OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 239 



which by reduction gives 

 ws 



=-F- 



Now, it is manifest, that the weight required to restore the equili- 

 brium, must be equal to the difference between the results of the 

 above analogies ; therefore, we obtain 



H __ w s ws 



~~7 7 r ' 



which, by a little farther reduction, becomes 



X = 77' ' (189). 



284. The practical rule which this equation affords, may be ex- 

 pressed in words at length in the following manner. 



RULE. Multiply the difference between the specific gravities 

 of the bodies, by their common weight in air, drawn into the 

 specific gravity of the fluid in which they are immersed, and 

 divide the result by the product of the specific gravities of the 

 bodies, for the weight to be added in order to restore the 



It may be proper here to observe, that the weight determined by this 

 rule must not be immersed in the fluid, it must only be attached to 

 that side of the balance on which the greatest weight is lost. 



285. EXAMPLE. Suppose that 84 Ibs. of brass, whose specific gravity 

 is 8.1 times greater than that of water, is equipoised in air by a piece 

 of copper, whose specific gravity is 9 times greater than that of water ; 

 how much weight must be applied to the ascending arm of the balance 

 to restore the equilibrium, the same being destroyed by immersing the 

 bodies in water, of which the specific gravity is expressed by unity ? 

 Here, by attending to the directions in the rule, we get 



84X1X(9 8.1) .. 



*= 8.1X9 =l-0371bB. 



Hence it appears, that if a mass of brass and of copper, each equal 

 to 84 Ibs. when weighed in air, be immersed in a vessel of water, the 

 copper will preponderate, in consequence of its greater specific gravity; 

 and in order that the equilibrium may be again restored, a weight of 

 1 .037 Ibs. must be attached to the ascending arm of the balance, or 

 that from which the brass is suspended . 



