ELEMENTARY PRINCIPLES OF FLUID PRESSURE. 9 



The pressure which it sustains in a direction perpendicular 

 to its surface, will be the same at every point of the revolution 

 .-, as if it remained constantly horizontal. 



20. INF. 7. If the perpendicular pressures upon a given surface be 

 equal, when it is immersed in two fluids of different densities : 



The perpendicular depths of the centres of gravity below 

 the surface, will vary inversely * as the densities or specific 

 gravities of the fluids. 



21. The above inferences are immediately deducible from the 

 general proposition, but it is probable that the last may require a 

 little illustration ; for which purpose 



Put p =. the pressure sustained by the plane in both the fluids, 

 a~ the area of the plane or the surface pressed, 

 s the density or specific gravity of one of the fluids, 

 d = the depth at which the given surface is immersed in it, 

 / the density or specific gravity of the other fluid, 

 and 5 = the depth of immersion. 



Then, according to the principle indicated by the general equation (2), 

 we have, in the case of the first fluid, 



pdas, 

 and in the case of the second fluid, it is 



p :zr 5 a s f ; 



but according to the conditions of the question, these expressions are 

 equal to one another, for the pressure is the same in both cases ; con- 

 sequently by comparison, we have 



d a s ~ S a /, 

 and this, by suppressing the common factor, becomes 



ds = W; 



therefore, by converting this equation into an analogy or proportion, 

 we shall exhibit the precise conditions of the inference ; hence, we have 



d : a : : / : s. 



* One quantity is said to vary inversely as another, when of two quantities the 

 one increases as the other decreases. 



