[Illustration: untitled, two vessels separated by a narrow canal]
Suppose that two different fluids, A, B, are contained in a vessel, and separated the one from the other by a vertical division; the heights being in an inverse ratio to the densities, so that the points, _a_ and _b_, in the two faces of the division, and situated in the same horizontal plane, shall support equal and opposite pressures: suppose also that the division is pierced with one or more holes of small diameter, or, in other words, that it is traversed by several very narrow canals, as _a_, _b_, perpendicular to the two faces, and which may be regarded at first as filled with air, or any other fluid.
If the substance of the division exerts upon each of the two liquids an action superior to the half of that which the liquid has upon itself, each liquid will enter into the canal _a_, _b_, just as it would rise above its ordinary level in a capillary tube of the same size and substance. It would also be urged, by the excess of pressure which it would exert at the extremity of the canal, against the elasticity of the included air. When the two fluids have penetrated the interior of _a_, _b_, the air will be pushed on both sides in different directions by forces each of which is equal to the primitive pressure augmented by the corresponding capillary force, _i. e._ augmented by forces proportional, according to the known theory of M. Laplace, to double the action of the tube on the liquid, less the proper action of the liquid itself. It will only be in the case when the capillary force shall be the same on both sides, that the air, after being compressed to a certain degree, will remain at rest: for whenever this force preponderates at one end of the canal, the air will be driven out at the opposite end, and the liquid with the strongest capillary attraction will entirely fill the canal.
Suppose this liquid to be A, then let us consider the forces which will act on the portion _a_, _b_, of this liquid. At the extremity _a_, it will be submitted to the attraction of the exterior fluid A: at the extremity _b_, it will be attracted in the opposite direction by the liquid B. Now the two liquids being different, their attractions will be unequal, and we will suppose that that of B, on the matter [p196] of A, is greater than that of A for itself. As to the action of the canal on the portion _a_, _b_, that will be equal, and exerted in contrary directions at its two extremities; it will not, therefore, be either adverse or favourable to the movement of the fluid in the canal: and the same will be the case with respect to the pressures exerted at _a_ and _b_, by the external liquids, as long as they are equal: nevertheless, the action of the canal, and the external pressures, will prevent the thread of fluid from being broken, so that it will move without interruption in the direction in which it is drawn by the greatest attraction, or from _a_ to _b_. Hence will result an elevation of the level of B, and, consequently, an increase of pressure at the extremity _b_, of the passage, and this elevation will proceed until the difference of pressure in _a_ and _b_ shall be equal to that of the attractions exerted by the two fluids A and B, on the thread _a b_; this effect will be produced the more rapidly as the division is pierced with a greater number of passages similar to that which has been considered.