Page:Elementary Text-book of Physics (Anthony, 1897).djvu/105

 they ascend vary for the different liquids. If, instead of changing the diameter, we change the thickness of the wall of the tube, no variation occurs in the amount of elevation or depression; and, finally, the rise or depression in the tube varies for any one liquid with its temperature.

78. Law of Force Assumed.—It is found that a force such as is given by the law of mass attraction is not sufficient to produce these phenomena. They can, however, be explained if we assume an additional attraction between the molecules, as we have already done. The expression, then, of the stress between two molecules $$m$$ and $$m'$$, at distance $$r$$, becomes $$F = \frac{mm'}{r^2} + mm'f(r).$$

The only law which it is necessary to assign to the function of $$r$$ in the second term is, that it is very great at insensible distances, diminishes rapidly as $$r$$ increases, and vanishes while $$r$$, though measurable, is still a very small quantity. For adjacent molecules this molecular attraction is so much greater than the mass attraction, that it is customary, in the discussion of capillary phenomena, to omit the term $$\frac{mm'}{r^2}$$ from the expression for the force. The distance through which this attraction is appreciable is often called the range of molecular action, and is denoted by the symbol $$\epsilon$$. It is a very small distance, but is assumed to be much greater than the distance between adjacent molecules. Other facts, however, connected with the behavior of gases, lead us to think that the distance between molecules and the range of molecular action are of the same order of magnitude. The theory has not been developed from this point of view, but it is easy to see that the auxiliary idea of surface tension is not incompatible with it, though the precise connection between it and the molecular forces will not have the same form as that given by the older theory.

79. Methods of Development.—The different methods which have been employed to deduce, from this assumed attraction, results which could be submitted to experimental verification, are worthy of notice. They are distinct, though compatible with one