The BRIGHTEST stars, were called FIRST magnitude. Stars that appear half as bright were SECOND magnitude, those dimmer still were called THIRD, etc.

The LARGER the number, the DIMMER the star. Objects BRIGHTER than the brightest star (1st magnitude), are expressed as negative values. Each magnitude corresponds to a factor of 2.5 in flux.

There are two kinds of magnitudes:

APPARENT MAGNITUDE, small m, refers to the flux of objects based on what we see on Earth, and will be affected by the distance of the source.

ABSOLUTE MAGNITUDE, capitol M. This is a measure of an intrinsic property of the star or object, and is thus independent of distance. There is a decided 'standard distance' from which all stars can be fairly compared. This distance is 10 parsecs (about 32 light years). By definition then, a stars absolute magnitude is simply its apparent magnitude if placed at a distance of 10 parsecs. Since only a few stars are at this real distance, nearly all stars have an absolute magnitude greater than or less than their apparent magnitude.

Distance Modulus
Defined as the difference between the apparent magnitude, m, and absolute magnitude, M. It tells you something about the distance. For example:

1) You are told a star has an apparent magnitude equal
to its absolute magnitude. How far away is the star?

2) You are told a star has an apparent magnitude greater
than its absolute magnitude. How far away is the star?

3) You are told a star has an apparent magnitude less than
its absolute magnitude. How far away is the star?

Hint: Remember a larger (positive) value for the magnitude means the source is dimmer! This can really mess with your mind!