NEWTON S PEINCIPIA. 367 



may determine the resistance opposed to its motion by the 

 fluid. The calculation is not brief, but the result arrived 

 at for the resistance is 



B, = 6 * /// p * V, 



where V is the velocity of the sphere and \J the constant 

 ratio of p to p. 



The calculation is founded on the supposition that V is 

 so small that its square may be neglected. The part of 

 the resistance, therefore, which depends on the simple 

 power of the velocity, does not vary as the surface exposed 

 to the fluid, but simply as the radius of the sphere. This 

 becomes important when we apply the above formula to 

 determine the terminal velocity of a very small sphere falling 

 in a fluid under the action of gravity. 



Let o- be the specific gravity of the sphere, p, as before, 

 that of the fluid ; then, if V be the terminal velocity, we 

 have 



4 

 GrSa V= *&amp;lt;ra*, 



According to the usual theory, the terminal velocity 

 would have been 



^ ( 1 la. 



Thus V varies as a 2 instead of \/a, and therefore becomes 

 very much smaller, when a is small, than that given by the 

 usual theory. Professor Stokes calculated that for a 

 sphere one thousandth of an inch in diameter, the terminal 

 velocity is 1 593 inches per second; for a sphere one ten- 

 thousandth of an inch in diameter, the velocity is O1593. 

 Those given by the usual theory are respectively 32-07 

 and 10*14 inches per second. 



