observers made different estimates, some calling a star of the second magnitude which others would call of the first, while others would designate a star of the third magnitude which others would call of the second. It is therefore impossible to state with absolute numerical precision what number of stars should be regarded of one magnitude and what of another.
An idea of the magnitude of a star can be readily gained by the casual observer. Looking at the heavens on almost any cloudless evening, we may assume that the two, three or more brightest stars which we see are of the first magnitude. As examples of those of the second magnitude, may be taken the five brightest stars of the Dipper, the Pole Star and the brighter stars of Cassiopeia. Some or all of these objects can be seen on any clear night of the year in our latitude. Stars of the third magnitude are so numerous that it is difficult to select any one for comparison. The brightest star of the Pleiades is really of this magnitude, but it does not appear so in consequence of the five other stars by which it is surrounded. At a distance of 15° from the Pole Star, Beta Ursa Minoris is always visible, and may be distinguished by being slightly redder than the Pole Star: it lies between two fainter stars, the brighter of which is of the third and the other of the fourth magnitude. The five readily visible but fainter stars of the Pleiades are about of the fourth magnitude. Of the fifth magnitude are the faintest stars which are easily visible to the naked eye, while the sixth comprises those which are barely visible with good eyes.
Modern astronomers, while adhering to the general system which has come down to them from ancient times, have sought to give it greater definiteness. Careful study showed that the actual amount of light corresponding to the different magnitudes varied nearly in geometrical progression from one magnitude to another, a conclusion which accords with the well-known psychological law that the intensity of sensation varies by equal amounts when the exciting cause varies in geometrical progression. It was found that an average star of the fifth magnitude gave between two and three times as much light as an average one of the sixth; one of the fourth gave between two and three times as much light as one of the fifth; and so on to the second. In the case of the first magnitude, the diversity is so great that it is scarcely possible to fix an average ratio. Sirius, for example, is really six times as bright as Altair, which is commonly taken as a standard for a first magnitude star. To give precision to their estimates, modern astronomers are gradually seeking to lay the subject of magnitudes on an exact basis by defining a change of one unit in the magnitude as corresponding to an increase of about two and one half times in the amount of light.