336 



OF THE POSITIONS OF EQUILIBRIUM, 



subjoined figures, whereas in all the previous cases, IK is the horizontal 

 surface of the fluid ; men and mo A Bra being the areas of the immersed 

 and extant portions of the body, corresponding to # 16.682 inches, 



and 2/z=:10.318 inches ; the subcontrary figures odp and oabcp being 

 the respective areas when #=: 10.318 inches, and y zn 16.682 inches. 



Bisect mn in F, and through the point F draw FP at right angles to 

 mn, meeting the diagonal AC in the point p, and join pm and PW; 

 then it is manifest, that the straight lines pm and PW are equal to one 

 another, as ought to be the case when the solid floats in a state of 

 equilibrium; and moreover, the area of the immersed portions men, 

 and odp, are to the area of the entire sections A BCD and abed, as the 

 specific gravity of the floating solid, is to that of the supporting fluid. 



426. If the conditions of the problem should be reversed, that is, 

 if three angles of the figure be immersed beneath the plane of floata- 

 tion, and one extant above it; then, by a similar mode of investiga- 

 tion, it may be shown, that 



\xy s' &(' s) 

 and furthermore, that 



.. __ 



~ ' 



2 ~ 2 



Now, these being similar equations to those which correspond to the 

 case of one angle being immersed beneath the surface of the fluid ; it 

 follows, that all the other steps of the investigation would also be 

 similar, and consequently they need not be repeated. 



PROBLEM LIX. 



427. Suppose that a solid homogeneous prismatic figure, 

 whose transverse section is rectangular, is found to float in a 

 state of equilibrium on the surface of a fluid with its two 

 edges immersed : 



