OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 245 



the cone, the rule in words would be the same in both cases, and 

 there fore, 4t need not be repeated. 



PROBLEM XL. 



291. If a solid body be weighed in vacuo and in a fluid, and 

 the different weights correctly noted : 



It is required from thence, to compare the specific gravities 

 of the solid, and the fluid in which it is immersed. 



The solution of this problem is extremely easy, for the difference 

 between the weight of the body in vacuo and in the fluid, gives the 

 weight lost ; therefore, 



Put w zr the weight indicated by the body when weighed in vacuo, 

 w'izr the weight when weighed in the fluid, 

 s the specific gravity of the fluid in which the body is 



weighed, and 

 s' zz the specific gravity of the body. 



Then we have w w' == the weight which the body loses by being 

 weighed in the fluid ; therefore, by the fifth proposition, we obtain 

 w w' : w : : s : s' ; that is 

 w w' s 



~^r -T' (194). 



consequently, since the one ratio is given, the latter can be found. 



292. EXAMPLE. Suppose a piece of metal to indicate 40 ounces 

 when weighed in vacuo, and 35 ounces when weighed in water ; what 

 is the specific gravity of the metal ? 



Here, by substituting the given numbers in equation (194), we get 

 4Q_ 35__1 _s_^ 

 40 " 8 "~ s ; 



hence, the specific gravity of the solid, is eight times greater than the 

 specific gravity of water. 



PROBLEM XLI. 



293. If two solid bodies be weighed in vacuo and in a fluid, 

 and the different weights correctly noted : 



It is required from thence, to compare the specific gravities 

 of the bodies. 



