242 Prof. C. Niven on the Theory of an 



fore, to dwell upon Cauchy's or more recent theories, which, 

 though more complete, possess some of its general features. 



One result of the present investigations, which is a little 

 startling, is, that part of the energy of the substance resides at 

 its surface. It may be that a more complete investigation 

 might show that this part of the energy must necessarily vanish ; 

 but I have preferred to leave for the present untouched the 

 question as to whether any or what physical interpretation 

 might be given of these terms. 



The coefficients which produce circular polarization contain 

 as a factor a quantity of the order of the molecular distance ; 

 and, conversely, the phenomena of the rotation of the plane of 

 polarization in quartz may be applied to form a rough estimate 

 of this distance. The result is not very widely different from 

 that which Sir W. Thomson and others have deduced from 

 other considerations. 



2. In dealing with the bending of a wire the mathematical 

 element chosen is a length ds of the wire bounded by two 

 cross sections ; and the stress which acts on the element across 

 one of these sections consists of a force and a couple, and not, 

 as in the case of the element-area in the interior of a homo- 

 geneous elastic solid, of a force only. In the case of a lamina, 

 the stress acting across any small element of a normal sec- 

 tion consists also of a force and a couple. These couples, 

 which, as already observed, do not present themselves in 

 specifying the stress inside a homogeneous elastic solid, arise 

 from the unequal contractions and expansions of the sub- 

 stance at different points of the normal section of the plate, or 

 cross section of the wire. Moreover the mathematical ma- 

 chinery used is of a coarser type than that employed in dealing 

 with a homogeneous solid — coarser in one dimension in the case 

 of the plate, and in two dimensions for the wire. Now if the 

 constitution of a solid itself be such that, though sensibly ho- 

 mogeneous on a large scale, it is really heterogeneous when 

 examined more closely, the forces across two neighbouring 

 indefinitely small parallel areas may not be parallel and pro- 

 portional to the areas. If, therefore, the mathematical element 

 were chosen large enough to eliminate all trace of this coarse- 

 ness of structure, the actions on the faces of the element might 

 not result each in a definite force but in a force and a couple — 

 what Dr. Ball calls a " wrench," or even in stress of a more 

 complex type. Sir W. Thomson has pointed out in ' Nature ' 

 (vol. i. p. 551) that this discontinuity is what is established in 

 Cauchy's theory of the dispersion of light ; and he has even 

 used Cauchy's results to obtain a numerical estimate of the 

 intermolecular spaces of matter. 



