UPWARD PRESSURE, BUOYANT EFFORT, 51 



COB. 1. If a body be supported entirely by a fluid, the 

 weight of the body must be equal to the weight of the fluid 

 displaced, and the centres of gravity of the body and of the 

 fluid displaced must lie in the same vertical line. 



Sen. These conditions hold good, whatever be the nature 

 of the fluid in which the body is floating. If it be hetero- 

 geneous, the displaced fluid must consist of horizontal strata 

 of the same kind as, and continuous with, the horizontal 

 strata of uniform density, in which the particles of the sur- 

 rounding fluid are necessarily arranged. If, for instance, a 

 "solid body float in water, partially immersed, its weight will 

 be equal to the weight of the water displaced, together with 

 the weight of the air displaced. 



The upward pressure of a fluid against a solid, and which 

 is equal to the weight of the displaced fluid, is called the 

 buoyant effort of a fluid. The centre of gravity of the dis- 

 placed fluid is called the centre of buoyancy. The buoyant 

 effort exerted by a fluid acts vertically upwards through the 

 centre of buoyancy. 



The enunciation and proof of this proposition are due to Archi- 

 medes, and it is a remarkable fact in the history of science, that no 

 further progress was made in Hydrostatics for 1800 years, and until 

 the time of Stevinus, Galileo, and Torricelli, the clear idea of fluid 

 action thus expounded by Archimedes remained barren of results. 



An anecdote is told of Archimedes, which practically illustrates the 

 accuracy of his conceptions. Hiero, king of Syracuse, had a certain 

 quantity of gold made into a crpwn, and suspecting that the goldsmith 

 had abstracted some of the gold and used a portion of alloy of the same 

 weight in its place, he applied to Archimedes to investigate whether 

 such was the case, and to ascertain the nature of the alloy. It is re- 

 lated that while Archimedes was in his bath, reflecting over the diffi- 

 cult problem which the king had given him, he observed the water 

 running over the sides of the bath, and it occurred to him that he was 

 displacing a quantity of water equal in volume to that of his own body, 

 and therefore that a quantity of pure gold equal in weight to the 

 crown would displace less water than the crown, the volume of any 

 weight of alloy being greater than that of an equal weight of gold. 



