The role of the vector potential of magnetic field in the equations of induction is refined. The concept of the vector potential of electric field is introduced. It is shown what concept is, as the kinetic inductance of charges plays in the electrodynamics not less important role, than dielectric and magnetic constant. Is developed the mathematical model of the dispersion of electromagnetic waves in the conductors and the dielectrics with the use of a physical quantity of dielectric constant, which does not depend on frequency. It is shown that in the confined plasma the transverse plasma resonance can exist. They are introduced the concept of kinetic capacity. Provides a new way to display the wave equation. The way of writing of the equations of induction with the use by the substantional derivative obtained their symmetrical form. Is introduced the scalar-vector potential, in which the scalar potential of charge and its field they depend on speed.. Because of the laws of symmetric induction in the framework of the laws Galileo transformations obtained conversion fields in the transition from one inertial reference system to another, called Mende transformation. The introduction of this potential made it possible within the framework the Galileo conversions to explain the phase aberration and the transverse Doppler effect, and also power interaction of the current carrying systems without the use of a postulate about the Lorentz force. Are examined the bases of trans-coordinate electrodynamics in time-spatial giperkontinuum, in which it is improved the apparatus for differential calculus of field functions it is introduced the Dubrovin operator. The results of the experimental studies, which showed, are given that the charge is not the invariant of speed. Received in return the law of conservation of 4-pulse of the new law of conservation of angular balance. For the specialists in the region of electrodynamics, radio physics, electronics, radio engineering, technical protection of information, theoretical and mathematical physics, and also students and graduate students of the corresponding specialties. Reviewers A. A. Rukhadzedoctor of physical and mathematical sciences, professor, laureate of state prizes and prize of M. V. Lomonosov. N. N. Gorobezdoctor of physical and mathematical sciences, professor, head of department of applied electrodynamics of Kharkov national university V. N. Karazin ISBN of Mende F.F. Specifically, support on the physical experiment and the comprehensive disclosure of the physical sense of models they are assumed as the basis in this work alternative of the ideology of electrodynamics stated. Finally, one additional brake of the development of scienceits excessive popularization in the commercial interests. The science, chained into the shackles of the yellow press, when on the covers of popular periodicals for the larger psychological effect are depicted allegedly the brilliant persons with the limited physical possibilities, tendentiously praised by journalists, who do not absolut...