large instruments of our time hardly reach much farther,
for visual observations. When, however, photographic plates are used, it
is easily possible to get impressions of 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 ZOeLLNER 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 ZOeLLNER'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