348 



OF THE POSITIONS OF EQUILIBRIUM. 



and for the least value of x, it is 

 a:zz20(0.7693375 v/ 3 X 0.7693375 X 0.2306625 0.5)zzl 1 .8 inches, 



the corresponding values of y as found from equation (274), are 

 y 11.8 inches, and y 18.96 inches. 



Now, the positions of equilibrium corresponding to the above values 

 of x and ?/, are 

 as represented 

 in the annexed 

 diagrams, where 1 

 IK is the hori- 

 zontal surface 

 of the fluid ; E F 

 and ef the lines 

 of floatation 



ABCD the position corresponding to am 18.96, and y rz 11.8 inches ; 

 the position abed, being that arising from the reversed values of x 

 and?/; that is, a; 11.8 and y 18.96 inches; EFCD being the 

 immersed part of the section in the one case, and efcd in the other. 



437. If the specific gravity be taken equal to the complement of 

 the above mean, we shall obtain two other positions of equilibrium in 

 which the body will float, corresponding precisely to the above figures 

 inverted, af- 

 ter the man- A^ ^^o 

 ner exhibited 

 in the mar- 

 ginal dia- 

 gram ; where 

 ABCD is the 

 position cor- 

 responding 



to 20 18.96zz 1.04 inches, and abed the position correspond- 

 ing to 20 11.8:^:8.2 inches; the immersed portions EFCD and 

 efcd in the one case, being equal to ABFE and abfe, the extant 

 portions in the other. 



It is moreover manifest, that the centres of gravity of the immersed 

 and extant portions of the section are situated in the same vertical ; 

 for they are connected by a straight line which passes through the 

 centre of gravity of the entire figure ABCD; but in the case of an 

 equilibrium, the centres of gravity of the whole, and the immersed 

 part, are situated in the same vertical line ; therefore also, the centres 



K 



