In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelismgeometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the context of Riemannian geometry. The importance of such theorems lies in their applications to derive a general formula for the redshift of spectral lines coming from distant objects. The formula derived in the present work can be applied to both cosmological and astrophysical redshifts. It takes into account the shifts resulting from gravitation, different motions of the source of photons, spin of the moving particle (photons) and the direction of the line of sight. It is shown that this formula cannot be derived in the context of Riemannian geometry, but it can be reduced to a formula given by KMW under certain conditions.

A relation between temperature and time has been constructed in the self-consistent model(SCM). This relation is used to calculate the a CMBR temperature. This temperature has been found to be 2.9K. The temperature gradient of microwave background radiation(CMBR) is calculated in the Self Consistent Model. Two relations between Hubble parameter and time derivative of the temperature, have been presented in two different cases. In the first case the temperature is treated as a function of time only, while in the other one, it is assumed to be a function in time and solid angle, beside the assumption that the universe expands adiabatically.