Page:Scientific Papers of Josiah Willard Gibbs.djvu/344

308 which, if it were uniform throughout the whole space between the fixed planes, would give the same discharge of water as the actual variable velocity) expressed in millimeters per second, and $$D$$ denotes the distance in millimeters between the fixed planes, which is supposed to be very small in proportion to their other dimensions. This is for the temperature of 24.5° C. For the same temperature, the experiments of Poiseuille give for the descent of water in long capillary tubes, which is equivalent to  for descent between parallel planes. The numerical coefficient in this equation differs considerably from that in (656), which is derived from experiments of an entirely different nature, but we may at least conclude that in a film of a liquid which has a viscosity and specific gravity not very different from those of water at the temperature mentioned the mean velocity of the interior relatively to the surfaces will not probably exceed $$1000 D^2$$. This is a velocity of .1mm per second for a thickness of .01mm, .06mm per minute for a thickness of .001 (which corresponds to the red of the fifth order in a film of water), and .036mm per hour for a thickness of .0001mm (which corresponds to the white of the first order). Such an internal current is evidently consistent with great persistence of the film, especially in those cases in which the film can exist in a state of the greatest tenuity. On the other hand, the above equations give so large a value of $$V$$ for thicknesses of 1mm or .1mm, that the film can evidently be formed without carrying up any great weight of liquid, and any such thicknesses as these can have only a momentary existence.

A little consideration will show that the phenomenon is essentially of the same nature when films are formed in any other way, as by dipping a ring or the mouth of a cup in the liquid and then withdrawing it. When the film is formed in the mouth of a pipe, it may sometimes be extended so as to form a large bubble. Since the elasticity (i.e., the increase of the tension with extension) is greater in the thinner parts, the thicker parts will be most extended, and the effect of this process (so far as it is not modified by gravity) will be to diminish the ratio of the greatest to the least thickness of the film. During this extension, as well as at other times, the increased elasticity due to imperfect communication of heat, etc., will serve to protect the bubble from fracture by shocks received from the air or the pipe. If the bubble is now laid upon a suitable support, the condition (613) will be realized almost instantly. The bubble will