NEWTON'S THEORY OF PLANETARY MOTIONS 87 



2. Were it possible for me to step into an aeroplane 

 or etherplane and be carried out into free space, other 

 things remaining equal, I should there merely need to 

 start the ball awhirling and it would then go on revolving 

 of its own accord forever. 



3. If I should beat the solid ball into a thin sheet 

 and fashion the same into a hollow ball ten times the 

 diameter of the first, the air resistance would then be 

 multiplied one hundred times and I should be obliged to 

 exert a hundredfold as much muscular energy as in the 

 first instance in order to keep the ball revolving at the 

 same speed. 



4. If a 64-lb. weight were substituted for the orig- 

 inal one-pound, the air resistance would be increased only 

 sixteen times; and, supposing me capable of managing 

 so ponderous an object, I should, once the ball was in full 

 swing, be obliged to exert myself only sixteen times as 

 much as in the first example and less than a sixth as much 

 as in the third. 



5. Finally, were an object held absolutely stationary 

 at any height above the earth and then let go, it should 

 continue so indefinitely, because, (1) since it is, by hy- 

 pothesis, not in motion it has no lateral resistance to 

 overcome, and (2) inasmuch as, by allegation, no energy 

 is used up in stretching the cord (resisting gravity), it 

 cannot possibly fall. Carrying this particular example 

 farther, let us imagine this otherwise stationary moon to 

 possess at this instant a projectile radial velocity away 

 from the earth exactly equal to the force of the earth's 

 gravity (i. e. 1-19 in. a second). What, now, should be 

 the natural result! Obviously, the body would neither 

 fall nor rise during the first second of time, but would 

 remain quite stationary, whereas in the succeeding second 

 it would start falling just as though no such projectile 

 movement had ever existed. This conclusion we can make 

 sure of by a simple experiment: At the earth's surface 

 gravity causes objects to fall 16 feet, instead of only 1-19 

 inch, in the first second. Now fling a bullet straight up 



