238 OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 



281. INF. 4. If two solid bodies of different magnitudes, indicate 

 equal weights when weighed in the same fluid : 



The lesser body will preponderate when they are placed in 

 a denser medium. 



282. INF. 5. If two or more solid bodies, when placed in the same 

 fluid, sustain equal diminutions of weight : 



The magnitudes of the several bodies are equal among 

 themselves. 



This is manifest, for the losses of weights are as the weights of the 

 quantities of fluid displaced ; and these are as the magnitudes of the 

 bodies which displace them. 



PROBLEM XXXVII. 



283. If two bodies of equal weights, but different specific 

 gravities, be exactly equipoised in air, and then immersed in a 

 fluid of greater specific gravity, the smaller body will prevail : 



It is therefore required to determine, what weight must 

 be added on the part of the greater body, to restore the 

 equilibrium. 



Put s zz: the specific gravity of the fluid, in which the bodies are 



immersed, after being equipoised in air, 

 / zz: the specific gravity of the greater body, 

 s" zz: the specific gravity of the smaller body, 

 w the common weight of each, 

 w' zz: the weight lost by the greater body, by reason of the 



immersion, 



w" zz: the weight lost by the lesser body, and 

 x zz: the weight which must be added to restore the equi- 

 librium. 



Then, because by the preceding proposition, when a body is im- 

 mersed in a fluid, the weight which it loses, is to its whole weight, as 

 the specific gravity of the fluid is to that of the body ; it follows, 



that 



s r : s : : w : w' ', 



and this, by reducing the proportion, gives w' zz: > 



S 



Again, for the weight lost by the lesser body, we have 



s" : s : : w : w" : 



