ON THE MERCURIAL COLUMN EQUILIBRATING ONE OF WATER. 179 



upward pressure of the heavier fluid in DCB; it follows, that these 

 pressures are equal to one another. But because the plane EF is 

 parallel to the horizon, the pressure of the fluid in B, is equal and 

 opposite to the pressure in cc, the fluid in de serving no other pur- 

 pose than for mutually transmitting the opposing pressures ; conse- 

 quently, the pressure of the lighter fluid in A b y is counterpoised by 

 the pressure of the heavier fluid in DC, the fluid in CCB& serving only 

 as a medium of communication. 



Put dinwG, the perpendicular depth of the plane EF, below the 

 surface of the lighter fluid at A, 



3 in w G, the perpendicular depth of the plane EF, below the 

 surface of the heavier fluid at D, 



p in the pressure on the plane, occasioned by the lighter fluid 

 in A 5, 



7/zz: the pressure on the plane, occasioned by the heavier fluid in 

 DC ; and let s and s' represent the corresponding spe- 

 cific gravities of the lighter and the heavier fluids. 



Then, since the pressures on the plane, occasioned by the actions 

 of the two fluids, are respectively as the depths of the centre of 

 gravity, and the specific gravity of the fluids jointly ; it follows, that 



p : p' : : ds : Ss' ; 



but according to the conditions of the proposition, these pressures are 

 equal to one another ; hence we have 



ds = Ss'; (138). 



and by converting this equation into an analogy, it becomes 



d : $ : : s f : s 



hence, the truth of the proposition is rendered manifest. 

 Let both sides of the equation numbered (138), be divided by s, the 

 specific gravity of the lighter fluid, and we shall obtain 



,7-!fl 



s * (139). 



184. Hence, in order to determine the perpendicular depth, or 

 altitude of a column of the lighter fluid, that will balance or keep in 

 equilibrio a given column of the heavier ; we must observe the follow- 

 ing practical rule. 



RULE. Multiply the altitude of the heavier fluid by its 

 specific gravity, and divide the product by the specific gravity 

 of the lighter fluid, for the altitude sought. 



N2 



