etween 3 and 4, and
then again perhaps it may return to between 2 and 3, and so forth. With
practice he learns to evaluate the brightness down to small fractions
of a magnitude, even a hundredth part of a magnitude is not quite
negligible.

For example, in observing the star RR Centauri five stars were in
general used for comparison by Dr Roberts, and in course of three months
he secured thereby 300 complete observations. When the period of the
cycle had been ascertained exactly, these 300 values were reduced to
mean values which appertained to certain mean places in the cycle, and
a mean light-curve was obtained in this way. Figures titled "Light curve
of RR Centauri" (Fig. 5) and "The light-curve and system of Beta Lyrae"
(Fig. 7) show examples of light curves.

I shall now follow out the results of the observation of RR Centauri
not only because it affords the easiest way of explaining these
investigations, but also because it is one of the stars which furnishes
the most striking results in connection with the object of this essay.
(See "Monthly notices R.A.S." Vol. 63, 1903, page 527.) This star has
a mean magnitude of about 7 1/2, and it is therefore invisible to
the naked eye. Its period of variability is 14h 32m 10s.76, the last
refinement of precision being of course only attained in the final
stages of reduction. Twenty-nine mean values of the magnitude were
determined, and they were nearly equally spaced over the whole cycle of
changes. The black dots in Fig. 5 exhibit the mean values determined by
Dr Roberts. The last three dots on the extreme right are merely the same
as the first three on the extreme left, and are repeated to show how
the next cycle would begin. The smooth dotted curve will be explained
hereafter, but, by reference to the scale of magnitudes on the margins
of the figure, it may be used to note that the dots might be brought
into a perfectly smooth curve by shifting some few of the dots by about
a hundredth of a magnitude.

This light-curve presents those characteristics which are due to
successive eclipses, but the exact form of the curve must depend on the
nature of the two mutually eclipsing stars. If we are to interpret the
curve with all possible completeness, it is necessary to make certain
assumptions as to the stars. It is assumed then that the stars are
equally bright all over their disks, and secondly that they are not
surrounded by an extensive absorptive atmosphere. This last