50), but considering that the Pole-star ([alpha] Ursæ 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 ), 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 2½. When exact photometry began (with instruments for measuring the magnitudes) in t