MEASURE OF STABILITY. 61 



If the point were below G, e would be negative and (2) 

 would be 



8 = P T " e sin 

 Hence, in general, we have 



8 = P ^ Sin 



the upper or lower sign being used according as the centre 

 of buoyancy is above or below the centre of gravity. 



COR. 1. If the displacement be small, the cross-sections 

 ACH and BCK can be treated as isosceles triangles, and 

 sin 6 = 6. Denoting the width AB = HK of the body at 

 the plane of flotation by 5, we have 



and RL = a = 

 which in (4) gives 



COR. 2. When the centre of buoyancy is above the cen- 

 tre of gravity of the body, the stability is positive, as also 

 in the case when the centre of buoyancy is below the centre 



J3 



of gravity while e is less than ^~-j ; in this case the equi- 

 librium is that of stability. 



J3 



If e is greater than T ^ , and the cent/e of buoyancy is 



below the centre of gravity of the body, the stability is neg- 

 ative, or the equilibrium is that of instability. 



J3 



If e is negative and equal to 1 -r-r , the stability is zero, 



and the equilibrium is that of indifference. 



That is, the centre of buoyancy may be 'below the centre 

 of gravity and yet the stability be positive, so long as e does 



