OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 247 



294. EXAMPLE. A solid body whose absolute weight is 23 ounces, 

 when weighed in a certain fluid, loses 3 ounces of its weight; and 

 another body of 800 ounces, when weighed in the same fluid, loses 

 1 02 ounces ; what is the ratio of their respective gravities ? 



Here, since the loss of the one is 3 ounces, and that of the other 

 102 ounces, it follows, that the specific gravities of the bodies, are to 

 one another as the numbers 391 and 400 ; for we have 



. 



And in like manner, if three or more bodies be weighed in the 

 same fluid, their specific gravities may be compared with one another, 

 and also with that of the fluid in which they are weighed. 



PROBLEM XLII. 



295. If a solid body of known specific gravity, be weighed in 

 several different fluids, and the weights correctly indicated : 



It is required from thence, to determine the ratio of their 

 respective gravities. 



This problem, it will readily be perceived, is exactly the reverse of 

 the preceding one, and therefore, the method of its solution may easily 

 be discovered ; it is, however, of equal utility in philosophical inqui- 

 ries, for which reason we have proposed it in this place. 

 Put Wzz the weight of the solid when weighed in vacuo, 

 s zz the specific gravity of the solid, 

 w zz the weight which it indicates in a fluid whose specific 



gravity is s', and 



w' zz the weight which it indicates in a fluid whose specific 

 gravity is s\ 



Then the weights which the body loses, by being weighed in the 

 two fluids, are respectively W w and W w' ; but the weight lost, 

 is to the whole weight, as the specific gravity of the fluid is to the 

 specific gravity of the solid ; hence, for the first fluid, we have 



W w: W ::s':s; 



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

 we get 



s'Wzzs(W w); 



therefore, by division, we obtain 



_*(W 



,_ 



(195). 



