248 or SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 



Again, for the second fluid, we have 



W w' : W ::" : s, 



and from this, by equating the products of the extremes and means, 

 we get 



f*W=r*(W **), 

 and this by division becomes 



W-tiQ 



~W~ (196). 



hence, by analogy, we obtain 



w v 



and finally, by suppressing the common quantities in the second and 

 fourth terms, we get 



,' : W w :: 5" : W w/; 



that is, the specific gravities of different fluids, are as the weights, 

 which the body loses. 



296. EXAMPLE. A mass of brick whose absolute weight is 64 

 ounces, and its specific gravity equal to twice the specific gravity of 

 water; when weighed in one fluid indicates 37 ounces, and when 

 weighed in another, it indicates only 30 ounces ; it is required from 

 thence, to determine the ratio of the respective gravities of the fluids, 

 and also the specific gravity of each ? 



Here it is manifest, that the weight lost by the solid when weighed 

 in one fluid, is 



W w 64 37 z= 27 ounces, 



and on being weighed in another fluid, it loses 



W w' = 64 30 34 ounces. 



Now, we have seen above, that the specific gravities of the fluid 

 in which the solid is weighed, are to one another, respectively as the 

 weights which the solid loses in them ; consequently, we have 



s' : s" : : 27 : 34. 



This is the ratio of the specific gravities ; but it appears from equa- 

 tions (195) and (196), that when the specific gravity of the solid is 

 known, the specific gravity of the fluid in which it is weighed can 

 easily be ascertained. 



If, therefore, we employ the specific gravity of the body as given in 

 the question, the specific gravity of the first fluid, by equation (195), 

 becomes 



