applied to Statical Electricity. 15 



These relations are independent of any theory about the internal 

 mechanism of dielectrics ; but when we find electromotive force 

 producing electric displacement in a dielectric, and when we find 

 the dielectric recovering from its state of electric displacement 

 with an equal electromotive force, we cannot help regarding the 

 phenomena as those of an elastic body, yielding to a pressure, 

 and recovering its form when the pressure is removed. 



According to our hypothesis, the magnetic medium is divided 

 into cells, separated by partitions formed of a stratum of particles 

 which play the part of electricity. When the electric particles 

 are urged in any direction, they will, by their tangential action 

 on the elastic substance of the cells, distort each cell, and call 

 into play an equal and opposite force arising from the elas- 

 ticity of the cells. When the force is removed, the cells will 

 recover their form, and the electricity will return to its former 

 position. 



In the following investigation I have considered the relation 

 between the displacement and the force producing it, on the 

 supposition that the cells are spherical. The actual form of the 

 cells probably does not differ from that of a sphere sufficiently 

 to make much difference in the numerical result. 



I have deduced from this result the relation between the 

 statical and dynamical measures of electricity, and have shown, 

 by a comparison of the electro-magnetic experiments of MM. 

 Kohlrausch and Weber with the velocity of light as found by 

 M. Eizeau, that the elasticity of the magnetic medium in air is 

 the same as that of the luminiferous medium, if these two coex- 

 istent, coextensive, and equally elastic media are not rather one 

 medium. 



It appears also from Prop. XV. that the attraction between 

 two electrified bodies depends on the value of E 2 , and that there- 

 fore it would be less in turpentine than in air, if the quantity of 

 electricity in each body remains the same. If, however, the 

 potentials of the two bodies were given, the attraction between 

 them would vary inversely as E 2 , and would be greater in turpen- 

 tine than in air. 



Prop. XII. — To find the conditions of equilibrium of an elastic 

 sphere whose surface is exposed to normal and tangential forces, 

 the tangential forces being proportional to the sine of the distance 

 from a given point on the sphere. 



Let the axis of z be the axis of spherical coordinates. 

 Let £, 7j, f be the displacements of any particle of the sphere 

 in the directions of x, y, and z. 



Let p xx , p yy , p zz be the stresses normal to planes perpendicular 

 to the three axes, and let p yX} p ZX} p xy be the stresses of distortion 

 in the planes yz, zx, and xy. 



