254 NEWTON S PUINCIPIA. 



A!. 2 a -f B .2 2 + C 2 af 



a form well adapted for a comparison with the results of 

 experiments. Taking the second, fourth, and sixth expe 

 riments of the set discussed above, we get three equations 

 to determine the three quantities A , B , C . 



A = .0000916, 



B = .0010847, 



C = .0029588. 



But the resistance will be expressed by 

 W f 7 7 3 



T{n A a +i5) B/a * + *&amp;lt; 



w r 3 i 



= y-- \ .0000583 a + .0007593 a ~*+ .0022169 a 2 [ 



where W is the weight of the body. Thus for such swift 

 motions in air as those varying from 4 to 120 inches per 

 second, the resistance varies as the square of the velocity. 

 Since a in the second case represents 1, in the fourth 4, 

 in the sixth 16, the resistance will be to the weight of the 

 globe, in the second case, as .0030345 to 121, in the fourth 

 .041748 to 121, in the sixth .61705 to 121. 



The next point to be determined is the manner in which 

 the resistance depends on the surface. For this purpose 

 Newton suspended a leaden ball of 2 inches diameter, 

 weighing 26 1 ounces troy, by the same thread that he 

 suspended the former ball, the length of the simple pen 

 dulum being 10 J feet. He found the resistance to the 

 ball was 7 times that on the former ball. But the ratio 

 of the squares of the diameters was llyf to 1 nearly. 

 * f Therefore the resistance of these equally swift balls was 

 in less than a duplicate ratio of the diameters. But the 

 resistance of the thread has not yet been considered, which 

 was certainly considerable. This could not be accurately 



