In 1897 physicists took the first e/m measurements at electrons, the consequence was a revival of the atomistic ideas in physics. The researches in geophysics also contributed to the construction of the modern physics. Four examples are dealt with this essay. 1) In 1899 J. J. Thomson was able to carry out the first direct determination of elementary electric charge with the help of the conformity with the natural laws at the formation of fog, found by C. T. R. Wilson. (...) 2) The cloud-chamber, called after C. T. R. Wilson, was the result of various constructions of for- or cloud-chambers, in it there were shown for the first time the tracks of α- and β-particles. 3) At the exploration of the photoelectric effect of the sunlight (especially of the ultraviolet share) Elster and Geitel made essential preliminary studies for the lightquanta-hypothesis of Einstein. 4) Elster and Geitel detected radioactive substances in the atmosphere and in the soil to be the main source of the atmospheric electricity. (shrink)

A dual form of the general relativistic and covariant generalization of the first vorticity theorem of Helmholtz is proven. This dual form is the generalization of Boltzmann's formulation of the Helmholtz theorem.

The article gives an overview on Albert Einstein's activity in relation to geophysics. Various aspects of his fundamental investigations and their significance for geophysical research are discussed.

The general theory of relativity gives an absolutely covariant formulation of Helmholtz's laws of vorticity which is valid in arbitrary reference systems. For small relative velocities ui, (with ui,u′≪ε2) these generally covariant laws deliver Helmholtz's first law for a vorticity ωi in a rigidly rotating references system $\frac{d}{{dt}}(\omega _i - \Omega _\iota ) = (\omega ^l - \Omega ^l )u_{l,i} $ with the angular velocity Ω of the rotation.

The relativistic formulation of Hide's “magnetic analogue” of Ertel's potential vorticity theorem is Dirac's “new classical theory of electrons”.

The covariant and relativistic generalization of the Helmholtz integral vorticity theorems and Thomson's circulation theorem are derived.

The general relativistic and covariant differential form of Helmholtz's first vorticity theorem is presented. We prove in relation with it an invariant kinematic identity which is the generalisation of the Helmholtz theorem for general continua.

The gauge-invariant relativistic wave mechanics corresponds to relativistic magneto-hydrodynamics according to Planck's version of the correspondence principle.