178 OUTLINES OF NATURAL PHILOSOPHY. 



ven area of the triangle BDE = 2c 2 ; then 



FH 2 =(a *) 2 +(6 yY and (* my) = c\ 



n 



where m is the cotangent, and n the sine of the 

 angle B. Therefore taking the Fluxion of FH* 

 substituting for x its value from the preceding 

 equation, and supposing the whole s 0, we have 

 (a x) (x 2 my) + b y y* = 0. By the com- 

 bination of this equation with the former, we may 

 obtain either an algebraic solution, by a biquadra- 

 tic equation, or a geometrical construction by the 

 intersection of two hyperbolas. 



See the solution of other problems of this kind, AR- 

 CHIMEDES de Humido Insidentibus, lib. n. BOSSUT, 

 Hydrod. torn. I. chap. xii. 166., &c 



261. When the equilibrium of a floating body is 

 disturbed, or when the centres of gravity of the 

 whole and of the part immersed, are not in the 

 same vertical line, if a vertical plane be made to 

 pass through both those centres^ the body will re- 

 volve on an axis passing through its centre of gra- 

 vity, and perpendicular to that plane. 



This follows from what has been proved concerning 

 the rotation of bodies, 



BOSSUT, Hydrod. torn. n. 179. ATWOOD, Phil. 

 Trans. 1796. 





