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Dr. J. Larmor. A Dynamical Theory 



Pfluger's recent dispersion carves for solid fuchsin and other selec- 

 tively absorbent solid substances ; but there is absolutely nothing in 

 these general features that would not fit one theory of dispersion as 

 well as another, — they all arise from the mere notion of sympathetic 

 vibration. The complete values of the index along the spectrum, 

 not merely those of its real part, must be available before any prefer- 

 ence can in this way be established. 



5. A main feature of the interaction between aether and matter 

 consists in the bodily mechanical forcives exerted on electrically and 

 magnetically polarised material media. In the theory a transition 

 has here to be made between the mere aggregate or sum of the vary- 

 ing energies of the individual molecules of a medium, and the co- 

 ordinated and averaged part of this sum which is the energy pertain- 

 ing to the element of volume of the medium in bulk : this farther 

 involves the definite enunciation of a general principle in molecular 

 mechanics which has hitherto found an application, and that a 

 restricted one, only in the theory of capillary attractions. In a 

 polarised medium, a distinction has thus to be drawn between the 

 averaged individual energies from which the forces polarising the 

 separate molecules are derived, and the organised mechanical energy 

 of the medium as a whole, which is the aggregate of these energies 

 after the local parts arising from the neighbouring molecules have 

 been excluded. In this mechanical energy the bodily forces on the 

 medium in bulk are involved : it must therefore be expressible as an 

 analytical function of the configuration of the medium in bulk, for 

 otherwise perpetual motions could supervene. In the study of the 

 mechanical actions in material media, consideration of the properties 

 of the molecules is available as a guide towards the mathematical 

 form of the function which represents the distribution of the 

 mechanical energy of the forces acting on the element of mass : but 

 the province of: molecular theory is ended in this general survey, and 

 the actual values of the coefficients in the energy function must be 

 determined by observation and experiment. 



In an electrically polarised material medium an expression for the 

 distribution of this mechanical energy is obtained, and the bodily 

 applied forces in the material are derived from it, the tractions 

 exerted on an interface between two media being deduced from the 

 forces that would act on a layer of gradual transition which in the 

 limit is taken indefinitely thin. The result is that in a medium 

 whose molecules are polarised to intensity i by a field of electric 

 force F, and isotropic so that % and F are in the same direction, there 

 is a bodily force (djdx, d/dy, d/dz)ji'dF. which could be balanced by a 

 hydrostatic pressure —ji'dF, and there is also a normal traction on 

 each interface equal to the difference in the values of — 2tt^' 2 towards 

 each side, where n' is the component of i along the normal. Thus 



