248 MAJOR A. E. OXLEY ON THE INFLUENCE OF MOLECULAR 



as to include the effects of mutual molecular influences. Such a representation of the 

 facts has led to the recognition of a large molecular forcive, in all crystalline media, 

 depending upon the nature and proximity of the molecules in any particular 

 crystalline grouping. The existence of this intrinsic molecular field can only be 

 inferred indirectly. Although the actual properties of the crystalline state depend 

 upon the operation of this field, yet, except in the case of substances of a 

 ferro-magnetic nature, there is no direct experimental evidence which discloses its 

 very great magnitude. 



From a theoretical point of view, there seems to be no doubt that the mutual 

 actions of the molecules are represented by enormous internal forcives in all crystalline 

 media. The usual method of determining the forcive at an internal point of the 

 material medium is to take a cavity whose dimensions are small in comparison with 

 ordinary lengths (e.g., 1 cm.) and yet large compared with molecular dimensions. A 

 convenient designation of the dimensions of the cavity is contained in the phrase 

 " physically small."* In molecular theory, the subdivision of the medium into 

 elements is not valid beyond the limits of physical smallness aiid only in media which 

 are absolutely continuous may the elements be pushed to limits of " mathematical 

 smallness." In a continuous medium our mathematical functions give us an accurate 

 estimate of the forcives and potentials operating at internal points ; in a medium 

 composed of discrete particles these same functions give us only an approximate 

 estimate. A discussion of the nearness of the approximation which can be obtained 

 for material media is of great importance from the point of view of our subject. For 

 the liquid state the question has been considered by Sir JOSEPH LARMOBf who found 

 that the part contributed to the forcive at any internal point by the molecules 

 immediately surrounding that point was, on account of rapid motions and irregular 

 distributions of the axes of the molecules, negligibly small. To quote from LARMOR| : 

 " The general conclusion may be expressed, in an adaptation of CAUCHY'S terminology, 

 by the principle that whenever the integrals in the formulae for mechanical forces on 

 a material medium cease to be convergent, their principal values must be substituted," 

 and again in the footnote to p. 265, 



"This statement (i.e., the above quotation) may be considered to be the 

 mathematical expression of the principle of the mutual compensation of molecular 

 forcives, for which, cf., ' Phil. Trans.', A, 1897, p. 260. The principal value of 

 CATTCHY, as regards the completely defined analytical integrals of Pure Mathematics, 

 would be the value at the centre of a minute spherical cavity. But the quantities 

 which, to avoid periphrasis, have been here called integrals, are really summations of 

 contributions from finite though very small, and complexly constituted, polarised 

 molecules ; the distribution of these molecules that occupy our minute cavity is entirely 



* LEATHEM, " Volume and Surface Integrals used in Physics," ' Cambridge Monographs," No. 1, p. 5. 

 t ' Either and Matter,' p. 261. 

 J Loc. cit.,'p. 265, 



