not yet been
sufficiently studied, seems however to be rather inconsiderable, and
must be neglected in the following.

The photographic magnitude of a star will in these lectures be denoted
by _m'_, corresponding to a visual magnitude _m_.

In practical astronomy use is also made of plates which, as the result
of a certain preparation (in colour baths or in other ways), have
acquired a distributive function nearly corresponding to that of the
eye, and especially have a maximum point at the same wave-lengths. Such
magnitudes are called _photo-visual_ (compare the memoir of PARKHURST in
A. J. 36 [1912]).

The photographic magnitude of a star is generally determined from
measurements of the diameter of the star on the plate. A simple
mathematical relation then permits us to determine _m'_. The diameter of
a star image increases with the time of exposure. This increase is due
in part to the diffraction of the telescope, to imperfect achromatism or
spherical aberration of the objective, to irregular grinding of the
glass, and especially to variations in the refraction of the air, which
produce an oscillation of the image around a mean position.

The _zero-point_ of the photographic magnitudes is so determined that
this magnitude coincides with the visual magnitude for such stars as
belong to the spectral type A0 and have _m_ = 6.0, according to the
proposal of the international solar conference at Bonn, 1911.

Determinations of the photographic or photo-visual magnitudes may now be
carried out with great accuracy. The methods for this are many and are
well summarised in the Report of the Council of the R. A. S. of the year
1913. The most effective and far-reaching method seems to be that
proposed by SCHWARZSCHILD, called the half-grating method, by which two
exposures are taken of the same part of the sky, while at one of the
exposures a certain grating is used that reduces the magnitudes by a
constant degree.

9. _Colour of the stars._ The radiation of a star is different for
different wave-lengths ([lambda]). As regarding other mass phenomena we
may therefore mention:--(1) the _total radiation_ or intensity (_I_),
(2) the _mean wave-length_ ([lambda]_0), (3) the _dispersion of the
wave-length_ ([sigma]). In the preceding paragraphs we have treated of
the total radiation of the stars as this is expressed through their
magnitudes. The mean wave-length is pretty closely defined by the
_colour_, whereas the dispersio