378 Prof. G. N. Antonoff on Interfacial 



positive and negative charges of approximately equal magni- 

 tude on the whole. On the other hand, molecules must 

 apparently be regarded as asymmetric, and therefore in 

 many cases can be treated as mathematical bipoles or 

 doublets in which the positive and negative charges are 

 effectively concentrated in points at definite distances apart, 

 such distances being characteristic of the molecules con- 

 cerned. These distances may as usual be called the lengths 

 of the molecular doublets. The use of molecular doublets, 

 as a means of interpreting the phenomena of surface tension, 

 was suggested by Sir Oliver Lodge *". In the following- 

 calculations, these doublets may be regarded as purely elec- 

 trical in type, and the paper, in one of its aspects, indicates 

 the extent to which a purely electrical theory of the forces 

 operative in liquids between contiguous molecules can account 

 for the observed phenomena. But magnetic polarity, if pre- 

 sent, would also be subject to the same laws of action between 

 neighbouring doublets. The investigation therefore does not 

 preclude the existence of magnetic forces also. Their only 

 effect would be to alter the absolute values of surface tension 

 and molecular pressure, and not their ratio or the nature of 

 the laws regulating their action. It is not without interest 

 that this theory, or even the combined electrical and mag- 

 netic theory, at once necessitates that the molecular attrac- 

 tions must be proportional to the inverse fourth power of 

 the distances in agreement with the conclusion reached by 

 Sutherland on experimental grounds f. 



If it be supposed that the molecules of liquids act as 

 doublets, — in all the considerations advanced in this paper, 

 only transparent liquids are under review,— they must be 

 arranged in such a manner that the extremities of opposite 

 sign are adjacent. Let the length of a doublet be I, 

 and the charges on its poles ±e. The component forces 

 between two such doublets in any relative positions are 

 known. 



A single doublet at the origin 0, pointing along the axis 

 of x, produces an external field whose potential at a point P 

 or (x, y, z) is, if r=OP, 



If a second doublet is situated at P, in the plane ssy y and 

 if the projections of its length parallel to the axes are Sx, 8y 9 



* Proc. Inst. Elec. Eng. Part 159, vol. xxxii. (1903). 

 t Loc. cit. 



