OF THE EQUILIBRIUM OF FLOATATION. 257 



308. INF. 1. If any homogeneous plane figure be divided symme- 

 trically by its vertical axis, and placed in a fluid of greater specific 

 gravity than itself : 



It will remain in equilibria with its bisecting axis vertical. 



309. INF. 2. If any homogeneous solid, generated by the revolu- 

 tion of a curve round its vertical axis, be placed in a fluid of greater 

 specific gravity than itself: 



It will remain in equilibria in that position, that is, with its 

 axis vertical. 



310. INF. 3. If in any homogeneous prismatic body, whose axis is 

 horizontal, the centre of gravity of the section made through its middle 

 parallel to its base, be in the same vertical line with the centre of 

 gravity of that part of the solid which falls below the plane of float- 

 ation : 



The body will remain in equilibria in that position, if placed 

 in a fluid of greater specific gravity than itself. 



This is manifest, for the centres of gravity of the whole prism, and 

 of the part immersed, may be conceived to lie in those points, and 

 consequently, the prismatic body is in a state of equilibrium. 



PROPOSITION VII. 



311. When a solid body floats upon a fluid of greater specific 

 gravity than itself, and has attained a state of equilibrium : 



The magnitude of the body, is to that of the part immersed 

 below the plane of floatation, as the specific gravity of the 

 fluid is to that of the floating body. 



For by the inference to the third proposition, when the body floats 

 in a state of equilibrium": 



The weight of the floating body, is equal to the weight of a 

 quantity of the fluid, whose magnitude is the same as that 

 portion of the solid which falls below the plane of floatation. 



And according to this principle, the truth of the above Proposition 

 is demonstrated ; for, 



Put m = the magnitude of the whole floating body, 

 m' the magnitude of the part immersed, 

 s := the specific gravity of the floating body, 

 w its weight, 



VOL. I. S 



