Distant Stars 
11 
9-11] 
known as “Cepheid variables” after their prototype 8 Cephei. The majority 
of the stars in the sky shine with a perfectly steady light, but a fair number, 
known as variable stars, shew fluctuations in brightness. These fluctuations 
are regular in some stars and irregular in others. Cepheid variables shew 
perfectly regular fluctuations, flashing out to some two or three times their 
original brightness at intervals which range from a few hours to several days 
for different stars, but are always absolutely uniform for the same star. These 
variables are very common in the mysterious objects known as “globular star- 
clusters,” closely packed groups of stars of approximately globular shape, and 
also occur in considerable numbers in star clouds such as the greater and 
lesser Magellanic cloud. Since the various Cepheid variables in any single 
one of these objects are at approximately the same distance from us, differences 
in their apparent brightness represent real differences in their output of 
radiation; no complication arises from the stars being at different distances. 
In 1912, Miss Leavitt of Harvard, studying the Cepheid variables in the 
lesser Magellanic cloud, discovered a relation between their time of fluctua 
tion and their brightness. Those which fluctuated most slowly were the 
brightest, the period being connected with the brightness by a definite law, 
so that when the brightness of a Cepheid variable had been observed, its period 
of fluctuation could be predicted with accuracy, and vice versa. Dr Shapley, 
now Director of Harvard Observatory, subsequently proved that this relation 
was true of Cepheid variables in general. Now a few Cepheids, although 
only a few, are so near that their distances can be measured by the direct 
parallactic method, and as the actual output of radiation of these stars is 
known, it is possible to deduce the output of radiation of any Cepheid variable 
in the sky whose period of fluctuation is known. For instance, all Cepheids 
which fluctuate in brightness every 40 hours, emit approximately 250 times 
as much radiation as the sun, or, to use the technical phrase, their “luminosity” 
is 250; Cepheids whose period is 10 days have a luminosity of 1600, while 
those whose period is 30 days have a luminosity of 10,000. The general 
relation between period and luminosity is known as the “period-luminosity” 
law; it tells us the luminosity of every Cepheid variable in the sky. 
Just as in the method of spectroscopic parallaxes, we can calculate the 
distance of a star of known luminosity by comparing its apparent brightness 
with that of a second star whose distance and luminosity are known. For 
instance, if a star is known to be as luminous as Sirius, but appears only 
one-hundredth part as bright as Sirius when seen in a telescope, we know 
that it must be ten times as distant as Sirius, because the apparent brightness 
falls off inversely as the square of the distance. By this method the distances 
of all the Cepheid variables can be determined, and so also the distances of 
the various star clusters and other objects in which they lie. Hertzsprung tirst 
used this method in 1913 to determine the distance of the lesser Magellanic 
Cloud.