234 OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES, 



and by taking away the denominators, we get 



Sw s'w~Sw' s uf, 

 from which, by transposing and collecting the terms, we obtain 



(10* w)S-=.sw' s'w, 

 and finally, by division, we have 



sw' s' w 



'' w' w ' (186). 



271. The practical rule or method of reducing this equation, may 

 be expressed in words in the following manner. 



- RULE. Divide the difference between the products of the 

 alternate weights and specific gravities, ly the difference of 

 the weights when weighed in air and in water, and the 

 quotient will express the specific gravity of the body. 



272. EXAMPLE. A certain body when weighed in water indicates 

 exactly 12 Ibs. avoirdupois ; but when the same body is weighed in 

 air, it indicates 13.9975 Ibs.; required the specific gravity of the 

 body, the specific gravities of water and air being as in the preceding 

 problem, or as 1 to .0012 ? 



The process performed according to the directions given in the 

 rule, or after the manner indicated in equation (186), will stand as 

 follows. 



1X13.9975 .0012X12 



13.9975 12 



Therefore, a body whose specific gravity is seven times the specific 

 gravity of water, will fulfil the conditions of the question. - 



PROBLEM XXXVI. 



273. If the weights which a solid body indicates, when weighed 

 in air and in water, together with its specific gravity and real 

 weight, are exactly ascertained : 



It is required from thence, to determine the magnitude of 

 the body, on the supposition that it is globular. 



If the specific gravity of the body and its real weight were unknown, 

 the solution of the present problem would include that of the two pre- 

 ceding ones ; but in order to abbreviate the investigation, we have 

 supposed the specific gravity and the real weight of the body to be 

 given ; the process of the solution is therefore as follows. 



