492 ON PHYSICAL LINES OF FORCE. 



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 elasticity 

 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 shewn, by a comparison of the 

 electro- magnetic experiments of MM. Kohlrausch and Weber with the velocity 

 of light as found by M. Fizeau, 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*, and that therefore 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*, and would be greater in turpentine 

 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 2 be the axis of spherical co-ordinates. 



Let , 77, be the displacements of any particle of the sphere in the direc- 

 tions of x, y, and z. 



Let PXB, p n , p a be the stresses normal to planes perpendicular to the three 

 axes, and let p v , p m p^ be the stresses of distortion in the planes yz, zx, 

 and xy. 



