LULA:. I. LIU tAilllll111 lb 21100 attracted downwards by the detached column be, i.e., by the liquid in the imaginary tube. Let C, depending on the force of cohesion, represent this downward action of the liquid. Also the part be of the liquid is attracted upwards by the tube ab by the attraction which we have represented by A. Thus the liquid column is acted on by two upward actious=2A, and a downward action, C. The whole force acting on it, excluding gravity, is 2A—C. Gravity would make the liquid rise to nn' at once, i.e., till it stood as high in the tube as in the vessel. Whether, then, it will rise above nn', or be depressed below it, must depend on whether 2A is greater than C, equal to it, or less than it. If 2A=C, the liquid will stand in the tube at the level nn', as if these forces did not act at all. If 2A be> C, then 2A—C will be an upward force, and the column will be raised above the level nu'. If 2A be
Regarding the forms of the upper surfaces of columns of liquid in capillary tubes, it can be demonstrated mathematically that the same relations of the forces of attraction and cohesion which determine the elevation or depression of the liquid column, determine also the form of its upper surface in the two cases of elevation and depression. In fact, the case of the elevated column resembles that of a cylinder of any very elastic substance (so elastic as to suffer change of form very readily under pressure), supported wholly by the rim, at one of its ends; or, what is the same thing, by vertical forces act ing in the lines composing its outer surface. Gravity draws down the concentric shells, of which the cylinder may be conceived to be composed, the further the more remote they are from the outermost, or that which is directly supported, the central rod being the most depressed. It would appear that the form of the surface has an important bearing on the cause of the production of the whole phenomena.
The third fact of observation—viz., that the liquid rises higher or is more depressed the finer the bore of the tube—is thus explained in the case of elevation: Since the action of adhesion is confined to the superficial layer of the fluid, and between the same substances is, caleris paribus, constant in quantity for an equal extent of surface, the wider the tube the shorter must be the column sustained, as the contents of the column raised by cohesion increase more rapidly when the bore increases than the attracting surface. The column increases with the square of the diameter of the tube,
while the attracting surface increases only with the diameter. The height, therefore, is inversely as the breadth of the tube. That the depression must increase as the bore of the tube diminishes, appears from reasoning similar to that employed in the case just discussed.
The degree of elevation varies with the nature of the fluid, the variation depending partly on the difference of cohesion between the particles of the fluid, and partly on the difference of 'adhesion between the fluid and glass. It is found that temperature affects these forces, so that the height diminishes as the temperature rises.
The depression of mercury in a fine glass tube makes it necessary to use a correc tion in reading off the height of the mercurial column in the barometer, .which, owing to it, stands always a little lower than the height due to the atmospheric pressure. Experience, however, has shown that the capillary depression is nearly one-half less in tubes which have had the mercury boiled within them than in unboiled tubes, as by the boiling a film of air, which in unboiled tubes adheres to the glass, is expelled. By widening the bore of the tube also, the error may be diminished so as to be neglected altogether. In a tube of + in. in diameter, in which the mercury has been boiled, the depression is 0.02 in., while with a similar tube of in. diameter it is only 0.003. The depression of mercury, it is found, is slightly increased by an elevation of temperature. It may be mentioned that in reading off the level of mercury in any instrument, such as the barometer, the height should be taken from the convexity of the curve. If the liquid used in the instrument, however, wets the tube, the height should be taken from the concavity.