Lectures on Stellar Statistics | Page 5

fainter stars, even with rather
modest instruments. The large 100-inch mirror of the Wilson
Observatory renders possible the photographic observations of stars of
the 20th apparent magnitude, and even fainter.
The observations of visual magnitudes are performed almost
exclusively with the photometer of ZÖLLNER in a more or less
improved form.
7. Absolute magnitude. The apparent magnitude of a star is changed as
the star changes its distance from the observer, the intensity increasing
indirectly as the square of the distance of the star. In order to make the
magnitudes of the stars comparable with each other it is convenient to
reduce them to their value at a certain unit of distance. As such we
choose one siriometer. The corresponding magnitude will be called the
absolute magnitude and is denoted by M.[4] We easily find from the
table given in the preceding paragraph that the absolute magnitude of
the sun, according to ZÖLLNER's value of m, amounts to +3.4, of the
moon to +31.2. For Jupiter we find M = +24.6, for Venus M = +25.3.
The other planets have approximately M = +30.
For the absolute magnitudes of those stars for which it has hitherto
been possible to carry out a determination, we find a value of M
between -8 and +13. We shall give in the third chapter short tables of
the absolutely brightest and faintest stars now known.

8. Photographic magnitudes. The magnitudes which have been
mentioned in the preceding paragraphs all refer to observations taken
with the eye, and are called visual magnitudes. The total intensity of a
star is, however, essentially dependent on the instrument used in
measuring the intensity. Besides the eye, the astronomers use a
photographic plate, bolometer, a photo-electric cell, and other
instruments. The difference in the results obtained with these
instruments is due to the circumstance that different parts of the
radiation are taken into account.
The usual photographic plates, which have their principal sensibility in
the violet parts of the spectrum, give us the photographic magnitudes
of the stars. It is, however, to be remarked that these magnitudes may
vary from one plate to another, according to the distributive function of
the plate (compare L. M. 67). This variation, which has 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
dispersion of the wave-length is found from the spectrum of the stars.
There are blue (B), white (W), yellow (Y) and red (R) stars, and
intermediate colours. The exact method is to define