

CAPILLARY TUBES. 



35 



ends, be immersed in a fluid which adheres to glass, 

 as water, the liquor within the tube will rise to 

 a sensible height above the surface of that without. 

 This phenomenon is explained by the attraction which 

 exists between the glass and the fluid. Such liquids 

 as do not adhere to glass (e. g., quicksilver) do not 

 rise in the tube : on the contrary, they stand lower 

 within than without it. The mutual action of the 

 elementary particles of matter, of which capillarity is 

 a noted instance, gives rise to phenomena as interest- 

 ing, and, in certain cases, as susceptible of being at- 

 tached to theory, by rigorous mathematical reasoning, 

 as the phenomena of universal gravitation. The as- 

 cent of liquids in capillary tubes engaged much of 

 the attention of experimental philosophers about the 

 beginning of the last century. Hauksbee found that 

 the ascent of the liquid does not depend in any way 

 on the thickness of the tube, and that when two 

 plates, forming any small angle with each other, are 

 plunged vertically into a fluid, the fluid which rises 

 between them takes the form of an equilateral hyper- 

 bola ; from which it followed, that, in tubes of the 

 same matter, the ascent of the liquid follows the in- 

 verse ratio of their interior diameters. In order to 

 explain these facts, all succeeding philosophers seem 

 to have agreed in assuming the existence of a cohe- 

 sive force among the particles of the liquid, and an 

 adhesive force between' the particles of the liquid and 

 those of the tube. But these attractive forces can only 

 be defined by their relative intensities at an equal dis- 

 tance, and the law according to which they diminish 

 as the distance is increased. Now, there are no data 

 from which either them relative intensities or the law 

 of their variation can be determined : we are, there- 

 fore, reduced to choose among a number of hypo- 

 thetical laws, all equally possible ; and the explana- 

 tion, of course, depends on the particular hypothesis 

 we adopt; hence the theories of Clairaut, Young, 

 Laplace, and Poisson. 



Clairaut was the first who attempted to reduce the 

 phenomena of capillarity to the laws of the equilibri- 

 um of fluids, and exactly analyzed all the forces that 

 concur to elevate the liquid in a. glass tube. He 

 showed that the portion of the liquid which is ele- 

 vated in the tube above the exterior level, is kept in 

 equilibrium by the action of two forces, one of which 

 is due to the attraction of the meniscus terminating 

 the column, and the other to the direct attraction of 

 the tube on the molecules of the liquid. Clairaut, 

 however, regarded this last force as the principal one, 

 and even supposed the attraction of the tube to ex- 

 tend as far as its axis ; but this supposition is con- 

 trary to the nature of molecular forces, which extend 

 only to insensible distances. The action of the tube 

 has, in fact, no influence on the elevation or depres- 

 sion of the contained liquid, excepting in so far as it 

 determines the angle under which the upper surface 

 of the fluid intersects the sides of the tube. Neglect- 

 ing, therefore, this force as insensible, there remains 

 only the action of the meniscus to support the weight 

 of the elevated column. But though Clairaut made 

 an erroneous supposition respecting the nature of 

 molecular action, and failed in the attempt to demon- 

 strate from theory, that the ascent of the liquid is in- 

 versely proportional to the diameter of the tube, he 

 showed that a number of hypotheses, regarding the 

 law of attraction, may be laid down, from any one of 

 which that law of ascent may be deduced ; and he 

 demonstrated a very remarkable result, namely, that 

 if the attraction of the matter of the tube on the fluid 

 differs only by its intensity, or co-efficient, from the 

 attraction of the fluid on itself, the fluid will rise 

 above the surrounding level when the first of these 

 intensities exceeds half the second. 



Young referred the phenomena of cohesion to the 



joint operation of attractive and repulsive forces 

 which, in the interior of fluids, exactly balance each 

 other, and assumed the repulsive force to increase in 

 a higher ratio than the attractive, when the mutual 

 distances of the molecules are diminished. From 

 these considerations he was led to discover a very 

 important fact in the theory of capillary action, 

 namely, the invariability of the angle which the sur- 

 face of the fluid makes with the sides of the tube. 



Laplace published his theory of capillary attraction 

 in 1806 and 1807, in two Supplements to the Me- 

 canique Celeste. Assuming the force of molecular 

 action to extend only to imperceptible distances, he 

 demonstrated that the form of the surface of the li- 

 quid is a principal cause of the capillary phenomena- 

 and not a secondary effect, and determined the part 

 of the phenomena which is due to the cohesive at- 

 traction of the molecules of the fluid to each other, 

 as well as that which results from their adhesion to 

 the molecules of the tube. The separate considera- 

 tion of the cohesive and adhesive forces leads to two 

 equations, which comprehend the whole theory of 

 capillarity a general equation, common to all those 

 points of the capillary surface of which the distance 

 from the sides of the tube is greater than the radius 

 of the sphere of molecular action ; and a particular 

 equation belonging to those points which are situ- 

 ated only at insensible distances from the surface of 

 the tube, or are within the sphere of its action. This 

 last equation will obviously express the angle which 

 the surface of the meniscus makes with the sides of 

 the tube ; an angle which, as it depends only on the 

 nature of the tube and that of the liquid, is constant, 

 and given in every case, the liquid and tube being 

 supposed homogeneous. Laplace further supposes, 

 in the case of elevation, that an infinitely thin film of 

 the liquid first attaches itself to the sides of the tube, 

 and thus forms an interior tube, which acts by its at- 

 traction alone to mise the column, and maintain it at 

 a determinate height. The height of the column, 

 consequently, depends on the cohesion and density 

 of the liquid. Poisson has reinvestigated the whole 

 theory of capillary attraction. Taking the most ge- 

 neral case of the problem, he considers not merely 

 the surface of a single liquid, but the surface formed 

 by the contact of two liquids of different specific gra- 

 vities, placed, the one above the other, in the same 

 tube, and deduces the two equations which determine 

 the form of the separating surface, and the angle un- 

 der which it intersects the sides of the tube. These 

 equations are, in form, the same as those of Laplace ; 

 but the definite integrals, which express the two con- 

 stant quantities they include, are very different ; and 

 their numerical values would be so likewise, if these, 

 instead of being determined experimentally, could be 

 calculated a priori from the analytical expressions. 

 This, however, cannot be done without a knowledge 

 of the law according to which the molecules of the 

 liquid attract each other, as well as of that which 

 regulates the action of the tube on the liquid. In 

 applying his general solution to the explanation of 

 the principal phenomena of capillarity, he has taken 

 occasion to correct some inaccuracies of Laplace. 

 The demonstration which Laplace had given of the 

 invariability of the angle which the surface of the 

 liquid makes with the sides of the tube was not alto- 

 gether satisfactory ; and he had even supposed that 

 it changes its value when the liquid reaches the sum- 

 mit of the tube. 



Poisson has demonstrated that the invariability of 

 this angle will always be preserved, unless the cur- 

 vature of the ulterior of the tube is infinitely great ; 

 or, in other words, unless its radius is infinitely small, 

 and of the same order of magnitude as the radius of 

 the sphere of molecular action. Hence the angle 



