Professor Hertzsprung of Leiden and Dr Shapley, then of Mount Wilson Observatory, were quick to seize upon the implications of this discovery. If two Cepheids _A_, _B_ in different parts of the sky are found to fluctuate with equal rapidities, then their intrinsic candle-powers must be equal. Thus any difference in their apparent brightness must be traceable to a difference in their distances from us. If _A_ looks a hundred times as bright as _B_, then _B_ must be at ten times the distance of _A_. In the same way, a third Cepheid _C_ may prove to be at ten times the distance of _B_. We now know that _C_ is a hundred times as remote as _A_. And if _D_ can be found ten times as distant as _C_, we know that _D_ is a thousand times as remote as _A_. So we can go on constructing and ever extending our measuring-rod; there is no limit until we reach distances so great that even Cepheid variables, which are exceptionally bright stars, fade into invisibility. So far we have only considered the comparative distances of Cepheids. The absolute distances of many of the nearer Cepheids have, however, been determined by the parallactic method already explained—i.e. by measuring their apparent motion in the sky, resulting from the earth’s motion round the sun. Taking any one of these stars as our original Cepheid _A_, we can step continually from one Cepheid to another, and so calculate the absolute distances of all the Cepheid variables in the sky. In this way the observed relation between the period of fluctuation and the brightness of Cepheid variables—commonly known as the “period-luminosity law”—can be made to provide a scale on which the absolute luminosity, or candle-power, of a Cepheid can be read off directly from the observed period of its light-fluctuations. The Cepheid variables may be regarded as lighthouses set up in distant parts of the universe. We can recognise them, just as a sailor recognises lighthouses, by the quality of their light. We can read off their candle-power from the period of their observed light-fluctuations as easily as the sailor could read off the candle-power of a lighthouse from an Admiralty chart. The apparent brightness of the Cepheid informs us as to its distance from us[7].