Tension and Complex Molecules, 381 



and rapidly decrease. Only the first two values o£ n need 

 to be retained, and we may write, for the total attraction of 

 a doublet towards one side, along its length, 



3fP 

 d 





This does not differ appreciably from the force due to the next 

 consecutive doublet in line. The force in the perpendicular 



3e 2 l 2 

 direction similarly is effectively —74-* or half the above 



value. The problem so far has been two-dimensional, but 

 it is evident that the three-dimensional problem gives the 

 same approximate solution, and we may conclude that when 

 such a doublet is one of a regularly disposed arrangement, 

 all doublets being parallel, it is pulled in each direction in its 



6eH 2 

 own line by a force — «-, and in a perpendicular direction 



by half this force. 



In a length nd parallel to the doublets or perpendicular to 



them, n doublets are situated. The number in unit length is 



-?, and if p is the number of doublets or molecules in unit 



volume of the liquid, 



1 

 IP***' 



If the surface doublets were arranged parallel to the surface, 

 the surface tension, or attraction along the surface per unit 

 length, would be 



&p 2 l 2 / 



~f j d=6eH 2 p 5 i* 



in one direction, but only half this value in the perpendicular 

 direction along the surface. We must therefore reject 

 this case, and adopt, on the other hand, that with all the 

 doublets arranged normally to the surface, the poles in any 

 line being alternately positive and negative. The surface 

 attraction per unit length is then 3e 2 l 2 p 513 and the inward 

 normal attraction is 6e 2 l 2 p 4:/ ' s on each doublet. It is not, of 

 course, implied that the surface poles form a rectangular lattice 

 arrangement at any instant. The magnitude d is the average 

 distance apart of contiguous poles belonging to different 

 Phil. Mag. S. 6. Vol. 36. No. 215. Nov. 1918. 2 D 



