of floating Bodies, and the Stability of Ships. 59 
The demonstration of this construction is founded on an 
obvious and elementary principle of mechanics. — It is this. — 
The common centre of gravity of any system of bodies (consi- 
dered as heavy points or centres of gravity), being given in 
position, if one of these bodies should be moved from its 
place, the corresponding motion of the common centre of gra- 
vity, estimated in any given direction, will be to the motion 
of the aforesaid body, estimated in the same direction, as the 
weight of the body moved is to the weight of the whole sys- 
tem. To apply this proposition. The volume IRMN (fig. 2.) 
may be assumed as a system of bodies, of which the common 
centre of gravity is E. One of the bodies composing this 
system, namely, the volume I W X, concentered in the point 
a, is transferred in consequence of the inclination of the solid 
through the angle S G K from the point a to the point d, in 
which the equal volume NXP is concentered : this will have 
the effect of moving the common centre of gravity of the 
system E. But it is required to find how much the position 
of this centre E has been changed in the direction EY parallel 
to AB, which is the given direction stated in the proposi- 
tion. The motion of the centre of gravity a, from a to d, es- 
timated in the given horizontal direction, is be: then, accord- 
ing to the mechanical proposition, as the volume W R M P 
or ADHB is to the volume IWX or NXP, so is the line 
be to ET, the corresponding motion of the centre of gravity 
E estimated in the given horizontal direction ; consequently 
if a line FTS is drawn through the point T parallel to the 
vertical line GO, the centre of gravity of the immersed part 
Q must be situated somewhere in the line FTS : subtract- 
ing from ET the line ER (which is the sine of the given 
I 2 
