658 



ON TirK COHESION OP I'LUIDS. 



result of their equal attractive forces bisects the 

 whole angle formed by the lines of direction ; 

 but that the result of their repulsive forces, 

 one of which is twice as great as the other, 

 divides it in the ratio of one to two, forming 

 with the former result an angle equal to one 

 sixth of the whole; so that the addition of a 

 third force is necessary, in order to retain 

 these two results in equilibrium ; and this 

 force must be in a constant ratio to the eva- 

 nescent angle which is the measure of the 

 curvature, the distance of the particles being 

 constant. The same reasoning may be ap- 

 plied to all the particles which are within tiie 

 influence of the cohesive force : and the con- 

 clusions are equally true if the cohesion is not 

 precisely constant, but varies less rapidly 

 than the repulsion. 



VII. COHESIVE ATTRACTION OF SOLIDS AND 

 FLUIDS. 



When the attraction of the particles of a 

 fluid for a solid is less than their attraction 

 for each other, there will be an equilibrium of, 

 the superficial forces, if the surface of the 

 fluid make with that of the solid a certain an- 

 gle, the versed sine of which is to the dia- 

 meter, as the mutual attraction of the fluid 

 and solid particles is to the attraction of the 

 particles of the fluid among each other. For, 

 when the fluid is surrounde<l by a vacuum or 

 by a gas, the cohesion of its superficial par- 

 ticles acts with full force in protlucing a ])res- 

 sure; but when it is any where in contact 

 with a solid substance of the same attractive 

 power with itself, the effects of this action 

 must be as much destroyed as if it were an 

 internal portion of the fluid. Thus, if we 

 imagined a cube of water to have one of its 

 halves congealed, without any other altera- 



tion of its properties, it is evident that its 

 form and the equilibrium of the cohesive 

 forces would remain undisturbed : the ten- 

 dency of the new angular surface of the fluid 

 water to contract would therefore be com- 

 pletely destroyed by the contact of a solid of 

 equal attractiv^e force. If the solid were of 

 smaller attractive force, the tendency to con- 

 tract would only be proportional to the dif- 

 ference of the attractive forces or densities, 

 theeftectof as many of the attractive particles 

 of the fluid being neutralised, as are equiva- 

 lent to a solid of a like density or attractive 



, power. For a similar reason, the tendencj' of a 

 given fluid, to contract the sum of the surfaces 

 of itself and a contiguous solid, will be sim- 

 ply as the density of the solid, or as the mu- 

 tual attractive force of the solid and fluid. 



"And it is indiff'erent whether we consider the 

 pressure produced by these supposwl super- 

 ficial tensions, or the force acting in the di- 

 rection of the surfaces to be compared. We 

 may therefore inquire into the conditions of 

 equilibrium of the three forces acting on the 

 angular particles, one in the direction of the 

 surface of the fluid only, a second in that of 

 the common surface of the solid and fluid, 

 and the third in that of the exposed surface 

 of the solid. Now, supposing the angle of the 

 fluid to be obtuse, the whole superficial co- 

 hesion of the fluid being represented by the 

 radius, the part which acts in the direction of 

 the surface of the solid will be pro|X)rlional 

 to the cosine of the inclination ,- and this 

 force, added to the force of the solid, will be 

 equiit to the force of the common surface of 

 the sohd and fluid, or to the difterence of 

 their forces ; consequenth', the cosine added 

 to twice the force of the solid, will be equal 

 to the whole force of the fluid, or to the ra- 



