CHAPTER IX. 



OF FLOATATION, AND THE DETERMINATION OF THE SPECIFIC 

 GRAVITIES OF BODIES IMMERSED IN FLUIDS. 



OF the several particulars with which we concluded the last 

 chapter, we shall speak in order, beginning with the theory of float- 

 ation and the determination of the specific gravity of bodies, the 

 leading principles of which are contained in the following proposition. 



PROPOSITION III. 



233. 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 upwards by a force, whose intensity is equi- 

 valent 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.* 



Let ABC represent a vertical section of a solid body floating on a 

 fluid, whose horizontal surface is DE, mn being the plane of floata- 

 tion, and men the immersed portion of the floating body. 



Take any two points G and H on 

 the surface of the solid, indefinitely 

 near to each other, and through the 

 points G and H thus arbitrarily as- 

 sumed, draw the straight lines G F 

 and HI, respectively parallel to DE 



the surface of the fluid, and meeting the opposite sides of the solid in 

 the points r and i, so that each point in either of the intercepted 

 portions GH and FI, may be considered as being at the same perpen- 

 dicular depth h& or ZF below the horizontal surface of the fluid. 



At H and i erect the perpendiculars H r and i s, which produce to 

 t and w, and through the points G and F, draw the straight lines G b 

 and F/, respectively perpendicular to the surface of the solid in the 



* The Plane of Floatation is the imaginary plane, in which the floating solid is 

 supposed to be intersected by the horizontal surface of the fluid. 



