256 Mr. T. Tate on a Method of determining 



results derived from it with those obtained by means of a com- 

 mon areometer of the best construction, and I have invariably- 

 found that they closely agree with each other. 



Let h = EN, the height of the column of water; 



^1= AK, the corresponding height of the column of 



liquid ; 

 P = the pressure of the atmosphere, expressed in inches 



of mercury, at the time of observation ; 

 p = that of the air, KBCN, enclosed in the tube ; 



the specific gravity of the liquid, s being that of 



water, and S that of mercury ; then we have 





P=i> + /«x g, 



and also 



and taking 5=1, 



j^=p + h,x'^, (1) 



h 

 ., = ^x.; 



^.=1;' ^^) 



that is, the specific gravity of the liquid is equal to the quotient 

 arising from the division of the length of the column of the 

 water by that of the column of the liquid. 



Suppose the liquid whose specific gravity is to be determined, 

 to be rectified alcohol, then in this case I have found /i = 10-25 



amUi = 12-20; .-. 5, = ^||§ = -8401. 



Tn order to determine the proportion of the parts of the in- 

 strument corresponding to the most economic form of construc- 

 tion, let 



a = the section of the wide tube CD ; 



ff,= the section of the tube AB; H = AB=EC; 



V = ea^ = the volume of the air in the tube at P pressure, 



that is, when the water stands at the level C ; 



V = the volume of the air, KBCN, at p pressure ; 



then we find 



J>Y=pv; v = Y-aJi^ + a{li-/i); 



and by equation (1), 



;; = P-/^,|; 



.-. PV=(p-/i,|){V-ffA + «(H-/0}. 



