184.] UNIFORM MOTION OF SPHERE. 229 



whence 



M- + 



Hence 



To find the total rate of dissipation of energy we must multiply 

 this by 27rrsm0rd8dr, and integrate with respect to 6 between 

 the limits and TT, and with respect to r between the limits a and 

 oo . The final result is 



If we substitute from (39), this becomes 



Now if P be the force which must act on the sphere in order to 

 maintain the motion, the rate at which this force works is PV, 

 whence 



or P= 6777*1 F. ....................... (43). 



In the case of a sphere of mean density a- falling under the 

 action of gravity, P is the excess of the weight f Tra-cfg over the 

 buoyancy fTrpcfy, so that the terminal velocity is given by 



(44). 



For a globule of water, of 001 in. radius, falling in air, Stokes 



finds*, 



V= 1 59 inches per second. 



* The value of /i employed in this calculation was deduced from Baily s 

 experiments on pendulums, and is about half as great as that found by Max 

 well (Art. 178). If we accept this latter value, the above value of V must be 

 halved. 



