OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 237 



This example corresponds to equation (187), and must therefore 

 be resolved by the first case of the foregoing rule, observing to bring 

 the numerator into the same denomination with the denominator, that 

 is, reducing Ibs. avoirdupois into ounces; or thus, 14Xl6:zrW, the 

 absolute weight, from which we get 





Hence it appears, that a globular body, whose specific gravity is 

 seven times greater than that of water, will weigh 14 Ibs. when its 

 diameter is 3.9313 inches, which corresponds very nearly with a globe 

 of cast iron. 



277. EXAMPLE 2. A globular body whose specific gravity and 

 absolute weight are unknown, indicates 12 Ibs. avoirdupois when 

 weighed in water, and 13.9975 Ibs. when weighed in air; what is its 

 magnitude, the specific gravity of water and air being to one another 

 as the numbers 1 and .0012 ? 



This second example corresponds to the conditions represented in 

 equation (188), and must therefore be resolved by the second case of 

 the foregoing rule, the numerator being brought into the same deno- 

 mination with the denominator, or the Ibs. avoirdupois being turned 

 into ounces, as (13.9975 12) 16, from which we obtain 



l - 3 -^- 7 ^= r =^^ 4 ^^9ieg nearly 4 inches, the same $**, 

 .5236(1 .0012) 

 as above. 



From the principles established in the foregoing Proposition (V), and 

 the problems derived from it, we deduce the following inferences. 



278. INF. 1. When bodies of equal weights, but of different magni- 

 tudes, are immersed in the same fluid : 



The weights which they lose, are reciprocally proportional 

 to their specific gravities, or directly proportional to their 



279. INF. 2. When a solid body is weighed in air, or in any other 

 fluid whatever : 



The difference between its absolute weight, and the weight 

 exhibited in the fluid, is the same as the weight of an equal 

 bulk of the fluid. 



280. INF. 3. If two solid bodies of different magnitudes, when 

 weighed in the same fluid indicate equal weights : 



The greater body will preponderate when they are brought 

 into a rarer medium. 



