On the estimation of distances in a curved universe with a non-static line element

Introduction. - In two previous articles,(1,2) I have shown that there is a possibility of relating the annihilation of matter in the universe to the observed red shift in the light from the extra-galactic nebulae, by ascribing to the universe a line element of the general form ds^2 = - e^g(t)/[1 + r2/4R^2]^2 * (dx^2 + dy^2 + dz^2) + dt^2, where r is an abbreviation for √(x^2+y^2+z^2) and R is a constant.