vii 



particles revolving, like "idle wheels" in mechanism, each on its 

 own axis, in directions opposed to those of the vortices. The motion 

 of those particles he identifies with electric currents in the medium, 

 and the description of how, by this mechanism, induced currents are 

 originated, forms an interesting part of the theory. The electro- 

 motive forces, that is, the forces on the particles from the vortices, are 

 then found in the most general case of a medium in motion, the 

 expressions being identical with those given in the " Electricity and 

 Magnetism," ii, § 598. 



Turning next to Statical Electricity, if we consider a dielectric 

 under inductive action, we may conceive the electricity in each of the 

 particles described above to be displaced, so that one side of the 

 particle is positive and the other negative, the total quantity remain- 

 ing the same. The general effect on the dielectric will, therefore, be 

 a displacement of the electricity, which will disappear when the 

 exciting cause disappears. We have here, then, something analogous 

 to the phenomena exhibited by an elastic body under a state of stress, 

 but recovering its form when the stress is removed. 



If we denote the displacement by h, on this analogy the force will be 

 given by an equation of the form R= — 47rE 3 7z, where E is a constant 

 depending on the dielectric. In addition to the properties already de- 

 scribed of the cells constituting the vortices, we must now suppose the 

 substance of which they consist possessed of a certain elastic resilience, 

 affecting by its tangential action the velocities of the particles, and in 

 its turn affected by them, being distorted and thrown into a state of 

 stress. If, for simplicity, we omit the magnetic effects and suppose 

 the cell to be spherical in form, and that its coefficients of cubic 

 elasticity and rigidity are \m and m, such being the relative values of 

 these, quantities in an isotropic elastic medium according to the 

 theory of Navier and Poisson,then it can be shown that E 3 = 7rm. 

 But the rate of propagation of transverse vibrations in an elastic 

 medium is given by ~V=^/m\p. And /a=7rp. Hence E=Vy 

 Now, the force between two charges e ]? e 2 at distance r, can be 

 deduced from the theory, viz;., it is E 3 e 1 e 2 /r 3 . Hence the number of 

 electrostatic units in one unit of the Vortices Theory, i.e., of the 

 Dynamical or Electromagnetic Theory, is E. If the medium be air 

 p==l, and therefore V = E. The value of E found by Weber and 

 Kohlrausch was 310,740,000 metres. On comparing this with 

 Fizeau's value of the velocity of light in air, viz., 314,858,000 metres 

 per second, Maxwell drew the inference, that " light consists in the 

 transverse uudulations of the same medium, which is the cause of the 

 electric and magnetic phenomena." He also proved that the specific 

 inductive capacity of a dielectric varies as the square of the index of 

 refraction, and inversely as the coefficient of magnetic induction. 

 The last point discussed under the Vortices Theory is Faraday's 



