OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 227 



vessel containing the fluid, abed a corresponding 

 section of the hollow cylinder, and EFGH that of 

 the attached or cylindrical body. 



Now, it is manifest, that in consequence of the 

 connection between the hollow cylinder and the 

 attached body, the downward pressure of the fluid 

 can have no effect upon that portion of the upper 

 surface of the body whose diameter is dc ; and be- 

 cause the hollow cylinder abed, is supposed to be 

 without weight, it can have no influence on the 

 downward tendency of the body EFGH : an equilibrium will therefore 

 obtain, when the downward pressure on the surface EeZ, CF, together 

 with the weight of the body, is equal to the upward pressure on the 

 bottom HG. 



Put d dc, the diameter of the hollow cylinder destitute of weight, 

 5 zz: EF, the diameter of the attached body, 

 I zz: EH, its perpendicular length, or vertical altitude, 

 a zz: the area of the end of the hollow cylinder, 

 A z that of the attached cylindrical body, 

 s zz: its specific gravity, greater than that of the fluid, 

 s' zzz the specific gravity of the fluid 

 w zz: the weight of the body, 

 p zz: the pressure on its upper surface, 

 p zz: the pressure on its base, and 

 x zz: e d, the distance below AB, the upper surface of the fluid. 



Then, by the mensuration of surfaces, the area of the lower extre- 

 mity of the hollow cylinder abed, becomes :z .7854J 2 , 



and that of the base of the attached body, is A zz: .78543* ; 

 and the difference of these, or the quantity of the upper surface of 

 the body, which is exposed to the downward pressure of the fluid, is 



A z=.7854(3 2 <Z); 



consequently, the downward pressure becomes p zz: .7854 (3 2 c? 2 ) s' x \ 

 but the absolute weight of the body is expressed by its magnitude or 

 solidity, drawn into its specific gravity ; consequently the expression 

 for the weight of the attached body becomes tuzz: A/szzr.78543 2 Js; 

 therefore, we have for the whole tendency downwards, 



p 4- w zz: .7854 (3 2 d*} s'x + .78543* /s, 

 and from this, by collecting the terms, we obtain 

 p 4- w = .7854 {(3 2 P) s' x + tf Is}, 

 Q 2 



