62 Prof. H. Lamb on the Theory of Electric 



2ttR 2 ' £ 



when it is near the walls'*. 



4. We may next consider the electromotive forces produced 

 by the passage of a liquid through a capillary tube or a porous 

 diaphragm. This subject has been studied experimentally by 

 Quincke, Edlund, Haga, Clark, and more recently by Dornf, 

 the general result being that the potential is higher on the 

 side where the pressure is least by an amount proportional to 

 the difference of pressure. The phenomenon is ascribed to a 

 sort of electric convection, the superficial electrified layer of 

 fluid carrying its charge with it as it slides over the walls of 

 the channels. In the case of a straight uniform tube, for 

 instance, there is in this way a transfer of positive electricity 

 along the walls, from the near to the farther end, which is 

 compensated, if no other path is open, by conduction back- 

 wards through the column of liquid in the tube. If the tube 

 be of varying section there will be a tendency also to con- 

 vergence of positive or negative electricity by convection at 

 intermediate points, and a consequent establishment of 

 " sources " and " sinks " as regards the conducting mass of 

 fluid in the interior. 



Taking the case of a tube of circular section, through which 

 fluid is forced by an excess of pressure P, and using the same 

 notation as in § 2, we find by the ordinary theory of Poi- 

 seuille's experiments 



w = 4^( R2 -' l2 + W/3). ' * ' < 26 > 



Hence the total quantity of electricity carried per second 

 along the wall of the tube is 



27rUp . m r = -gj-. p. 



If no other conducting channel is open the electricity thus 

 carried forward will return by ordinary conduction through 

 the column of liquid in the tube. Since the resistance of 

 this column is a\L/7rR 2 , the difference of potential between 

 the ends of the tube is 



f-* E (27) 



* It is to be noticed that one of Quincke's observations remains unex- 

 plained, viz., the fact that in sufficiently wide tubes the direction of motion 

 of particles near the walls varied with the strength of the current. 



f For references see Wiedemann, Elektricitat, ii. pp. 153 et seq. 



