Capillary Attraction. 343. 



consequently, the force with which it is elevated will be 

 2 q q'. If we represent the bulk of the column BF by 6, 

 its density by A, and the force of gravity by g, then A b will 

 represent the weight of the elevated column ; but, as this weight 

 is in equilibrium with the forces by which it is raised, we shall 

 have the following equation ; 



g A b = 2 q 0'. 



If the force 2 9 is less than 9', then I will be negative, and the 

 fluid will be depressed in the tube; but as long as 2 q is greater 

 than <?', b will be positive, and the fluid will rise above its natural 

 level. 



Since the attractive forces, both of the glass and fluid, are in- 

 sensible at sensible distances, the surface of the tube AB will act 

 sensibly only on the film of fluid immediately in contact with 

 it. We may therefore neglect the consideration of the curvature, 

 and consider the inner surface as developed upon a plane. The 

 force q will therefore be proportional to the width of this plane > 

 or, which is the same thing, to the interior circumference of the 

 tube. Calling c, therefore, the circumference of the tube, we 

 shall have q = p c, p being a constant quantity representing 

 the force of attraction of the tube AB for the fluid, in the 

 case where the attractions of different bodies are expressed 

 by the same function of the distance. In every case, however, 

 p expresses a quantity dependent on the attraction of the matter 

 of the tube, and independent of its figure and magnitude. In 

 like manner we shall have q' = p' c ; p' expressing the same 

 thing with regard to the attraction of the fluid for itself, that ;? 

 expresses with regard to the attraction of the tube for the fluid. 

 By substituting these values of <?, <?', in the preceding equation, 

 we shall have 



/) (i.) 



If we now substitute, in this general formula, the value of c in 

 terms of the radius, if it is a capillary tube, or in terms of the sides, 

 if the section is a rectangle, and the value of b in terms of the radius 

 and altitude of the fluid column, we shall obtain an equation by 

 which the heights of ascent may be calculated for tubes of all 

 diameters, when the height, belonging to any given diameter, has 

 been ascertained by direct experiment. 



