Lectures on Stellar Statistics | Page 4

the ear, the intervals between the notes are apprehended as equal. The magnitudes play the same r?le in relation to the quantities of light as do the logarithms to the corresponding numbers. If a star is considered to have a brightness intermediate between two other stars it is not the difference but the ratio of the quantities of light that is equal in each case.
The branch of astronomy (or physics) which deals with intensities of radiation is called photometry. In order to determine a certain scale for the magnitudes we must choose, in a certain manner, the zero-point of the scale and the scale-ratio.
Both may be chosen arbitrarily. The zero-point is now almost unanimously chosen by astronomers in accordance with that used by the Harvard Observatory. No rigorous definition of the Harvard zero-point, as far as I can see, has yet been given (compare however H. A. 50[3]), but considering that the Pole-star ([alpha] Urs? Minoris) is used at Harvard as a fundamental star of comparison for the brighter stars, and that, according to the observations at Harvard and those of HERTZSPRUNG (A. N. 4518 [1911]), the light of the Pole-star is very nearly invariable, we may say that the zero-point of the photometric scale is chosen in such a manner that for the Pole-star m = 2.12. If the magnitudes are given in another scale than the Harvard-scale (H. S.), it is necessary to apply the zero-point correction. This amounts, for the Potsdam catalogue, to -0m.16.
It is further necessary to determine the scale-ratio. Our magnitudes for the stars emanate from PTOLEMY. It was found that the scale-ratio--giving the ratio of the light-intensities of two consecutive classes of magnitudes--according to the older values of the magnitudes, was approximately equal to 2?. When exact photometry began (with instruments for measuring the magnitudes) in the 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. MüLLER.
The apparent magnitude of the sun is given by Z?LLNER (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 Z?LLNER in a more or less improved form.
7. Absolute magnitude. The apparent magnitude of a star is changed as the star changes its distance