/ UNIVERSITY 



V Of .yS 



OF TIIR EQUILIBRIUM OF FLOATATION. 273 



It will float in equilibria between them, when the weight 

 of the fiuids respectively displaced, are together equal to the 

 weight of the solid body which causes the displacement ; the 

 specific gravities of the fluid being supposed known. 



Let A BCD be a vertical section passing through the centre of gravity 

 of the floating body, and suppose that 

 IK is the common surface of the two 

 fluids, in which the solid is quiescent, 

 GH being the surface of the lighter fluid. 



Now, it is manifest, that since the 

 body ABCD is specifically heavier than 

 one of the fluids, and specifically lighter 

 than the other, it cannot be entirely at 



rest in either, but must rest between them in such a position, that the 

 sum of the weights of the fluids displaced shall be equal to the whole 

 weight of the solid. 



Let EFD be perpendicular to i K, the common surface of the fluids 

 in which the body floats ; then it is evident, that the pressure down- 

 ward on any point of the base D, is equal to the weight of the incum- 

 bent line of solid particles, whose altitude is BD the thickness of the 

 body, together with the weight of EB the superincumbent column of 

 trie lighter fluid ; and again, the pressure upwards on the same point 

 D, is equal to the weight of a column of the heavier fluid whose alti- 

 tude FD, together with the weight of a column of the lighter fluid, 

 whose altitude is EF. 



Put d EB, the depth of the body below the upper surface of the 



lighter fluid, 

 d' EF, the whole depth of the lighter fluid, or the depth of 



the common surface, 

 3 FD, the depth of the body below the common surface, or 



the surface 1 of the heavier fluid, 

 $ = BD, the whole thickness of the solid body, 

 5 = the specific gravity of the lighter fluid, 

 s' zz the specific gravity of the heavier fluid, 

 s" = the specific gravity of the solid body, 

 p rzr the downward pressure, and 

 p' ~ the upward pressure. 



Then, because the weight of any body, whether it be fluid or solid, 

 is expressed by the product of its magnitude drawn into its specific 

 gravity, it follows that the downward pressure on the point D, is 



VOL. I. T 



