226 OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES, 



and consequently, it tends upwards, with a force equal to the dif- 

 ference between its own weight and that of an equal bulk of the 

 fluid ; and continuing to ascend, it will attain a position in which its 

 weight is equal to that of a quantity of the fluid of the same magni- 

 tude as the part immersed ; and this is what we understand by the 

 relative levity of the body in the fluid. 



259. These inferences being admitted, we shall now proceed to 

 exemplify the general formula resulting from our proposition, viz. 

 that in which we have 



The practical rule for reducing this equation, may be expressed in 

 general terms in the following manner. 



RULE. Multiply the common magnitude of the body and 

 the fluid, by the difference of their specific gravities, and 

 the product will be the force of ascent or descent, according 

 as the specific gravity of the body is less or greater than that 

 of the fluid in which it is placed. 



260. EXAMPLE. A mass of dry oak, whose magnitude is equal to 

 7 cubic feet, and specific gravity equal to 0.8 (that of water being 

 unity), is plunged into a vessel of fluid, whose specific gravity is 

 0.932 ; with what force will it ascend ? 



Here, according to the rule, we have 



/=: m (s s'} =: 7(.932 .8) .924 of a cubic foot of the 

 body whose specific gravity is 0.932; consequently, for the force in 

 Ibs. avoirdupois, we have 1 : 62.5 : : 924 : 57.75 Ibs. 



PROBLEM XXXIII. 



261. In a vessel filled with an incompressible and non-elastic 

 fluid, is placed a hollow cylinder, which we shall consider as 

 being perfectly void of gravity or weight; to the bottom of 

 which, a cylindrical body of a given magnitude, and whose 

 specific gravity is greater than that of the fluid, is so closely 

 fitted that no fluid can enter : 



It is required to determine, how far below the surface of 

 the fluid the body will descend, before the tendency down- 

 wards, and the pressure upwards, are in equilibria with one 

 another. 



Let A BCD in the annexed diagram, be a vertical section of the 



