OF THE EQUILIBRIUM OF FLUIDS. ipi 



(283), and the number of particles is directly as the length: 

 consequently the absolute pressure will be equal, and there 

 will be an equilibrium ; and if the fluid in either arm be 

 higher, it will preponderate. The pressure on the tube at 

 any part is only the effect of the particle immediately in 

 contact with it, and acts in the direction perpendicular to 

 the tube, therefore if another similar row of particles in 

 equilibrium were placed on the first, this pressure, acting 

 in the same direction, would not disturb the equilibrium 

 of the particles among themselves, however they might be 

 situated with respect to the first. And conceiving any 

 fluid to be divided into an infinite number of tubes, bent 

 or straight, in which the particles form a continuous series, 

 there can be no force to preserve the equilibrium in each 

 of them, unless the height of each portion be equal. 



312. Theorem. "370.'' The pressure 

 of a fluid on every particle of the vessel con- 

 taining it, or of any other surface, real or 

 imaginary, in contact with it, is equal to the 

 weight of a column of the fluid, of which the 

 base is equal to that particle, and the height 

 to its depth below the surface of the fluid. 



Imagine an equable tube to be so bent, 

 that one of its arms may be vertical, and the 

 other perpendicular to the given surface : 

 then drawing a horizontal line AB, the fluid 

 in the portion of the tube AB will remain in 

 equilibrium, and will only transmit the pres- 

 sure of BC to the surface at A, and this will be true 

 whatever be the position of the imaginary tube ; and since 



