Solids immersed in Fluids. 307 



body in any given position in a fluid, it is only necessary 

 to destroy the vertical part of the pressure ; and to effect this, 

 two things are required, namely, (1.) A downward effort 

 equal to that of the upward pressure of the fluid ; and (2.) 

 A coincidence of these efforts in the same vertical line. Now 

 the vertical upward pressure or buoyancy of the fluid is equal 

 to the weight of the portion of fluid displaced 5 hence, if the por- 

 tion of fluid displaced weighs more than the immersed body, the 

 body will float, and it will elevate itself until the portion of fluid an- 

 swering to the part immersed, shall weigh just as much as the entire 

 body. 



Accordingly, if when a body floats, we add to it a certain 

 weight, or take a certain weight from it, it will sink or rise 

 until the increase or diminution of the fluid displaced shall 

 become equal to this new weight. If the weight added or sub- 

 tracted be small compared with that of the body itself, the quan- 

 tity IK, by which the section AB is depressed or elevated, will Fig.207. 

 be so much the less, according to the smallness of this new 

 weight compared with the extent of the section AB. When, 

 therefore, this new weight is inconsiderable, and the section AB 

 is large, AB, and A'B' may be considered as equal, and the 

 difference in the bulk of fluid displaced, occasioned by the sup- 

 posed change of weight, may be estimated by the surface AB 

 multiplied by IK, that is, by AB X IK. Therefore if w repre- 

 sent the weight of a cubic foot of the fluid,! w X AB X IK will 

 express the weight of the bulk in question, the surface AB, and 

 the altitude IK being estimated in feet. Thus, if w' be the weight 

 added or subtracted, we shall have 



w x AB x IK = a/, 

 from which we deduce 



IK = 



that is, in the case of a vessel, for example, in order to find how 

 much a certain addition to the cargo will sink the vessel, we divide 



t This in the case of fresh water is at a mean very nearly 

 and in that of sea water 



