﻿280 Mr. B. Moore on a Relation between the 



It might be supposed that the action of this force would 

 cause a rise of level in the tube A. And so it would if the 

 whole cross-section of the capillary were within the range of 

 capillary action ; but in a capillary tube, even as fine as one 

 can draw it out, the greater part of the section is still outside 

 the radius of capillary action, and as soon as any difference 

 in pressure is caused by the action of surface-tension, it is 

 effaced by a back flow along the central part of the capillary 

 from A towards B. 



However, under the circumstances in which osmotic pres- 

 sure becomes evident, it is extremely probable that the 

 diameters of the capillaries placing solution and solvent in 

 communication are so exceedingly small that the whole of 

 their cross-section is well within this radius of capillary 

 action. That this is so appears to be proven, not only by the 

 usual mode of formation of such semipermeable walls by 

 causing a precipitate in a finely divided condition in pores 

 already minute, so that the two fluids are only in communi- 

 cation by minute passages between the molecules of this pre- 

 cipitate which must most probably be of molecular dimensions, 

 but also by a simple calculation based on the assumption that 

 osmotic pressure is due to difference in surface-tension acting 

 as above described. 



This calculation leads to an interesting value for the dimen- 

 sions of the pores and may be stated as follows : — Let T be 

 the difference between the surface-tension of a solution and 

 that of the pure solvent, P the osmotic pressure in this solu- 

 tion, supposed to be due to the action of this difference in 

 surface-tension, and r the radius of a capillary opening placing 

 the solution and the solvent in communication. Then, foi 

 a position of equilibrium, the difference in surface-ten sioi 

 acting on the perimeter of the capillary must balance the 

 osmotic pressure acting on its cross-section, and we therefore 



2T 

 conclude that the equation 27n\T = 7rr 2 P, or r— -^ , must hold 



good. 



From this equation, the necessary value which r must have, 

 to account for osmotic pressure in the manner suggested, can 

 easily be calculated. 



Rother* gives for the surface-tension of a solution of 

 sodium chloride in water the equation a=7'357 + Olo66y, 

 where a. is the surface-tension in milligrams per millimetre, 

 7*357 the surface-tension of water in the same units, and y 

 the number of gram-equivalents of the substance dissolved in 

 100 equivalents of water, that is in 900 grams. Converting 



* Wied. Aim. xvii. p- 353 (1882). 



