446 MISCELLANEOUS HYDROSTATIC QUESTIONS, WITH THEIR SOLUTIONS. 



mensuration, the solidity of the segment is (9x3 12 X 2) x 36 x 

 .5236 zn 282.744 cubic inches ; consequently, the whole weight of the 

 body, is 282.744X0.03617 10.226 Ibs., the decimal fraction 0.3617 

 being the number of Ibs. in a cubic inch of fresh water. (See note to 

 art. 329, page 268.) 



Having thus determined the weight of the globe, the specific gravity 

 of the material may be found in various ways ; but we shall here 

 determine it by the principle of Proposition VII. art. 311, page 257; 

 from which we have the following process, viz. 



9 8 : (27 12)X36 : : 1000 : 740|f, the specific gravity sought. 



575. QUESTION 6. An irregular piece of lead ore, weighs in air 12 

 ounces, but in water only 7 ; and another piece of the same material, 

 weighs in air 14| ounces, but in water only 9 : it is required to 

 compare their densities or specific gravities ? 



This question may be very simply resolved, by the principle stated 

 in Proposition V. art. 264, page 229 ; which is the same as the 

 principle employed by Dr. Hutton for the same purpose; from it 

 we have 



12 7 : 12 : : 1000 : 2400, the specific gravity of the 

 lightest fragment ; and again, we have 



14.5 9 : 14.5 : : 1000 : 2636.36, the specific gravity 

 of the heavier piece. 



The specific gravities are therefore to one another, as the numbers 

 2400 and 2636.36. Dr. Hutton makes the ratio as 145 to 132. (See 

 question 52, page 298, vol. ii. 10th ed. Course, 1831 ;) his formulae 

 will be found in arts. 250 or 251. 



The above solution however, is not correct, for the weight of the 

 body in air is not its real weight, as it would be exhibited in vacuo ; 

 the correct specific gravity will therefore be obtained by equation 

 (186), art. 270, page 234; and the operation is as follows, the 

 specific gravity of air being 1|-, that of water being 1000. 



of the lighter fragment ; and for the specific gravity of the heavier, 

 we have 



14.5X1000-9X1* . d 



14.5 _ 9 34 - J6 - 



By the results of our solution, it appears that the heavier fragment 

 is also the densest; by Dr. Hutton's solution, exactly the reverse is 

 the case. 



