522 Mr. J. Larmor. [May 14, 



Generalised Polarisation Theory. 



The problem of determining how far these remarkable conclusions 

 will still hold good when a more general view of the nature of di- 

 electric polarisation is assumed was considered by von Helmholtz* 

 in a series of memoirs. 



The most general conception of the polarisation of a medium 

 which has been formed is the Poisson theory of magnetisation. The 

 magnetised element, whether actually produced by the orientation of 

 polar molecules or otherwise, may be mathematically considered to 

 be formed by the displacement of a quantity of ideal magnetic matter 

 from its negative to its positive pole, thereby producing defect at the 

 one end, and excess at the other end. The element is defined mag- 

 netically by its moment, which is the product of the displaced 

 quantity and the distance through which it is displaced. The dis- 

 placement per unit volume, measured by this product, is equal to the 

 magnetic moment per unit volume, whether the magnetised mole- 

 cules fill up the whole of that volume or are a system of discrete 

 particles with unoccupied space between them. 



In the electric analogue we replace ideal magnetic matter by ideal 

 electric matter ; the displacement thus measured constitutes the elec- 

 tric displacement, and its rate of change per unit time represents the 

 displacement current in the dielectric. We have to consider whether 

 a displacement current of this type suffices to make all electric 

 currents circuital ; and it will be sufficient and convenient to examine 

 the case of a condenser which is charged through a wire connecting 

 its two plates. In the first place this notion of electric displacement 

 leads to the same distribution of potential between the plates as the 

 ordinary one, adopted by Maxwell ; for in the theory of induced 

 magnetism there occurs a vector quantity of circuital character, the 

 magnetic induction of Maxwell, of which the components are 

 /t((fV/rfx), ft(dVjdy), p(dVjdz), and which, therefore, leads to 

 the characteristic equation of the potential 



A/ *T\+d-( d ^\+jL( ^Y\ o 

 dx \ dx / dy\ dy / dz\ dz / 



corresponding to the one given above. If the displacement in the 

 dielectric is *(dV/<fcO, - K (dVjdy), -r((TV/<fc), then 



ft = H-4JTC. 



The displacement in a unit cube may, of course, be considered as a 

 displacement across the opposite faces of the cube. 



Now, considering the case of a plane condenser, let F be the electric 

 force in the dielectric between the plates ; then the displacement is 



* ' Wissenschaftliehe Abhandlungen,' I, p. 545, et tey. 



