XXX11 INTRODUCTION. 



duced, though not voluminous, fully show the different ways of 

 solving the ancient problem of Archimedes 



To find the respective weights of two known ingredients 

 in a given compound. 



The principle enunciated above, may be popularly expounded 

 in the following manner. Every body placed on a surface of 

 water, has a tendency to sink by its own weight : it is, however, 

 resisted by a force equivalent to an equal bulk of the fluid, or 

 of as much fluid as will fill the space occupied by the body. 

 Should the body be heavier than the fluid, bulk for bulk, its 

 greater weight will cause it to descend, for the upward pressure 

 of the fluid will not prevent the descent. When, on the other 

 hand, the body is specifically, that is to say bulk for bulk, 

 lighter than the fluid, its pressure downwards will be less than 

 the upward pressure of the fluid at the same depth; conse- 

 quently, as the greater force necessarily overcomes the less, 

 and the upward pressure is the greater, the body will rise. 

 When the body and the fluid have the same specific gravity, 

 then equal masses of each are of the same weight, and the de- 

 scending force being equally balanced by the ascending force, 

 the body will float with its upper surface coincident with the 

 surface of the fluid, or in any other position whatever in which 

 it may be placed. 



It is very obvious from these laws, that if, by any contrivance 

 or change, the specific gravity of a body can be so altered and 

 varied, as to be at one time greater, at another time less, and 

 then equal to the specific gravity of the fluid in which it is 

 placed, the said body will sink, or rise, or remain at rest, accord- 

 ing to the variations produced in its specific gravity. Lecturers 

 amuse their audiences with glass images, which, upon the 

 principle here adverted to, ascend or descend, or remain in mid- 

 water, at the pleasure of these philosophers. 



The doctrine of the Equilibrium of Floatation, which appears 

 in Chapter XL, is as old as the days of Archimedes, who ex- 

 amines the conditions which are requisite to produce and pre- 

 serve the equilibrium of a solid floating in a fluid. He shows 

 that when a body floats in a state of equilibrium on the surface 

 of an incompressible fluid, 



