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 molecidar theory, the subdivision of the medium into 
elements is not valid beyond the limits of physical smallness and 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 LarmorI who found 
that the part contributed to the forcive at any internal point by the molecules 
immediately surrounding that point was, on account ol 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 (be., 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 
Cauchy, 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 ‘ .lather and Matter,’ p. 261. 
^ Loc. cit., p. 265. 
