EORELLI ON SWIMMING. 



381 



The mass of water a may be considered equal in weight to the body 

 of lead pih, and the mass e to the wood lih. These will form two 

 weights,, ap and el, the former of which will turn and fall downwards 

 by bending the arm to which the lead is affixed, and the latter upwards 

 to which the wood is affixed. The centre of gravity of the whole body 

 pi remains in the same situation, that is, it neither rises nor falls in 

 the water; therefore the right line cb joining the lineal centre with 

 the centres of gravity, will turn round upon the immoveable centre b, 

 by describing the arc of a circle cd (with the radius be) so far like a 

 pendulum, until it reaches bd perpendicular to the horizon and the 

 centre of gravity c nearest the centre of the earth, and thence p will 

 occupy the lowest, and / the highest situation. 



Secondly. When the speciHc gravity of the compound body is 

 either greater or less than water, then it (pi) always rises or sinks in 

 the water, and the two collateral weights ap and el balancing them- 

 selves in the same manner as a ship, turn round the lineal centre b, 

 equally yielding to their tendency as if the ships and centre of the 

 magnitude were altogether at rest. Therefore it is necessary that the 

 heavier part p fall along with the common centre of gravity c towards 

 the lowest place, that is nearest the earth's centre ; and the lighter part 

 / rises upwards as already mentioned. 



If the same compound body pi float upon the water, the result will 

 be the same. To illustrate this, let the spherical figure ehfg (fig. 2.) 



Fig. 2. 



c.t ^\ T? 



/ e 



A \ h 



/ ( 



A { h 



i y 



whose centre of magnitude b is the centre of the sphere, but c the 

 centre of gravity, and let the portion ehf be above the water rs. It 

 is evident that the compound body pi, in whatever manner it revolves 

 round the centre b, the portion Jge, which is immersed, will always be 

 of the same magnitude, because the mass of water equal to the part 

 immersed is of the same weight as the whole compound pi. Hence it 

 follows that the sphere pi rests in such a position equally well as if it 



