Pressure of Fluids. 293 



point K, repeated as many times as there are points in CD. Ac- F . 

 cordingly, if we suppose the heavy fluid contained in ACDF, 

 divided into horizontal strata, the upper stratum would commu- 

 nicate to the bottom CD no other action than that which would 

 be communicated by the filament a 6; and the same being true 

 of each stratum, the bottom CD will only receive the pressure 

 that would arise from the sum of the filaments a b, 6 c, c d, &c. ; 

 and since this pressure would transmit itself equally to all the 

 points of CD, it is equal to the area of CD multiplied by the 

 sum of the pressures exerted upon some one point by the sum 

 of the filaments 06, fee, c d, &c. ; from all which we derive the 

 following conclusions, namely ; 



1. If the fluid ACDF be homogeneous, that is, composed of parts 

 of the same nature, of the same gravity, ta\, the pressure upon the 

 bottom CD will be. expressed by CD X a g ; or, in other words, will 

 be measured by the weight of the prism or cylinder which has CD for 

 its base and a g/br its altitude. 



2. If the fluid is composed of strata of different densities, the 

 pressure upon CD will be expressed by CD multiplied by the sum of 

 the specific gravities of each stratum ; 1 say by the sum of the spe- 

 cific gravities, and not by the sum of the weights ; for it is not 

 on the quantity of the fluid contained in each stratum that the 

 pressure depends but simply on the proper gravity of each fila- 

 ment. 



It is important to observe that the above propositions hold 

 true, whether the vessel grows larger toward the top, as in the 

 present instance, or whether it is constructed from the bottom 

 upward, as represented in figure 195. The pressure which the 

 fluid contained in ACDF exerts upon CD, is the same as if the 

 cylinder ECDG were filled with the fluid, the altitude being the 

 same in both cases. This constitutes what is called the hydro- 

 static paradox, and is often expressed in the following words, 

 namely ; any quantity of water or other fluid, however small, may 

 be made to balance and support a quantity however large. The 

 principle is well illustrated by an instrument called the hydro- 

 static bellows ; see figure 196, in which EF, CD represents two 

 thick boards 16 or 18 inches in diameter, firmly connected to- 

 gether by pliable leather attached to the edges, which allows a 



