Translated from Russian by Jury Sarychev
C.F. Gauss, being already by famous mathematician, almost at the end of the life has mused upon consequences of a finite of velocity of interaction on distance. After 15 years of meditations and the operations he derived in 1835 the law of interacting forces depending upon mutual velocity of interacting bodies (for the particle – particle electrodynamics) .
The great mathematician, he has appeared also ingenious physicist. He reasoned as follows. If the velocity of propagation is finite, therefore, interacting bodies moving with velocity of interaction relatively each other, can not interact, as the potential of interaction from each body can not reach another, i.e. will delay completely. It means that the unknown laws on the dependence of the interacting forces from velocity of interacting bodies exist. More over we know two extreme cases of this law. The first case of the law is when the relative velocity of interacting bodies is equal to zero, and thus the law of interaction is the Coulomb's law. The second case is when the reciprocal velocity of bodies is equal to velocity of interaction, and then the force of interaction is equal to zero. It was principal logical basis, imaginary simulation of statuses of the matter's motion fixed in the mathematical form. It was a vast step forward in comparison with pure Galilean – Newtonian empiricism.
The new mechanism methodology of physics arose in entrails of the scientific world from whirlwinds of Descartes, in searches of mechanisms of interactions of Lomonosov and Lessazh, in wave theories of light of the Huygens, Young, Fresnel and another. And then one was ripped by a powerful flow in activities of the Gauss, Maxwell, Helmholtz, B'erkness, Hertz...
The majority of these works was created with the help "of mental simulation of a status of movement of an ether" (Maxwell). Can we assert after that the ether has served as a "scaffolding" for creation of theories and we can take away this scaffolding? No, we can not. It was "material", "base" and "frame" for construction of physics! Remove ether, and all will fail. How possible is it to assert what without ether there is a whirlwind (rot) or inflation (div)? Or how possible is it to simulate interaction of bodies without ether?
The methodology of a relativity theory with its postulates and refusal from determinism, from mental notion of movement of a matter (refusal from "narrow – minded" common sense), from a causality and with transmission to mathematics of the physics function, was step back in relation to Galilean – Newtonian empiricism. Not to say anything about mechanical theories based on simulation of processes.
The relativity theory has corrupted minds of the researchers, has disaccustomed them to think, to analyze, to search and to doubt. It is enough for the new theory to invent two – three postulates and mathematics will make all remaining.
Mathematics is language of physics. However even mathematicians permanently speak us that mathematics is grindstone: what you'll put – that you'll grind. Mathematician Gauss understood it. The modern physicists do not understand it. Have a look in the scientific physical magazines, and you will see infinite mathematical researches there, which are carrying on in anywhere.
Gauss has died, not having had time to publish, may be, principal work in his life. His young friend, former colleague on Goettingen (Germany), Weber should made it for him. However we shall not speak now about the ethical side of matter. Nevertheless, after becoming famous, Weber published Gauss' elaboration in his complete works. Understood all importance of Gauss' investigations, Weber inferred his law of the delayed potential having taken as a basis only empiric law of Ampere for two interacting conductors with current. He made it without understanding of the physical nature, without the modeling of process of interaction, without mental notion of process of the potential lag.
Weber has ignored a principal phrase of Gauss in the letter to him. The most subsequent physicists have not paid the special attention to it too. Firstly, Gauss has informed Weber that he inferred this law from mental simulation of the mechanism of interaction. Though "...(he) could not make precise imagine about the propagation of electrodynamics action from one particle to another". Secondly, primarily realized and logically justified Gauss introduced in his equation the notion of the velocity of interaction that he has equated to velocity of light (and it was long before Poincare!)
Though Weber, have known about that from Gauss, he introduced the velocity of light as a conversion factor from the electrostatic metering system of units to electrodynamic one and, thus, hides from scientific community depth sense of the law, having presented it for a formalism.
Formalism of Weber  was enthusiastically assimilated only because one linked electrical phenomena to velocity of light. But the destiny has played a malicious joke with him just for that. Two great physicists, Helmholtz and Maxwell, have perceived a formalism of Weber as the law of a long-range action in an electrodynamics (you see, coefficient is not velocity of propagation!) and have acted with its sharp criticism.
Helmholtz has seen in the law of Weber a violation of law of conservation of energy. And it is fair, since the delay of a potential in itself means incomplete realization of spent energy instantly, and with some lateness. Recollect "energy of interaction already has left one body, but yet has not reached another"! (Maxwell).
The error of Helmholtz is "very well made out" by him in the foreword to the book of a Hertz "Principles of the mechanics stated in new link" . He writes: "the Laws of an electrodynamics were derived from a hypothesis of Weber, which tried to reduce an explanation of electrical and magnetic phenomena to a certain modification of Newtonian supposition about forces, directly and rectilinearly operating on distance... In a hypothesis of Weber the supposition was made, that the distribution of this force in infinite space occurs instantly to infinite velocity... F. Neumann, his son K. Neumann, Rimann, and Grossmann advanced the similar hypotheses. Later Clausius did so... Clear outputs did not follow this mixed assembly of hypotheses at all. It was necessary to resort to complicated calculations, to decomposition of separate forces on their variously directed components etc. So the sphere of an electrodynamics has turned into desert without roads in that time. The facts based on observations, and consequence from the rather doubtful theories – all this was combined pell-mell among themselves."
What great mistake, what terrible intolerant critic! And it is all only because Weber has hidden consideration of Gauss... But where is analytical mind of Helmholtz itself?!
The Maxwell, unlike Helmholtz, after acquaintance with work of Gauss completely has reconsidered his positions. At the end of "Treatise about an electricity..."  he devotes the whole chapter to the laws of Gauss and Weber. Where he, at first, shows, that both laws are derived from the law of an Ampere, in the same way. Secondly, both laws are a consequence of a short-range picture. In third, they conform to electrodynamics on the whole. But equations of the Maxwell have already darkened the laws of Gauss and Weber, and they unfairly were left in a shade.
Complete or nearly complete rehabilitation of the laws of delayed potential has taken place only in middle of 20 centuries in works of Feynman . He has shown, that formulas of delay of a potential "cover principle of operation of generators of a current and feature of behavior of light i.e., all phenomena of an electricity and magnetism are present in his work on these law... The formula of delay of a potential gives the complete and exact description of process of radiation; it cover even all relativistic effects". Feynman used a delaying potential in work on a quantum electrodynamics.
However now road to a delayed potential was closed by a formalism of the relativity theory which has perverted all principal concepts and ideals of a classical mechanics and has substituted law of delay of a potential by its artifice – fourth coordinate of a space-time...
The laws of Gauss and Weber do not take into account movement of interacting particles, as well as the equations of Maxwell – movement of electromagnetic systems, relatively an ether, therefore inconsistencies with experiments arise at movement of particles relatively an ether. A Hertz corrected the equations of the Maxwell; the law of Weber is corrected by Clausius.
In 1892 at elaboration of the electronic theory  (the electrodynamics of particle – field) Lorentz synthesized two approaches. The first approach is Maxwell's one for expression of an electrical and magnetic field. The second approach is the law of the delay potential in Clausius' form . He (Lorenz) has obtained the famous formula of interaction of an electron with an electromagnetic field, which one all we use now with success.
Thus, we have three equivalent electrodynamics: the Weber – Clausius' (particle – particle), Lorentz' (particle – field) and Maxwell – Hertz' (field – field).
The law of the Gauss requires the special consideration, since. The Maxwell not incidentally has shown equal rights of the laws of Gauss and Weber, having derived them both from the formula of Ampere. If we accept conclusion of Umov  that the flux of energy from a body is necessary for existence of a potential energy, the law of Gauss in this case could be found just. If we accept existence of a potential energy as initially given property, an infringement of the law of conservation of energy at movement on orbit appears in the law of Gauss. In this case law of Weber is just.
However the mechanism methodology of Gauss is magnificent because it allows finding the law of delay of a potential at any interaction (even by transmission of pressure in pipes) as well as at gravitation too.
I shall not tell about efforts of many scientists, which have obtained the laws of gravitation with delay of a potential. Their correspondence discussion was instructive and very interesting. Among them it is possible to see familiar names: the Maxwell, Poincare, Larmour, Clausius... And already forgotten: Riemann, Ritz, Seegers, Levi and many others.
The Maxwell tried to apply the mechanism methodology of Gauss, but has failed, as could not create any efficient theory of the mechanism of gravitation. "Being unable to understand, how the medium can have such properties, I can not advance further in this direction in searches of reasons of a gravitation" he has written.
But the man was found, which one has bypassed difficulties of simulation of the mechanism of interaction. The name of this man was Paul Gerber the teacher from Stargard. In article , published in 1898, he expressed the thought of a Newton that the action between bodies should be transferred through the medium. And here he makes conclusion, that velocity of interaction can not be indefinitely high and depends on properties of medium. If it so, the lag of potential can not be local; it is distributed on all distance between bodies. From here Gerber make conclusion that it is possible to introduce the inversely proportionality of a potential, depended from velocity of mass, in the standard equation of Lagrange. Thus he has obtained the law of interaction with a delaying potential (like Weber's law containing three terms).
The first term is something, as Newtonian law of universal gravitation; the second term is value of decrease of force of interaction from velocity; and third term is gravitational waves, which should be radiated at acceleration of bodies. Like in Weber's law, here distance between interacting bodies is the scalar quantity. The delay of a potential occurs only in the event if the first derivative of distance on time is not equal to zero (distance changes along a line conditionally connecting interacting bodies). And the radiation of waves occurs, if second derivative of distance on time is not equal to zero too. Besides it is visible from the formula, that the lag of a potential is of the second order of smallness, i.e. depends on a square of velocity of a body divided by a square of velocity of interaction. That reminds of Lorentz' factor.
Gerber, as well as Gauss, has derived that interaction of bodies is carried out through ether, and the ether is the light-carrying medium. He has made the conclusion, that the velocity of interaction is equal to velocity of light (by analogy with the sound velocity in air is equal to the velocity of the pressure transference). Having substituted velocity of light instead of velocity of interaction, he has obtained abnormal offsets of perihelions of all planets, including moon, which corresponds to observable events.
Thus, we see that the classic mechanics with its invariant of space, time and mass was on correct path and solved all arising problems. There was no necessity neither in fourth coordinate of space – time nor, in geometry of Riemann, nor in the pseudoeuclidean geometry of Minkowski, nor in tensor calculations, nor in a heaping of paradoxes and in waiving common sense...
Simulating the process of delay of a potential, I have found out, that the lag occurs non-uniformly and is realized in "pulsatory" movement of a body. Calculating frequency and length of "pulsatory" oscillations, I have obtained the formula of de Broglie and have found that for gravitation and the electrodynamics exist different constants for dependence of energy of movement on frequency. Therefore, I have come out on a wave quantum mechanics both for electromagnetic, and for gravitational interactions. And it, in turn, speaks that the delayed potential has not told its last word yet.
Is published earlier:
"Science of Kazakhstan", 5 (65), March 1...15, 1996.