254 OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 



therefore, by transposition, we get 



s(rv + nf rv"} rz: n> s' (TV" w), 



and finally, by division, we shall obtain 



__ ?v' s'(w" TV) 



~ w + rv'-w" ' (199). 



305. The practical rule by which the reduction of the above equa- 

 tion is effected, may be expressed in words at length in the following, 

 manner. 



RULE. From the weight of the vessel with the solid in it, 

 when filled up with water -, subtract the weight of the vessel 

 when full of water only ; then multiply the remainder by the 

 specific gravity of the air at the time of observation, and 

 subtract the product from the iveight of the solid in air for a 

 first number. 



To the vjeight of the vessel when full of water, add the 

 weight of the solid when weighed in air, and from the sum, 

 subtract the weight of the vessel with the solid in it, when 

 filled up with water, and the remainder mill be a second 

 number. 



Divide the first number by the second, and the quotient 

 will give the specific gravity of the solid. 



306. EXAMPLE. The weight of a vessel when full of water is 68 Ibs. 

 avoirdupois, and the weight of a solid body when weighed in air of a 

 medium temperature, is 34 Ibs. ; now, when the solid is placed in the 

 vessel, its bulk of water is expelled, and the vessel being then weighed, 

 is found to indicate 86 Ibs. ; required the specific gravity of the solid 

 body? 



When the air is of a medium temperature, its specific gravity is very 

 nearly expressed by the fraction 0.0012, that of water being unity; 

 therefore, by proceeding according to the rule, we have 



_ 34 -.0012(86- 68) _ 



68 + 3486 



which, by referring to a table of specific gravities, is found to correspond 

 very nearly with the opal stone, a silicious material of very great value, 

 for the senator Nonius preferred banishment to parting with his 

 favourite opal, which was coveted by Antony. 



I 



