Color Excesses for Supergiants and Classical Cepheids. V. The Period-Color and Period-Luminosity Relations: a Revision.

The results of Paper III are revised in accordance with the most recent photometric data for field cepheids and for the cepheids in galactic clusters It is shown that not all previous photometry of cepheids is equally precise A period-mean color relation, based on the methods of earlier papers in this series, and the colors of 31 cepheids given primarily by Bahner et at. (1961), Weaver et at. (1961), and Irwin (1961), is derived; it can be represented by the expression ((B - V)) = -0.101 (log P)2 + 0.5375 (log P) + 0.2644. New absolute magnitudes for the galactic-cluster cepheids are derived on the basis of Johnson's (t960b) revision of the method of photometric cluster parallaxes. With assumed slopes of -254 and -2.25 for the visual and blue period-mean luminosity relations, zero points of - 1.67 and - 1.33, respectively, are derived. The explicit dependence of Q (the pulsational constant) on P is obtained, subject to the assumption that the form of the evolutionary tracks and the equation giving the effective temperature scale remain invariant with P. Machinery is described whereby distances of considerable precision may be computed for classical cepheids.