OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 251 



PROBLEM XLIV. 



301. If a solid body is weighed in a fluid of greater specific 

 gravity than itself, and of which the specific gravity is given : 



It is required from thence, to determine the specific gravity 

 of the solid. 



The usual method of resolving this problem, is, to attach the body 

 whose specific gravity is required, to another body specifically heavier 

 than the fluid, and of a sufficient magnitude to cause the compound 

 mass to sink ; then, by observing the weights indicated by the sub- 

 sidiary body, and by the compound mass, when they are separately 

 placed in the fluid, the specific gravity of the lighter body will become 

 known. 



Put rv zz the weight of the lighter body when weighed in vacuo, 

 TV zz the difference between the weight of the compound mass, 

 and that of the heavier body, when weighed separately 

 in the fluid, 



s zz: the specific gravity of the fluid, and 

 s' zz the specific gravity of the solid required. 



Now, it is manifest, that the effort of buoyancy, or the force of 

 ascent of the lighter body, is equal to the difference between the 

 weight of the compound mass in the fluid, and that of the heavier 

 body in the fluid ; therefore, 



w' zz: the force of ascent of the lighter body. 



But, the force of ascent of the lighter body, or, as it is more ele- 

 gantly denominated, the effort of buoyancy, is evidently equivalent to 

 the excess of the weight of a quantity of the fluid, equal in magnitude 

 to the lighter body, above the weight of the lighter body when weighed 

 in vacuo ; consequently, the weight of a quantity of the fluid, equal 

 in bulk to the lighter body, is expressed by rv -\- w' ; hence, we have 



from which, by reducing the proportion, we get 

 . sw 



rV-\-n' 



Or put W zz the weight of the compound mass when weighed in the 

 fluid, and W zz: the corresponding weight of the heavier body when 

 weighed separately ; then we have 



/ -\\r \\rt . 



rv w vv , 



