The role, which electromechanical analogies play in the analytical mechanics of mass points, is well-known. For the electrodynamic equations, such analogies in the modern theoretical physics are not only unknown, but are even denied. In work [3], mathematically rigorous mechanical interpretation of the Maxwell equations is given, and it is shown that they are completely identical to the equations of oscillations of a non-compressible elastic medium. Thus it follows that in the Maxwell equations there is an infinite velocity of the propagation of extension waves, which is in the explicit contradiction with special relativity theory. In other words, electrodynamics and special relativity theory are incompatible. These analogies were established by Maxwell himself for the absence of charges, and in [3] they are proved for the general case.
The modified Maxwell equations are proposed [3 - 5]. In the modified theory, all the waves propagate with finite velocities, one of them has to be greater than the light velocity in vacuum. If this to consider the limit case, when this velocity tends to the infinity, the modified equations give the Maxwell equations in the limit. The waves with the ``superlight'' velocity are longitudinal. One cannot eliminate the possibility that these waves describe the phenomenon of radiation propagating with the velocity greater than the light velocity, which is claimed to be experimentally observed by some astronomers.
It is established [3 - 5] that in terms of this theory electrostatic states present hyperlight waves and are realised far from the wave front.
It is shown [3], that neither classical, nor modified Maxwell equations cannot describe correctly the interaction between the electrons and the nucleus of the atom. The way to solve this problem is indicated.
It is shown [6], that the mathematical description of an elastic continuum of two-spin particles of a special type is reduced to the classical Maxwell equations. The mechanical analogy proposed above allows to state unambigously that the vector of electric field is axial, and the vector of magnetic field is polar.