Gravitational, varying within

Let us now analyze some specific systems. First, we examine a column of pure fluid perpendicular to the surface of the earth [Fig. 21.1 (c)] and at equilibrium. In this case, it can be shown by the following argument that the pressure within the fluid varies with position in the gravitational field. 

Robert Dicke (1961) later hit on an interesting rejoinder. As noted, Dirac had taken it to be more than mere coincidence that the Hubble age should happen to have the value A, thus linking it to the other two cosmic features. Dicke showed that this was indeed not a coincidence, but his explanation was quite different from Dirac s. Observers can exist in the universe only after heavy elements have had time to form, and within the maximum lifetime of a massive star. Calculations show that, given the components from which the other two constants are constructed, the Hubble age during the epoch of man, as Dicke called it, would necessarily be of the order of A. The relationship between H and the other two does not therefore indicate an invariant relationship, as Dirac thought, but is a selection effect, a constraint set on the value of Tby the conditions of human observership. Ihere is no reason, then, to make the gravitational constant or the mass of the universe vary. 

There are nine components of (unknown) stresses at any point in a stressed body, and they generally vary from point to point within the body. These stresses must be in equilibrium with each other and with other body forces (such as gravitational and inertial forces). For elastostatic problems, the body forces are typically assumed to be zero, and are not considered further. For simplicity, therefore, the equilibrium of an element dx, dy, 1) under plane stress (a22 = = xz = = 0) is... 

Is the gravitational constant a constant According to Newton and Einstein, the gravitational permittivity HAtzG is a constant. If one has confidence in the Formal Graph approach, comparison with electrodynamics, where the electric permittivity e may vary depending on the medium, leads to ranoval of this constancy for some media. This is still a subject of research within the framework of a theory that would unify all forces in physics. 

A tall column of a gas mixture in a gravitational field, and a liquid solution in the cell of a spinning centrifuge rotor, are systems with equilibrium states that are nonuniform in pressure and composition. This section derives the ways in which pressure and composition vary spatially within these kinds of systems at equilibrium. 

---