OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 231 



By equating the products of the extreme and mean terms in the 

 preceding analogy, we obtain 



sw" s'w, 



and dividing by s, we have 

 s'w 



but according to our notation, w" denotes the weight which the body 

 loses ; consequently, the weight which it retains in the fluid, becomes 



s'w w (s s') 



W W'-^HW m - . /1Q/|\ 



s . s ( 184 )- 



265. If, therefore, the weight of the body, together with its specific 

 gravity, be known, before it is immersed in a fluid of a given specific 

 gravity ; its weight after immersion can easily be ascertained by the 

 following practical rule. 



RULE. From the specific gravity of the body, subtract that 

 of the fluid in which it is immersed ; multiply the remainder 

 by the weight of the body, and divide the product by its 

 specific gravity for the weight which it retains after im- 

 mersion. 



266. EXAMPLE. A piece of cast iron which weighs 14 Ibs. is 

 plunged into a cistern of water; what force will be required to 

 sustain the iron at rest in any point, its specific gravity being to that 

 of water as 7 to 1 ? 



Here, by operating according to the rule, we have 



14(71) 



- ~ 12 Ibs. avoirdupois. 



From which it appears, that 14 Ibs. of cast iron being suspended 

 in water, loses 2 Ibs. of its weight ; or which is the same thing, the 

 upward pressure of the water exceeds its downward pressure, by a 

 force which is equivalent- to 2 Ibs. 



COROL. We may also infer from the above, that the weights which 

 the same body loses by being immersed in different fluids : 

 Are as the specific gravities of the fluids. 



PROBLEM XXXIV. 



267. If a body be weighed in air and in water respectively, 

 and the weights be exactly ascertained : 



It is required, from the weights thus exhibited, to deter- 

 mine the real weight. 



