Meanwhile photometric measures of the stars, according to various methods, had been undertaken. In 1856, Pogson showed that the scale of magnitudes of Ptolemy, which is still in use, could be nearly represented by assuming the unit to be the constant ratio, 2.512, whose logarithm is 0.4. This has been generally adopted as the basis of the standard photometric scale. The photometer devised by Zöllner has been more widely used than any other. In this instrument an artificial star is reduced any desired amount, by polarized light, until it appears to equal the real star, both being seen side by side in the telescope. Work with this instrument has attained its greatest perfection at the Potsdam Observatory, where measures of the light of the northern stars, whose magnitude is 7.5 and brighter, have been in progress since 1886. The resulting magnitudes have been published for 12,046 stars, included in declination between—2° and—60°. The accidental errors are extremely small, but as the results of different catalogues differ systematically from one another, we can not be sure which is right and what is the real accuracy attained in each case. In 1885 the Uranometria Oxoniensis was published. It gives the magnitudes of 2,784 northern stars north of declination—10°. This work is a remarkable one, especially as its author, Professor Pritchard, began his astronomical career at the age of sixty-three. The method he employed was reducing the light of the stars by means of a wedge of shade glass until they became invisible, and then determining the brightness from the position of the wedge. A careful and laborious investigation, extending over many years has been carried on by Mr. H. M. Parkhurst, using a modification of this method.
For several years before the Oxford and Potsdam measures described above were undertaken, photometric observations were in progress at Harvard. In 1877 a large number of comparisons of adjacent stars were made with a polarizing photometer. Two images of each star were formed with a double image prism, and the relative brightness was varied by turning a Nicol prism until the ordinary image of one star appeared equal to the extraordinary image of the other. Several important sources of error were detected, which once known were easily eliminated. A bright star will greatly affect the apparent brightness of an adjacent faint one, the error often exceeding a magnitude. Systematic errors amounting to several tenths of a magnitude depend upon the relative positions of the images compared. They are perhaps due to the varying sensitiveness of the different parts of the retina. This photometer has many important advantages. However bad the images may be, they are always exactly alike, and may, therefore, be compared with accuracy. Both stars are affected equally by passing clouds, so that this photometer may be used whenever the stars are visible and at times when other photometric work is impossible. The diminution in light also follows a simple geometrical law, and is readily computed with great accuracy. There is no unknown constant to be
