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 we obtain Lorentz's transformation

The formulae of transformation of the electric and magnetic vectors are obtained at once from the general formulae; they are

These agree with the formulae of Einstein, Lorentz's formulae for the convection currents being slightly different.

In the case of an inversion with regard to a hypersphere whose centre is at the origin, and whose radius is a real quantity k, the formulas of transformation are

Putting $$s=it,\ x^{2}+y^{2}+z^{2}=r^{2}$$, we get the real spherical wave transformation

This transformation has a negative Jacobian; the formulae for transforming the components of the electric and magnetic force have been obtained by E. Cunningham.

It should be noticed that