386 GENREAL PROPOSITIONS. 



paradox ; because, in consequence of it, a very small quantity 

 of water may be made to produce all the effects of a very great 

 weight. Mr. Bramah's very ingenious press is founded upon this 

 property of fluids. If the side and bottom of a vessel be equal, 

 then the pressure on the bottom is twice , as great as on the sides. 

 Hence, if we wish to inclose a pond of water by a wall, it is obvi. 

 ous that the thickness of the wall at the bottom must be greater 

 than at the top, as it has a much greater pressure to withstand. If 

 the wall at the bottom be -|ths of the height of the water, it will 

 just balance the pressure of the water. A secure wall would re. 

 quire to be thicker. 



4. When a boay floats in water, it loses a portion of its own 

 weight, just equal to that of the water which it displaces. The 

 same proposition holds if the body be plunged entirely under the 

 surface; in which ca<e the bulk of water displaced is just equal to 

 the bulk of the body immersed. This principle was first observed 

 by Archimedes, and he founded on it the method of ascertaining 

 the specific gravity of bodies, as at present practised. Let vv be 

 the weight of any body in air; w' its weight when immersed in wa- 

 ter, then w w' is the weight of the water equal to the bulk of tiie 

 body. Let 1 be the specific gravity of water, and s the specific 

 gravity of w, then we have 1 : 5 : : w w' : w ; which gives us 5 :n 



w 



;, the specific gravity required. As the weight of water va- 



w w 



ries with the temperature, it is usual to take specific gravities at the 

 temperature of 60. 



5. When a body floats in witter it affects a particular position, 

 and this position is such, that the line which joins the centre of 

 gravity of the body and the centre of gravity of the immersed part, 

 is always vertical. Hence a body floating in water may have such 

 a form as to have no stability, but to float indifferently in any po- 

 sition whatever. The form must be such, that the centre of gravity 

 of the immersed part always retains the very same position, what- 

 ever part of the body is under water. This is obviously the case 

 with a sphere : or a body floating in water may have a great deal 

 of stability or tendency to return to a particular position : or it may 

 have a particular position which it prefers, but from which it is very 

 easily driven. Stability is obviously an important requisite in ship- 

 building. Now the lower the centre of gravity of a ship is below 



