140 A TREATISE ON METAMORPHISM. 



more, in capillary tubes "the velocity of flow through a tube of variable 

 section will be less than the velocity of flow through a tube having a 

 uniform section equal to the mean section of the first tube, because of 

 the viscosity or internal friction of the expanding or contracting stream.'" 1 



Daniell expresses a part of the laws of capillary flow in words, instead 

 of in a formula, as follows: "The flow in capillary tubes is proportional not 

 to the square, but to the fourth power of the radius; the velocity is propor- 

 tional not to the square root of the pressure, but to the pressure itself. 

 The resistance in capillary tubes varies directly as the velocity; in wide 

 tubes approximate^ as the square of the velocity. This seems discrepant; 

 but it is due to the formation of eddies in the wider tubes; in a capillary 

 tube the flow is steady." 6 



From the foregoing it follows that the flow in a tube with a radius 

 one-fifth millimeter in diameter is sixteen times as great as in a tube 

 one-tenth millimeter in diameter. Furthermore, in a tube of any definite 

 length, if the pressure be doubled the flow is doubled; if trebled the flow is 

 trebled, etc. However, experimental work by King upon the flowage of 

 water through capillary openings of sandstones and sands gave results 

 showing that under the conditions in which he performed his experiments 

 the flowage increased faster than the pressure. The pressure in the experi- 

 ments varied from a small fraction of an atmosphere to somewhat more than 

 an atmosphere. The departure from Poiseuille's law varied from less than 

 1 per cent to more than 50 per cent, c In the experiments the departures 

 seemed to be greater, on the average, when very low pressures were used 

 than when moderate pressures were used. The very variable results may 

 be partly explained by the conditions under which the experiments were 

 performed, but it is entirely possible that the departures are partly to be 

 explained by the relative importance of internal friction due to viscosity 

 when the rates of movements are slow. (See pp. 141-143.) 



Also, according to Poiseuille's law, the flowage is inversely as the 

 viscosity. When it is remembered that the viscosity of water decreases 

 rapidly with increase of temperature, it is seen that this is a very important 



«Slichter, C. S., Theoretical investigation of the motion of ground water: Nineteenth Ann. Kept. 

 U. S. Geol. Survey, pt. 2, 1899, p. 320. 



&Daniell, Alfred, A text-hook of the principles of physics, 3d ed., Macmillan Co., New York, 

 1895, p. 316. 



(■King, F. EL, Principles and conditions of movements of ground water: Nineteenth Ann. Kept. 

 U. S. Geol. Survey, pt. 2, 1899, pp. 135-157. 



