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. MÜLLER. The apparent magnitude of the sun is given by ZÖLLNER (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 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 ZÖLLNER in a more or less improved form.