he middle of last
century, the scale-ratio was therefore put equal to 2.5. Later it was
found more convenient to choose it equal to 2.512, the logarithm of
which number has the value 0.4. The magnitudes being themselves
logarithms of a kind, it is evidently more convenient to use a simple
value of the logarithm of the ratio of intensity than to use this ratio
itself. This scale-ratio is often called the POGSON-scale (used by
POGSON in his "Catalogue of 53 known variable stars", Astr. Obs. of the
Radcliffe Observatory, 1856), and is now exclusively used.

It follows from the definition of the scale-ratio that two stars for
which the light intensities are in the ratio 100:1 differ by exactly 5
magnitudes. A star of the 6th magnitude is 100 times fainter than a star
of the first magnitude, a star of the 11th magnitude 10000 times, of the
16th magnitude a million times, and a star of the 21st magnitude 100
million times fainter than a star of the first magnitude. The star
magnitudes are now, with a certain reservation for systematic errors,
determined with an accuracy of 0m.1, and closer. Evidently, however,
there will correspond to an error of 0.1 in the magnitude a considerable
uncertainty in the light ratios, when these differ considerably from
each other.

Sun -26m.60
Full moon -11m.77
Venus - 4m.28
Jupiter - 2m.35
Mars - 1m.79
Mercury - 0m.90
Saturn + 0m.88
Uranus + 5m.86
Neptune + 7m.66

A consequence of the definition of _m_ is that we also have to do with
_negative_ magnitudes (as well as with negative logarithms). Thus, for
example, for _Sirius_ _m_ = -1.58. The magnitudes of the greater
planets, as well as those of the moon and the sun, are also negative, as
will be seen from the adjoining table, where the values are taken from
"Die Photometrie der Gestirne" by G. MUeLLER.

The apparent magnitude of the sun is given by ZOeLLNER (1864). The other
values are all found in Potsdam, and allude generally to the maximum
value of the apparent magnitude of the moon and the planets.

The brightest star is _Sirius_, which has the magnitude _m_ = -1.58. The
magnitude of the faintest visible star evidently depends on the
penetrating power of the instrument used. The telescope of WILLIAM
HERSCHEL, used by him and his son in their star-gauges and other stellar
researches, allowed of the discerning of stars down to the 14th
magnitude. The