OF THE EQUILIBRIUM OF FLOATATION. 261 



Taking, therefore, the data as proposed in the foregoing example, 

 and we shall obtain 



20X1 

 #~ , Q S7 , =r 156.29 inches; consequently, 



the magnitude, or cubical contents of the body, is 



156.29X 156.29X 156.29 = 3815627.7 inches. 

 In addition to the foregoing examples, which might very appro- 

 priately have been ranked under the head of problems, the seventh 

 proposition affords the following inferences. 



316. INF. 1. If two bodies floating on the same fluid, be in a state 

 of equilibrium : 



The specific gravities of those bodies, will be to one another 

 directly as the parts below the plane of floatation , and in- 

 versely as the whole magnitudes of the bodies. 



317. lNF.^2. If the same body float upon two different fluids, and 

 be in a state of equilibrium on each : 



The specific gravities of the fluids, will be to one another, 

 inversely as the parts of the body below the plane of floatation. 



318. INF. 3. If different bodies float in equilibrio on the surfaces 

 of different fluids, and if the parts below the planes of floatation be 

 equal among themselves : 



The specific gravities of the fluids, will be to one another 

 directly as the weights of the bodies, or directly as the magni- 

 tudes of the bodies drawn into their specific gravities. 



319. INF. 4. If any number of bodies of the same weight, but of 

 different specific gravities, float in equilibrio on the surface of the 

 same fluid : 



The magnitudes of the parts below the plane of floatation, 

 are equal to one another. 



320. INF. 5. If a body float in equilibrio on the surface of a given 

 fluid, and if the part below the plane of floatation be increased or 

 diminished by a given quantity : 



The absolute weight of the body, (in order that the equili- 

 brium may still obtain,) must be increased or decreased by a 

 weight, which is equal to the weight of the portion of the fluid 

 that is more or less displaced, in consequence of increasing or 

 diminishing the immersed part of the body, or that which falls 

 below the plane of floatation. 



