XXX INTRODUCTION. 



1st. That when a body floats, or when it is in a state of 

 buoyancy on the surface of a fluid of greater specific gravity 

 than itself, 



It is pressed uptvards by a force, whose intensity is 

 equivalent to the absolute weight of a quantity of the 

 fluid, of which the magnitude is the same as that portion 

 of the body below the plane of floatation, or the horizontal 

 surface of the fluid. 



2dly. That if a solid homogeneous body be placed in a fluid 

 of a greater or less specific gravity than itself, 



It will ascend or descend with a force which is equiva- 

 lent to the difference between its oivn weight and that of 

 an equal bulk of the fluid; 



a proposition which is almost self-evident, but which leads to a 

 series of inferences, practically of vast importance in the me- 

 chanics of fluids. 



Archimedes, the Sicilian philosopher, first established the fun- 

 damental laws of fluid equilibrium, and the specific gravity of 

 bodies immersed in fluids. Having determined the conditions 

 which are requisite to produce and measure the equilibrium of a 

 solid floating on a fluid, the philosopher readily perceived that 



Two bodies equal in bulk, and immersed in a fluid 

 lighter than either of them, lose equal quantities of their 

 weight ; 



or inversely, that when 



Two bodies lose equal quantities of their weight in a 

 fluid, they are of equal volume ; 



this is the 7th Prob. of his first book De Humido Insidentibus, 

 or Of bodies floating on a fluid. Mathematicians generally 

 suppose Archimedes employed this proposition to solve the well- 

 known problem proposed to him by Hiero, king of Syracuse, 

 who having employed a goldsmith to make a crown of pure 

 gold, and suspecting that the artist had not kept faith with him, 

 applied to Archimedes to discover the truth without injuring 

 the crown. The philosopher, it is said, laboured in vain at the 



