394 Hydrodynamics. 



(5.) Hence the greatest velocity that a globe acquires in de- 

 scending through a fluid, by means of its relative weight in the 

 fluid, will . be found by putting the resisting force equal to that 

 weight. For, after the velocity has arrived at such a degree that the 

 resisting force is equal to the weight that urges it, it will increase 

 no longer, and the globe will afterwards continue to descend with 

 that velocity uniformly. Now, s' and s being the specific gravi- 

 ties respectively of the globe and fluid, s 7 s will be the rela- 

 tive gravity of the globe in the fluid, and therefore 



w i^D 3 (s 7 s) 

 is the weight by which it is urged ; also 



71 S V 2 D 2 



m = ~^j- 



is the resistance ; consequently 



71 S V 2 D 2 , , 



_ = 1* D (S'_S), 



when the velocity becomes uniform ; from which equation is 

 found 



I/ S' Sv 



v = (2 . f D . 



<^\ e s 



for the above uniform motion or greatest velocity. 



By comparing this with the general equations, v = \/g s, it 

 will be seen that the greatest velocity is that acquired by the 



accelerating force , in describing the space f D, or that 



acquired by gravity in describing freely the space 



s 7 s 



If s' = 2 s, or the specific gravity of the globe be double that 



s' - s 

 of the fluid, = 1 = the natural force of gravity ; and the 



globe will attain its greatest velocity in describing f D or f- of its 

 diameter. It is further evident, that if the globe be very small, 

 it will soon attain its greatest velocity, whatever its density 

 may be. 



