MISCELLANEOUS HYDROSTATIC QUESTIONS, WITH THEIR SOLUTIONS. 447 



576. QUESTION 7. An irregular fragment of glass, weighs in air 171 

 grains, but in water it weighs only 120 grains; what is its real 

 weight ; that is, what would it weigh in vacuo ? 



The answer to this question is obtained by equation (185), art. 267, 

 page 232 ; and the operation as there indicated is simply as follows. 

 171X1000 120XH lry 



the real weight of the glass in vacuo. 



577. QUESTION 8. A fragment of magnet weighs 102 grains in air, 

 and in water it weighs only 79 grains ; what is its real weight, or what 

 does it weigh in vacuo ? 



The solution of this question is effected exactly in the same manner 

 as the preceding, the conditions from which the data are obtained 

 being precisely the same; that is, the body is weighed in air and 

 in water ; consequently, the operation is as under. 



102X1000 79X1|- 

 ' 



the real weight of the magnet in vacuo. 



From the real weights of these materials, as determined in the above 

 examples, the absolute specific gravities can be found by the principle 

 of Proposition V. page 229 ; for the weights lost, are to the whole 

 weights, as the specific gravity of water, is to the specific gravities of 

 the substances in question ; hence we have 



120 : 171-gVVs- : : 1000 : 3350^, the specific gravity 

 of the glass. 



79 : 102 y V : : 100 : 443 Hf the specific gravity of 

 the magnet. 



Dr. Hutton makes the specific gravities of the glass and the 

 magnet, respectively equal to 3933 and 5202, and says that the 

 ratio is very nearly as 10 to 13; our own numbers give the same 

 ratio. 



578. QUESTION 9. Taking the specific gravity of glass equal to 3350, 

 suppose that a globe is found to weigh 10 Ibs. avoirdupoise ; what is 

 its diameter ? 



The cubic inch of glass of the given specific gravity weighs 

 0.1211695 of alb.; therefore, according to the equation 187, page 

 235, we have 



/ Z-T 



in 5.402 inches nearly. 



.5236X0.1211695 



