The column IK, on the other hand, which is in a state of equilibrium with AIL, is acted upon by the force of gravity through the whole extent of the column, also by other forces at the upper and lower extremities of the tube. The forces exerted at the upper part of the co lumn, are the attraction of the tube upon the particles of water, and the reciprocal attraction of these particles; but as every particle is as much drawn upwards as down wards by the first of these forces, the consideration of it may be dropped. In order to estimate the other force, let a horizontal plane VX touch the concavity at I, a par ticle ji, situated infinitely near to I, is attracted by all the particles above VX, and by all below it whose sphere of activity comprehends that particle; and as the parti cles above p arc fewer than those below it, the result of these forces must be a force acting downwards.
In order to estimate the value of the forces which act at the lower end 0 of the tube, let us suppose that the tube has a prolongation to the bottom of the vessel, form ed of matter of the same density as the water. Let a particle R be situated a little above the extremity of the tube, and another Q as much below that extremity, they will be equally acted upon by the water above that place, and by the water between the fictitious prolongation of the tube, and therefore these forces will destroy one an other. By applying to the case of the particle R the same reasoning that was used for the particle e, it will appear, that the result of its attraction by the tube is an attraction upwards. The particle R is likewise attracted downwards by the supposed prolongation of the tube, and the difference between these is the real effect. The other particle Q. is also- drawn upwards by the tithe with the same force as R, since, by the hypothesis, it is as far dis tant from the points D, G, as the particle R is from the points d, g, where, with respect to it, the real attraction of the tube commences. The particle Q is attracted also downwards, by the supposed prolongation of the tube, and the difference of these actions is the real effect. hence the double of this force is the sum of all the forces that act at the lower part of the tube. These forces, when combined with those exerted at the top of the tube, and with the force of gravity, give the total expression, which should be combined with that of the forces with m hich the column AIL is actuated.
Clairaut then observes, that there is an infinitude of possible laws of attraction, which will give a sensible quantity for the elevation of the fluid above the level MN when the diameter of the tube is very small, and a quan tity next to nothing when the diameter is considerable; and lie remarks, that we may select the law which gives the inverse ratio between the diameter of the tube and the height of the liquid, conformable to Exp. 4.
It follows from the expression obtained by Clairaut, dint if any solid, AB, (Plate Cti. Fig. In.) possesses half the attracting power of the fluid CD, the surface of the fluid will remain horizontal ; for the attraction being represtuted by DA, DE, and DC ;—DA and DE may be combined into DB, ay(' DB and DC into DE, which is vertical. The water will, therefore, not be raised, since the surface of a fluid at rest must be perpendicu lar to the resulting direction of all the forces which act upon it.
When the attracting power of the solid is more than half as great, the resultant of the forces will be GF in Fig. 11, and therefore the fluid must rise towards the solid, in order to be perpendicular to GF. When the attractive power of the solid is less than that of the fluid, the resultant will be HF in Fig. 11: and therefore, as in the case of mercury, the surface must be depressed, in order to be perpendicular to the force.
The subject of capillary attraction was next taken up by Septet. in 1751, who referred all the phenomena to the attraction of the superficial particles of the fluids. He deduces this principle from the doctrine of attraction. He supposes the attraction of the tube to be insensible at sensible distances ; and he has shewn that the curvature of each part of the surface of a fluid is proportional to its distance from the general level ; and without much error, he has obtained from experiments the magnitude of this curvature at a given height, both for water and mercury.
M. AIonge has followed Segner in ascribing the capil lary phenomena to the cohesive attraction of the superfi cial particles of the fluids ; and he maintains that the surfaces must be formed into curves of the nature of lintearix, resulting from the uniform tension of a surface resisting the pressure of a fluid, which is either uniform, or varies acefording to a given law.
In a very ingenious paper on the cohesion of fluids, which was read by Dr Young in the Royal Society in 1805, that able mathematician has given a new theory of capillary attraction. He has reduced all the pheno mena of cohesion to the joint operation of a cohesive and a repulsive force, which balance each other in the inter nal parts of a fluid, where the particles are brought so near that the repulsion is exactly equal to the cohesive force by which they are attracted ; and he assumes only, that the repulsion is more increased than the cohesion, by the mutual approach of the particles. By this means Dr Young has connected together a variety of facts which had hitherto been unexplained ; and we regret that our limits will not permit us to give a more detailed account of his ingenious speculations.