OF THE COHESION OF FLUIDS. 331 



C, and a repulsive force R, holding each other in equili- 

 brium, but extending to the different distances c and r, 

 they will balance each other, in this hypothetical case, if 

 c^Czzr^R, that is, if the primitive forces of the single 

 pairs of particles be inversely as the squares of the minute 

 distances, to v^rhich they extend. 



Scholium. It is obvious that the length u is indiffe- 



771 



rent to the force, since m must vary as u, and — must re- 



u 



main constant, when the density is given. 



384. Theorem. If a fluid, composed of 

 cohesive and repulsive particles, holding each 

 other in equilibrium, be contained between 

 two parallel surfaces, of unlimited extent, the 

 equal and opposite forces, acting on either of 



the surfaces M, will be g d^ c^ Mf; d being 



the density, and 9r the circumference of a circle 

 divided by its diameter. 



The number of particles in the space Mu being dMu, the 

 number of those, which are within the limits of the sphere 

 of action of each particle, will be ef-jTrc'. Supposing now 

 the distances of the particles to be varied by a slight 

 change of the density ; it is evident that the variation of 

 the density will be in the triplicate proportion of that of 

 the distances, since if d=.x^, dd^Qx- dx; and the varia- 

 tion of the whole space Mu being Mdu, that of the density 



^dzz — du — , and that of any linear distance c will be Sc 

 u 



= — 4 SJ -r=i Sm — , which will be the variation of the 

 a u 



