266 OF THE EQUILIBRIUM OF FLOATATION. 



cident with the surface of the fluid ; but in consequence of the addi- 

 tional weight abed, the body descends through the space GH, where 

 it again attains a state of quiescence, and the plane of floatation 

 mounts to AB. 



Now, it is manifest, that when the body is acted on by means of its 

 own weight only, (in which case, DE is coincident with the surface of 

 the fluid,) the weight of the whole body is equivalent to that of a 

 quantity of the fluid, whose magnitude is DCE; but when the weight 

 abed is applied, the compound weight is equivalent to that of a 

 quantity of the fluid, whose magnitude is ACB; consequently, the 

 subsidiary weight abed, and the weight of a quantity of the fluid, 

 whose magnitude is ABED, are equal to one another. 



Draw the -straight line ef parallel and indefinitely near to DE; 

 then is DE/e, the small elementary increase of the immersed portion 

 of the body, corresponding to any indefinitely small increase of the 

 weight abed. 



Put a =. the area of the horizontal section passing through AB, 

 determinable from the position and the figure of the 

 body, before the weight abed is applied, 

 n :z: the weight abed, 



rv nr the fluxion or small elementary variation of w ; 

 x G H, the distance through which the body passes in con- 



sequence of the weight n being applied. 

 x zz the fluxion or elementary variation of x, corresponding 



to w, and 

 s =: the specific gravity of the fluid. 



Then, because the line ef is supposed to be indefinitely near to D E, 

 it follows, that the portion of the body whose section is D E/e, may be 

 considered as uniform in area between its bases, and consequently, its 

 magnitude is expressed by ax ; but DE/C, is equal to the quantity of 

 fluid displaced by reason of the elementary weight TV, and it is a well 

 attested principle in hydrostatics, that the weight of the quantity of 

 fluid displaced, and that of the body which displaces it, are equal to 

 one another ; therefore we have 



and the aggregate of the small elementary weights, or the whole weight 

 added, is 



?y = /as*. (205). 



This is the general form of the equation of equilibrium ; but it 

 admits of various modifications, according to the conditions of the 



