284 OF THE EQUILIBRIUM OF FLOATATION. 



s m the specific gravity of the fluid sought, and 



w=. the entire weight of the aerometer, always known. 



Then, it is manifest, that the capacity or volume of the phial, 

 together with the magnitude of the immersed wire, is equal to the 

 quantity of fluid displaced ; and the weight of this quantity of fluid 

 is equal to the weight of the aerometer ; but by the principles of men- 

 suration, the magnitude of the immersed wire is expressed by Trr*l; 

 consequently, the quantity of fluid displaced is c-f-7rr 2 /, and the 

 magnitude of any body multiplied by its specific gravity is equal to 

 its weight ; hence we have 



t0 = (c + **/)*; (220). 



therefore, by division, we obtain 

 w 



(221). 



357. Here follows the practical rule for reducing the equation. 



RULE. Divide the entire given weight of the aerometer, by 

 the capacity or volume of the phial, increased by the quantity 

 of wire immersed, and the quotient will give the specific gra- 

 vity of the fluid. 



358. EXAMPLE. The whole weight of an aerometer, when so loaded 

 as to have the attached wire depressed 15 inches below the surface of 

 the fluid, is 23 ounces; required the specific gravity of the fluid, 

 supposing the diameter of the wire to be one twelfth of an inch, and 

 the capacity of the phial 40 inches ? 



Here, by the mensuration of solids, the magnitude of the wire is 



IGX^TXTT^ - 082 of a cubic inch, very nearly; 

 therefore, the whole quantity of fluid displaced, is 

 40 4- 0.082 zz: 40.082 cubic inches ; 

 therefore, by the rule, we obtain 



The number 0.5738, which we have obtained from the above calcu- 

 lation, expresses the weight of one cubic inch of the fluid in ounces ; 

 but since it is customary to express the specific gravity of bodies in 

 ounces per cubic foot, it becomes necessary, for the sake of compari- 

 son, to reduce the above result to that standard ; hence we have 



s zn 0.5738 X 1728 z= 991 .5264 ounces per cubic foot for 

 the specific gravity of the fluid on which the experiment was tried. 



