EXAMPLES. 



less than jV6, two values may be assigned to the density 

 of the solid which will cause it to float in indifferent equi- 

 librium. 



If, for instance, b = h, we have 



p = | 



^ = 0.78868 or 0.21132. 



COR. 3. When j > V6, the value of p is imaginary, 



ft 



i. e.,-if the ratio of the breadth of the solid to the height is 

 greater than A/6, no value can be given to the density 

 which will cause the stability to vanish. In this case the 

 solid, placed with EF horizontal, must in all cases continue 

 to float permanently in that position, whatever may be the 

 density, providing it is always less than that of the fluid. 



COK. 4. The term - - in (1), or 



in (2), is the dis- 

 tance between the centre of buoyancy and the metacentre. 



2. Determine the angle of inclination 6, in order that the 

 parallelepiped EFDC may 

 be in a position of indiffer- 

 ent equilibrium. 



Let b = the breadth EF 

 of the section of the paral- 

 lelopiped, y = the depth 

 of immersion AC = BD, 

 and e angle AOH. Then 



Fig. 25 



A = ABDC = HKDC 

 = ty, (1) 



A t = AOH = BOK. 



and AH = BK = 



But AO = OB = 



therefore 



tan 



=#*tan0. 



(2) 



