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There are two competing formulations of time in physics. Newton defended in the Principia the utilization of absolute time which, according to him "flows equably without relation to anything external." Leibniz, on the other hand, was against this concept and proposed relative time to replace it: "As for my opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistences, as time is an order of successions." Leibniz's ideas were accepted and developed by Ernst Mach in his book The Science of Mechanics. Mach proposed to replace Newton's absolute time by the angle of rotation of the planets relative to the frame of fixed stars.

In this work we consider the implementation of relational time and its consequences for physics. We concentrate our analysis in a single phenomenon, namely, the flattening of the Earth due to its diurnal rotation. We consider the figure of the Earth in Newtonian mechanics. We point out some philosophical problems with this classical formulation. We then present the flattening of the Earth from the point of view of Relational Mechanics, which is a mathematical implementation of Mach's principle utilizing Weber's law for gravitation.

We derive the virial theorem for Weber's law applied to gravitation and electromagnetism.

Mach's principle is compared with the principle of physical proportions. Laws that are compatible and others not compatible with the latter principle are discussed. Avenues for the implementation of this principle are also outlined.

In (Assis 1998, pp. 241-249) and (Assis 1999, pp. 199-205) it was said that if we double the average matter density of the distant universe (galaxies), while keeping constant the matter density of the earth and all sizes and distances, the acceleration of free fall halves (that is, goes to 4.9m/s² instead of the usual 9.8m/s²). Guala-Valverde concluded that in this case the acceleration of free fall should go to (9.8m/s²) / 2, see (Guala-Valverde 1999a and 1999b, p. 25). But this was only due to a misunderstanding. Guala-Valverde was thinking on doubling the average inertial mass density of distant galaxies, while Assis was talking of doubling the average gravitational mass density of distant matter (see (Assis 1998, pp. 207, 211 and 246) or (Assis 1999, pp. 170, 174 or 204). This solves all misunderstandings. That is, Guala-Valverde and Assis agree that doubling the gravitational mass density of distant matter (while keeping unalterable Hubble's constant, the gravitational mass of the earth and its radius) will make the acceleration of free fall go to 4.9 m/s². So our results are not clashing, it was all due to a misunderstanding.

We propose the principle of physical proportions, according to which all laws of physics may depend only on the ratio of quantities of the same type.  We present examples of laws that satisfy this principle, and others that do not.  These examples suggest that the theories leading to these laws must be incomplete.

In this work it is analysed three basic electromagnetic systems of units utilized during last century by Amp?re, Gauss, Weber, Maxwell and all the others: The electrostatic, electrodynamic and electromagnetic ones. It is presented how the basic equations of electromagnetism are written in these systems (and also in the present day international system of units MKSA). Then it is shown how the constant c was introduced in physics by Weber's force. It is shown that it has the unit of a velocity and is the ratio of electromagnetic and electrostatit units of charge. Weber and Kohlrausch's experiment to determine c is presented, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchoff and Weber obtained independently of one another, both working in the framework of Weber's electrodynamics, the fact that an electromagnetic signal (of current or potential) propagate at light velocity along a thin wire of negligible resistivity.

Several arguments favouring instantaneous action at a distance are presented. The action at a distance laws of Newton, Coulomb, Amp?re and Weber are analysed. Historical evidence that Weber's electrodynamics led to the propagation of electromagnetic signals with finite velocity prior to the development of Maxwell's equations are emphasized. The implementation of Mach's principle with Weber's law applied to gravitation is discussed.

We study the oscillation of a charged particle near a capacitor in four different models: Classical me-chanics, Weber's electrodynamics plus classical mechanics, relativistic mechanics, and Weber's electrodynamics plus the mechanics of Erwin Schr?dinger. We show that only the third and fourth models yield physically reasonable results.

We calculate the surface charges, potential and fields in a long cylindrical coaxial cable with inner and outer conductors of finite conductivities and finite areas. It is shown that there is an electric field outside the return conductor. PACS: 41.20 -q, 41.20 Gz.

We present the history of estimates of the temperature of intergalactic space. We begin with the works of Guillaume and Eddington on the temperature of interstellar space due to starlight belonging to our Milky Way galaxy. Then we discuss works relating to cosmic radiation, concentrating on Regener and Nernst. We also discuss Finlay-Freundlich's and Max Born's important research on this topic. Finally, we present the work of Gamow and collaborators. We show that the models based on a Universe in dynamical equilibrium without expansion predicted the 2.7 K temperature prior to and better than models based on the Big Bang.

We comment on and translate Gustav Kirchhoff?s important paper of 1857 entitled ?On the motion of electricity in conductors.? The significance of this paper is that Kirchhoff proved with action at a distance that electric disturbances travel along wires of negligible resistance with the velocity of light. He accomplished this with the laws of Newtonian electrodynamics (Coulomb, Ampere, F. Neumann and Weber) before Maxwell had formulated his equations.

Unipolar induction is the generation of current on a conductor for the case in which the conductor and the magnet are in relative rotary motion. A typical case of unipolar induction is shown in figure 1. Since Faraday's experiments of 1932 on electromagnetic induction on rotation systems there are intense debates concerning the location of the seat of the electromotive force (emf)².

Two mechanisms utilized to explain the operation of railguns are explained: one based on Ampere's force and the other on the transfer of momentum through electromagnetic waves. It is shown how the former is compatible with the data while the latter has problems with the quantitative figures and the case of the immobilized projectile.

We present the results for the electric and magnetic fields due to linear and circular current distributions according to Weber's theory. We show how the electric field predicted by Weber's law is compatible with the anomalous diffusion in plasmas. Finally, we discuss some modem experiments related to this topic and compare the results of these experiments with a prediction based on Weber's law.

We present Weber's force law and the classical results that follow from it.  We discuss the historical controversy surrounding Ampere's law of force between current elements versus Grassmann-Biot-Savart's law.  Then we make a review of modern experiments related to this topic and to the electric field generated by a steady and stationary neutral current.  Finally we analyze some theoretical aspects of Weber's law as its extension through retarded potentials to include electromagnetic radiation, and its relation to alternative interpretations of experiments devised to show the mass radiation with velocity.