1. Introduction.—One of the most important of Milne's discoveries is undoubtedly the significance of time-scale regraduations and, in particular, the relation between atomic t-time and gravitational τ-time. Although in Milne's work t-time is more fundamental than τ-time, this relationship is not inevitable, as was shown in an axiomatic development of cosmology given recently by the author. There the τ-scale was the more fundamental, and it was not found necessary to introduce Milne's t-scale. The object of the present paper is to discuss this primitive τ-scale still further, and to show how the t-scale may be introduced by means of an axiom. The unpublished work mentioned above is not required for this purpose because the cosmological models considered here were described in earlier papers (Walker, 1937, 1940 b). We also examine the various constants, absolute and conventional, which are connected with the different scales of time and length, and with different models.