Cosmological Application of Relativity

The following topics are considered: 1. Time as coordinate, introduction of proper time through a metric of space time. 2. Geometrical description of matter, the cosmical constant as a second constant demanded by the logical structure of the theory. 3. Detailed computation of the gravitational equations for a general non-static field of spherical symmetry. 4. Schwarzschild's and de Sitter's solutions free from artificial singularities. 5. Map representation of elliptical space, expanding space, Friedmann's equation, reduction to elliptic functions, numerical results. 6. Geodesics of space time, application to proper velocities and red-shift. Discussion of the time scale, numerical value of the cosmical constant, data on density. 7. Use of statical coordinates, the instability of Einstein's universe when no restriction is imposed on the symmetry of fluctuations, formation of the nebulae from fast-moving clouds of gases. 8. Discussion of the problem of the clusters of nebulae. 9. The cosmic rays as remnants of primitive matter. Explanation of the large amount of hydrogen and helium in the stars.