could see it move, 

 and would wonder at the unusual aspect of Nature. Hence we are sure that 

 gravity is not any where near as strong at the moon's distance as on the earth's 

 surface. Let us try again, and since the moon is sixty radii of the earth away, 

 conceive gravity to be one-sixtieth as strong. Divide 386 by sixty, and the quo- 

 tient is 6.4333 inches, which we will assume as the velocity gravity can impart in 

 one second at the moon's distance. Using this as a multiplier in the same com- 

 putation as before, and we obtain orbital velocity per second of 311,152 inches to 

 balance gravity. By dividing the circumference of the lunar orbit by this num- 

 ber, we find the time of revolution, which is three days, twelve hours and thirty 

 minutes, and are assured that gravity is far less than one-sixtieth of what it is on 

 the earth, because the moon requires over twenty-seven days to make circuit. 

 We have not yet found the law, and how shall we proceed ? Is the problem capa- 

 ble of solution ? Let us take a reverse method and begin with the actual velocity 

 of the moon on its orbit, and see how much attraction the centrifugal force gen- 

 erated by that motion balances. Centrifugal force produced by a revolving body 

 is equal to the square of its velocity, divided by the radius of its orbit. The 

 moon goes around the earth in 2,360,591 seconds, with velocity of 40,098 inches 

 per second. Square this velocity and divide the product by the number of inches 

 in the mean distance of the centre of the moon from the centre of the earth, 

 and the quotient will be 0.1072 of an inch. That is, the centrifugal force de- 

 veloped by the moon's orbital motion is equal to a force which, acting one second 

 on a body at rest, could at the close of the second cause it to move with that ve- 

 locity per second. But we know this force to be equal to the gravity of the earth 

 at the distance of the moon, because the moon does not come any nearer. Now 

 how much weaker is this gravity than it is on the surface of the earth ? Divide 

 386 by 0.1072 and the quotient is 3,600; it is 3,600 times less, but behold 

 3,600 is the square of sixty, and sixty is the ratio of the distance of the moon 

 from the centre of the earth to the distance of the surface of the earth from its 

 centre. The mighty mind of Newton saw the great results of this law, as they would 

 be developed from age to age ; and his intellect beheld that in time to come, it 

 would enable man to weigh suns so distant that light requires years to traverse 

 the awful chasm to reach our world. Newton published the law and rendered his 

 genius the subject of admiration so long as intellectual man shall inhabit the 

 earth. It is this: "Every particle of matter attracts every other directly as to 

 mass, but inversely as to distance squared." 



