OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 221 



consequently, by division, we obtain 

 32r+3ffd_ 36484 



36 s n 4860 ~ 



therefore, by multiplication we shall have 



7.507X27 = 202.689, 



and finally, by evolution, it is 



x= y 202.689= 14.23 inches. 



COROL. Hence it appears, that when the specific gravities of the 

 fluid and the immersed body, are equal to one another, the fluid rises 

 in the vessel to the height of 14.23 inches ; but when the specific 

 gravities are to each other as 1 : 0.6, it rises only to 13.414; the 

 reason of the difference, however, is manifest, for in the case of equal 

 specific gravities, the spherical body is wholly immersed ; but when 

 the specific gravities are unequal, only a part of the body falls below 

 the plane of floatation. From the above we deduce the following 

 inferences. 



245. INFERENCE 1. If a homogeneous body be immersed in a fluid 

 of the same density with itself: 



It will remain at rest> or in a state of quiescence, in all 

 places and in all positions. 



Let ABCD represent a vessel, filled with an incompressible and 

 non-elastic fluid to the height D, and let G be a 

 homogeneous body, of the same density or specific 

 gravity as the fluid. 



Now, it is manifest, that when the body G is put 

 into the vessel and left to itself, it will by reason of 

 its own weight, sink below ab the original surface, 

 and raise the fluid to the height E D, where the body 

 will be entirely under the fluid, and the whole mass 

 in a state of equilibrium with the surface at EF. 



Then it is evident, that the body being of the same density as the 

 fluid in which it is placed, it will press the fluid under it, just as much as 

 the same quantity of the fluid would do if put in its stead, and conse- 

 quently, the pressure exerted by the solid, together with that of the 

 superincumbent fluid, presses downwards with the same energy, as if 

 it were a column of fluid of equal depth. 



Therefore, the pressure of the body against the fluid at H, is equal 

 to the pressure of the fluid against the body there; consequently, 



