308 EQUILIBKIUM OF HETEEOGENEOUS SUBSTANCES. 



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 



F=337D 2 



for the descent of water in long capillary tubes, which is equivalent to 



F=899D 2 (657) 



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 "l mm per 

 second for a thickness of 'Ol mm , '06 mm per minute for a thickness of 

 001 (which corresponds to the red of the fifth order in a film of 

 water), and -036 mm per hour for a thickness of '0001 mm (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 l mm or -l mm } 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 



* Ibid. , p. 653 ; or Mtmoirea des Savants fitrangers, vol. ix, p. 532. 



