NEWTON S PRINCIPIA. 233 



5. In order to investigate the resistances of fluids by ex 

 periment, Newton procured a square wooden vessel whose 

 length and breadth on the inside was nine inches, English 

 measure, and depth nine feet and a half. This he filled 

 with rain-water, and having provided globes made of wax, 

 with lead inclosed therein, he observed the times of the 

 descents of these globes, the height through which they 

 descended being 112 inches. 



The resistance being supposed to vary as the square of 

 the velocity, the heights, fallen in any time t, is given by 



u 2 U* -*JLt \ 



x u t -7 log. 2 -f log. (1 + s J 



where u is the &quot; terminal velocity,&quot; and g the relative 

 force of gravity. It is necessary to find u. Let A be the 

 weight of the globe in vacuo, B its weight in the resisting 

 medium. Then the density of the medium is 



A- B 



where a is the radius of the globe, and g the force of 

 gravity ; and therefore the resistance to the globe when 

 moving with velocity u, is 



3 A-B 



n* 



1 n - . O. , 



lo a g 



and this is to be equal to the weight of the body, which is 

 B ; therefore 



16 B 

 U ^T A=B a * 



-!* , 



The value of B can be found by weighing the globe in 

 water. To find A we must weigh it in air, suppose we 



