In principle, a decision between the simplest cosmological models (exploding cases with A = 0, k = +1,0, - 1, or the steady-state case) is possible from the observed velocity-distance relation. Two numbers are needed. These are H and the deceleration parameter, k0/R,H'. This paper discusses the determination of H. Problems connected with the use of cepheid variables as distance indicators are discussed. Because of a finite width of the instability region for cepheids in the color-magnitude (C-M) diagram, intrinsic scatter in the period-color and period-luminosity (PJ relation is expected. The observed period-color relation at median light for field cepheids in our Galaxy shows that Eggen's type C variables are oscillating in a higher mode than cepheids of Eggen type A, B. The data show Q /Qc 1.9. If the region of instability for cepheids in the C-M diagram has a width of A(B - V) = 0.2 mag, then the P-L relation is expected to have a scatter of 1.2 mag. The intrinsically bluest cepheids should be the brightest. Arp's two-color data for cepheids in the SMC confirm these predictions. The brightest stars are discussed as distance indicators for galaxies beyond the local group. It is probable that knots identified by Hubble as brightest stars in more distant resolved galaxies are really H ii regions. From data in M100, the stars appear to be 1.8 mag. fainter than the knots. This correction, together with a correction of 2.3 mag. to Hubble's moduli for galaxies in the local group, suggests a total correction of about 4.1 mag. to the 1936 scale of distances. This gives H 75 km/sec 106 pc or H-' 13 X l0 years, with a possible uncertainty of a factor of 2. The connection of this value of H with the time scale of exploding cosmologies is briefly discussed.