OF THE EQUILIBRIUM OF FLOATATION. 283 



different kinds of water whose specific gravities are required to be 

 found.* 



The white iron vessel DEFG, is used for holding the fluid on which 

 the experiment is to be performed ; it is generally about three feet in 

 length, and from three to four inches in diameter, according to the 

 circumstances under which it may happen to be employed. The small 

 scale DH, is attached for the purpose of measuring the different depths 

 to which the instrument sinks when differently loaded, or when it is 

 immersed in fluids of different specific gravities. 



The indications of this instrument are so extremely delicate, that if 

 a small quantity of alcohol, or a little common salt, be added to the 

 fluid, the phial will ascend or descend through a very sensible dis- 

 tance, which circumstance greatly enhances the value of the aerometer; 

 for in proportion to its sensibility and the delicacy of its indications, 

 are its importance and utility to be appreciated. 



We come now to consider the theory of this instrument, and we 

 shall just remark in passing, that the same principles, under very 

 slight and obvious modifications, will apply to any other hydrometric 

 instrument, of a similar, or nearly similar nature and construction, to 

 that which forms the subject of our present discussion. 



PROBLEM LII. 



356. Having given the capacity or volume of the phial, toge- 

 ther with the dimensions of the immersed wire, and the entire 

 weight of the aerometer : 



It is required to determine the specific gravity of the fluid, 

 in which the instrument settles in a state of equilibrium. 



Now, because the weight of any body when floating in equilibrio, 

 whatever may be its form and the substance of which it is composed, 

 is equal to the weight of the fluid which it displaces ; it follows, that if 

 we put c =: the capacity or volume of the phial immersed in the fluid, 

 I zz the length of the immersed wire, 

 r nr the radius of its transverse section, 



TTZZ: 3.1416, the number which expresses the circumference of 

 a circle whose diameter is equal to unity, 



* To the bottom of the box B we have affixed the arm a b, from one extremity of 

 which is suspended the wire cd carrying the index i, the whole being truly balanced 

 by the small ball b attached to the other extremity of the horizontal arm ab. In all 

 other respects the instrument is that of Deparcieux. 



