Cepheid variables of the same period are closely similar to one another. A Cepheid of period 5⅓ days found in any part of the universe will be practically a replica of δ Cephei; in particular it will be a star of the same absolute brightness. This is a fact discovered by observation, and is not predicted by any part of the theory yet explored. The brightness, as we have seen, depends mainly on the mass; the period, on the other hand, depends mainly on the density; so that the observed relation between brightness and period involves a relation between mass and density. Presumably this relation signifies that for a given mass there is just one special density--one stage in the course of condensation of the star--at which pulsations are liable to occur; at other densities the star can only burn steadily. This property renders the Cepheid extremely useful to astronomers. It serves as a standard candle--a source of known light-power. In an ordinary way you cannot tell the _real_ brightness of a light merely by looking at it. If it appears dim, that may mean either real faintness or great distance. At night time on the sea you observe many lights whose distance and real brightness you cannot estimate; your judgement of the real brightness may be wrong by a factor of a quintillion if you happen to mistake Arcturus for a ship’s light. But among them you may notice a light which goes through a regular series of changes in a certain number of seconds; that tells you that it is such-and-such a lighthouse, known to project a light of so many thousand candlepower. You may now estimate with certainty how far off it is--provided, of course, that there is no fog intervening. So, too, when we look up at the sky, most of the lights that we see might be at any distance and have any real brightness. Even the most refined measurements of parallax only succeed in locating a few of the nearer lights. But if we see a light winking in the Cepheid manner with a period of 5⅓ days, we know that it is a replica of δ Cephei and is a light of 700 sun-power. Or if the period is any other number of days we can assign the proper sun-power for that period. From this we can judge the distance. The apparent brightness, which is a combination of distance and true brightness, is measured; then it is a simple calculation to answer the question, At what distance must a light of 700 sun-power be placed in order to give the apparent brightness observed? How about interference by fog? Careful discussions have been made, and it appears that notwithstanding the cosmical cloud in interstellar space there is ordinarily no appreciable absorption or scattering of the starlight on its way to us. With the Cepheids serving as standard candles distances in the stellar universe have been surveyed far exceeding those reached by previous methods. If the distances were merely those of the Cepheid variables themselves that would not be so important, but much more information is yielded.