A physical interpretation is given of the mathematical theorem that a Riemannian space can be defined by means of the system of local tangent flat spaces. This leads naturally to an elucidation of the status of Rosen's flat space in the general relativity theory. Comparison flat spaces can be chosen arbitrarily, and if taken as giving the metric of space time lead to different arbitrary values of ether drift. In particular, the flat-space tangent to the Riemannian space along the history of the observer (at the origin) is locally equivalent with the Riemannian space, and no ether drift would be involved in using it in place of the Riemannian space as a method of extrapolating measurements to great distances. It is further shown that the formal simplifications achieved by introducing the comparison metric do not depend on its flatness. A de Sitter type of isotropic empty space is introduced by means of which the distribution and laws of motion of matter can be expressed in terms of the differences between actual space containing matter and the empty comparison space. Comparison spaces in general are essentially ideal, and can be introduced to bring out the non-ideal characteristics of actual space.

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