656 



ON THE COHESION OP FLUIDS. 



sion of the intervening fluid. This force va- 

 ries ultimately in the inverse ratio of the 

 square of the distance ; for, if two plates ap- 

 proach each other, the height of the fluid, 

 that rises between then>, is increased in the 

 simple inverse ratio of the distance ; and 

 the mean action, or negative pressure of the 

 fluid, on each particle of the surface, is also 

 increased in the same ratio. When the float- 

 ing bodies are both surrounded by a depres- 

 sion, the same law prevails, and its demon- 

 stration is still more simple and obvious. The 

 repulsion of a wet and a dry body does not 

 appear to follow the same proportion : for it 

 by no means approaches to infinity upon the 

 supposition of perfect contact ; its maximum 

 is mejisured by half the sum of the elevation 

 and depression on the remote sides of the 

 substances, and as the distance increases, this 

 maximum is only dinrinished by a quantity, 

 which is initially as the square of the distance. 

 The figures of the solids concerned modify 

 also sometimes the law of attraction, so that, 

 for bodies surrounded by a depression, there 

 is sometimes a maximum, beyond which 

 ihe force again diminishes; and it is hence 

 that a light body floating on mercury, in a 

 vessel little larger than itself, is held in a 

 stable equilibrium without touching the sides. 

 The reason of this will become apparent, 

 when we examine ihe direction of the surface 

 necessarily assumed, by the mercury, in order 

 to preserve the appropriate angle of contact; 

 the tension acting with less force, when the 

 surface attaches-itself tothe angular termina- 

 tion of the float in a direction less horizontal. 

 The apparent attraction produced between 

 solids, by the interposition of a fluid, does not 

 depend on their being partially immersed in 

 it; on the contrary, its eifects are still more 



powerfully exhibited in other situations ; and, 

 when the cohesion between two solids is in- 

 creased and extended by the intervention of 

 a drop of water or of oil, the superficial co- 

 hesion of these fluids is fully sufficient to ex- 

 plain the additional effect. When wholly 

 immersed in water, the cohesion between 

 two pieces of glass is little or not at all greater 

 than when dry : but if a small portion only 

 of a fluid be interposed, the curved surface, 

 that -it exposes tothe air, will evidently be 

 capable of resisting as great a force, as it 

 would support from the pressure of the co- 

 lumn of fluid, that it is capable of sustaining 

 in a vertical situation ; and in order to apply 

 this force, we must employ, in the separation 

 of the plates, as great a force as is equivalent 

 to the pressure of a column, of the height ap- 

 propriate to their distance.Morveau found that 

 twodiscs of glass, 3 inches French in diameter,, 

 at the distance of one tenth of a line, appeared 

 to cohere with a force of 47 19 grains, which 

 is equivalent to the pressure of a colnmn 23 

 lines in height: hence the product of the 

 height and the distance of the plates is 2.3 

 lines, instead of 2.65, which was the result of 

 Monge's experiments on the actual ascent of 

 water. The difference is much smaller than 

 the difference of the various experiments on 

 the ascent of fluids ; and it may easily have 

 arisen from a want of perfect parallelism in 

 the plates; for there is no force tending to 

 preserve this parallelism. The error, in the 

 extreme case of the plates coming into con- 

 tact at one point, may reduce the apparent 

 cohesion to one half. 



The same theory is sufficient to explain 

 the law of the force, by which a drop is at- 

 tracted towards the junction of two plates, 

 inclined to each other, and which is found to 



