182 OF THE PRESSURE OF UNMIXABLE FLUIDS OF DIFFERENT DENSITIES 



Let AB be the interior diameter of the circular tube, and ci, IE the 

 spaces occupied by the fluids when they have 

 attained the state of quiescence, GI being the 

 common surface, or the plane in which the 

 communication occurs. 



Through the common surface IG, the surface 

 of the heavier fluid at c, and the surface of the 

 lighter at E, draw the lines GH, CD and EF 

 respectively parallel to the horizon, and meeting 

 the diameter AB at right angles in the points H, D and F ; then is DH 

 the vertical altitude of the heavier fluid, above the common surface IG, 

 and FH is the vertical altitude of the lighter fluid, as referred to the 

 same plane. 



Put d z=: FH, the perpendicular altitude of the lighter fluid, 

 S nr DH, the perpendicular altitude of the heavier fluid, 

 s =i the specific gravity of the lighter fluid, 

 s' =: the specific gravity of the heavier fluid, 

 c G or G E, the portion of the circular tube which is occupied 



by each of the fluids, 

 x zr c B, the number of degrees between the highest and lowest 



points of the heavier fluid. * 



Then, because by the preceding proposition, the perpendicular 

 altitudes of two fluids of different densities, which communicate with 

 one another through the branches of a bent tube, are inversely as the 

 densities or specific gravities ; it follows, that 



d : 5 : : s' : s, 



and from this analogy, by making the product of the mean terms 

 equal to the product of the extremes, we obtain 



c?snrs' ; 



the very same result as equation (138), and if both sides be divided 

 by 5, we shall obtain 



Now, if the specific gravity of the lighter fluid be expressed by 

 unity, while that of the heavier is denoted by m ; then the above 

 equation becomes 



d = md. (140). 



By referring to the diagram, it will readily appear, that the space 

 occupied by both the fluids, when in a state of equilibrium, is repre- 

 sented by 



