the Specific Gravity of Liquids. 257 



Solving this equality for the value of -, substituting AjS^ for 

 h, aud putting (jj for — , we obtain 



But since es^ is small, in all actual cases, as compared with 

 PS — /ij^i, we have approximately 



^^VlT^Vi ^^^ 



Now assuming s, to be the least specific gravity of all the 

 liquids eligible for examination, then in order that there maybe 

 no redundancy of length in the tube E C, we must take H = /«i ; 

 in this case equation (4) becomes 



§=v/r=i;, (5) 



which expresses the ratio of the diameters of the tubes A B and 

 CD in terms of the specific gravity of the lightest liquid. 

 Moreover we have 



^, = -, and the descent of the water in CD = /^l— A. 



S 1 



Taking s^ = '7h, we get ^= I ; and taking h = 10, we get 

 fh= .4? =13i, and h-h=lS^-lO=3l. 



Hence the following dimensions of the different parts of the 

 instrument may be adopted: AB = 13| inches; DC = 3i inches; 

 d or diam. DC = 1 inch; and f/j or diam. AB = i inch. 



In order to show the advantage derived from the enlargement 

 of the tube CD, take d=d^ in equation (4), then 



which shows that, in order to have the columns /* and h^ the 

 same as in the foregoing case, II or E C must be equal to the 

 sum of these columns, which is h in excess of the length deter- 

 mined by the economic condition expressed by equation (5). 

 For example, when /<j = 13i, and A = 10, then H = 23|. 



The advantages of the new areometer, as compared with the 

 areometer in common use, are as follows : — 



1. A comparatively small quantity of the liquid is required in 

 order to find its specific gravity. It has been shown that with 

 this instrument about an ounce weight of the liquid is sufficient 

 for determining its specific gravity, wlicreas with the common 

 areometer it requires not less than seven ounces. 



