ON THK COHESION OF FLUIDS. 



657 



vary in the inverse ratio of the square of the 

 distance ; whence it was inferred by Newton 

 that the primitive force of cohesion varies 

 in the simple inverse ratio of the distance, 

 while other experiments lead us to suppose 

 that cohesive forces iu general vary in the 

 direct ratio of the distance. But the difficulty 

 is removed, and the whole of the effects are 

 satisfactorily explained, by considering the 

 state of the marginal surface of the drop. If the 

 plates were parallel, the capillary action would 

 be equal on both sides of the drop : but when 

 they are inclined, the curvature of the sur- 

 face at the thinnest part requires a force pro- 

 portional to the appropriate height to coun- 

 teract it; and this force is greater than that 

 which acts on the opposite side. But if the 

 two plates are inclined to the horizon, the 

 deficiency may be made up by the hydro- 

 static weight of the drop itsell"; and the 

 same inclination will serve for a larger 

 or a smaller drop at the same place. Now 

 when the drop approaches to the line of con- 

 tact, the difference of the appropriate heights 

 for a small drop of a given diameter will in- 

 crease as the square of the distance decreases ; 

 for the fluxion of the reciprocal of any quan- 

 tity varies inversely as the square of tliatquan- 

 tity ; and, in order to preserve the equilibrium, 

 the sine of the angle of elevation of the two 

 plates must be nearly in the inverse ratio of 

 the square of the distance of the drop from 

 the line of contact, as it actually appears to 

 have been in Hauksbee's experiments. 



VI. PHYSICAL FOUNDATION OF THE LAW 

 OF SUPERFjIClAL COHESION. 



We have now examined the principal 

 phenomena which are reducible to the sim- 

 ple theory of the action of the superficial 



VOL. II. 



panicles of a fluid. We are next to investi- 

 gate the natural foundations upon which 

 that theory appears ultimately to rest. We 

 may suppose the particles of liquids, and 

 j)robably those of solids also, to possess that: 

 power of repulsion, which has been demon- 

 stratively shown by Newton to exist in aeri- 

 form fluids, and which varies in the simple 

 inverse ratio of the distance of the particles 

 from each other. In airs and vapours this 

 ■force appears to act uncontrolled; but in li- 

 quids, it is overcome by a cohesive force, 

 while the particles still retain a power of mov- 

 ing freely in all directions; and in solids the 

 same cohesion is accompanied by a stronger 

 or weaker resistance to all lateral motion, 

 which is perfectly independent of the cohe- 

 sive force, and which must be cautiously 

 distinguished from it. It is simplest to sup- 

 ])ose the force of cohesion nearly or perfectly 

 constant in its magnitude, throughout the 

 minute distance to which it extends, and 

 owing its apparent diversity to the contrary 

 action of the repulsive force, which varies 

 with the distance. Now in the internal parts 

 of a liquid these forces hold each other in 

 a perfect equilibrium, the particles being 

 brought so near, that the repulsion becomes 

 precisely equal to the cohesive force that 

 urges them together: but whenever there is 

 a curved or angular surface, it may be found, 

 by collecting the actions of the diflerent parti- 

 cles, that the cohesionraust necessarily prevail 

 over the repulsion, and must urge the super- 

 ficial parts inwards, with a force proportional 

 to the curvature, and thus produce the efleet 

 of a uniform tension of the surface. For, 

 if we consider the efl"ect of any two particles 

 in a curved line on a third at an equal dis- 

 tance beyond them, we sludl find that the 

 4 p 



