1822.] Difereme in tJ^ Specific Gravity of Bodies. 413 



of levity seems to operate, the effect is to be attributed to the 

 superior specific gravity of the fluid, and is relatively the same 

 as if a body of the same specific as the fluid were to fall through 

 a fluid of the same specific gravity as the body, the difference of 

 specific gravity being the moving force. In order to ascertain 

 the velocity with which a certain volume of cork would rise in 

 water, the same result would be obtained by considering the 

 fluid as being of the specific gravity of the cork, and a sohd of 

 the volume of the cork, but of the specific gravity of the fluid, 

 the velocity at any point will be the same, the direction being 

 upwards instead of downwards. 



What will be the greatest velocity vi^hich a sphere of cork of 

 one inch in diameter can acquire in rising through a column of 



water ? The theorem v — ( — ^ '^ ^ ' "^ ^' ) will become v = 

 C^^3b" ^) • Let :r=:l inch =-0833 feet ; B = and -24/= I, 



. 16 X 16 X -083 X -76 cc r c l i 



then V = g ^ ,^^ = 22*5 feet nearly. 



What must be the diameter of a sphere of cork to acquire a 

 uniform velocity of one inch per second? 



Here x = rz — tt — ^. ; this will give x in feet ; and x = 

 16 ^(/-Bj' ° ' 



.. ^ i/ Va^ nr = '000312 in inches. 



12 X 16 X 16 X -76 



When fluids of different specific gravities are mixed together 

 having no chemical affinity for each other, as is the case with 

 oil and water, or water and mercury, the lighter fluid ascends 

 with the same velocity, and in every respect is similar to a sohd 

 body of the same specific gravity with the fluid, if the lighter 

 fluid be kept in a distinct volume, as is the case with a balloon. 

 It is exactly the same as if a body of uniform density having the 

 mean specific gravity of the gas, and the matter containing it, 

 and the theorem applied to the case of cork rising in water, 

 would equally apply in this case. If a constant stream of the 

 lighter fluid be introduced into the denser one, and the succes- 

 sion kept up, a uniform velocity will be established which will be 

 as the square root of the height, and as the difference of density 

 between the two fluids to the greater density. It will be the 

 same thing whether the fluids are naturally of different specific 

 gravities, or the volume of one part of the fluid be changed by a 

 change of temperature. This may be illustrated by filling a tall 

 glass vessel with hot water containing small pieces of amber, a 

 substance very nearly of the same specific gravity with water ; 

 the sides of the vessel exposed to the air become cooled, and 

 the water in contact loosing its heat becomes specifically 

 heavier and descends ; and as this is taking place all round the 

 vessel, an upward current takes place in the middle of the column 



