246 OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 



The intelligent reader will readily perceive, that the present 

 problem is only an extension of that which immediately pj^cedes it, 

 and is proposed with the design of detecting the law, by which the 

 specific gravities of different bodies are compared ; for which purpose, 



Put W = the weight of the heavier body when weighed in vacuo, 

 Wizr its weight when weighed in the fluid, 

 w the weight of the lighter body when weighed in vacuo, 

 w f zn its weight when weighed in the fluid, 

 s = the specific gravity of the fluid in which the bodies are 



weighed, 



s' zz: the specific gravity of the heavier body, and 

 s" zz: the specific gravity of the lighter. 



Then, the weights which the bodies lose by being weighed in the 

 fluid, are respectively W W, and w w', and because the weight 

 lost, is to the whole weight, as the specific gravity of the fluid is to 

 the specific gravity of the solid ; it follows in the case of the heavier 

 body, that 



W W : W ::s : s' f 



and in the case of the lighter body, it is 



w w : w : : s : s" ; 



therefore, by equating the products of the extreme and mean terms in 

 each of these analogies, we have 



s ' ( W W) = s W, and *" (w w') zz: s w ; 



consequently, by division, we obtain 



sW sw 



-, and s zz: 



W W " w w' 



hence, by analogy, we have 



' sW " sw 



W W : w w" 



and finally, by suppressing s, it becomes 



W w 



f * '/. _______ 



W W ' w w'' 



Hence it appears, that the specific gravities of the two bodies, are 

 to one another, as their absolute weights divided by the weights which 

 they lose in the fluid; and it is manifest, that the same law will 

 extend to any number of bodies whatever ; therefore, the method of 

 comparison has been determined. 



