214 Prof. F. Elgar. The Variation of 



stability will depend, not only on the conditions which enter into 

 M. Bouguer's solution, but also on the shape given to the sides of the 

 vessel above and beneath the water-line or section, of which M. 

 Bouguer's theorem takes no account." It may be added that 

 Bougaer's theorem also neglects to take into account the volume of 

 the above- water part of a ship, and to some extent the form of the 

 below-water part; as well as the absolute height of the centre of 

 gravity, which has been already referred to. 



Atwood lays down a general theorem for determining the righting 

 moments, at any required angles of inclination, possessed by a ship 

 having a given draught of water and a fixed height of centre of 



FIG. 8. 



gravity. It is the following : Let fig. 8 represent the transverse 

 section of a ship which is inclined to an angle WOW l =0 from the 

 upright water-line WL. Let G be the position of the centre of 

 gravity; B the centre of gravity of the volume of the displaced fluid 

 or centre of buoyancy when upright; and B l the position to which it 

 has been moved by the inclination of the vessel through the angle 0. 

 The original form of the under-water volume WAL has now been 

 changed by the addition of the wedge-shaped piece LOLj and the 

 deduction of the wedge-shaped piece WOWj. The volumes of these 

 wedges must be equal, because the displacement has not been changed 

 by the mere act of inclination. Let g l be the centre of gravity of the 

 wedge WOWj, g z that of LOLj, and v the volume of each wedge. 

 Then the horizontal shift, BB, of the centre of buoyancy x the volume 

 of displacement, or VxBB,=ux hfa. But BR=GZ + BGsin0, and 



therefore GZ=^ x h^ BG sin 0. 



This is the formula by which the stability of a ship at various 

 angles of inclination is ordinarily computed ; GZ being the arm 

 of the couple at the ends of which the weight of the ship and the 



