B A Position (3), stars at apocenter * * Interval, 20 hours. Position (4), B eclipses * Interval, 16 hours. Position (1) is repeated * * _U_ Pegasi is a star which proved as perplexing as Tau Cygni. It was first supposed to be of the Algol type, with a period of about two days. Then it was found that a number of minima occurred during this period, and that the actual interval between them was only a few hours. The great difficulty in the case arises from the minuteness of the variation, which is but little more than half a magnitude between the extremes. The observations of Wendell, at the Harvard Observatory, with the polarizing photometer, enabled Pickering to reach a conclusion which, though it may still be open to some doubt, seems to be the most likely yet attainable. The star is of the Beta Lyræ type; its complete period is 8 hours 59 minutes 41 seconds, or 19 seconds less than nine hours; during this period it passes through two equal maxima, each of magnitude 9.3, and two unequal minima 9.76 and 9.9, alternately. [Illustration: FIG. 3. LIGHT CURVE OF U PEGASI, OF THE BETA LYRÆ TYPE, FROM OBSERVATIONS BY WENDELL AT THE HARVARD OBSERVATORY. MAGNITUDE AT MAXIMUM, 9.32; AT PRINCIPAL MINIMUM, 9.90; AT SECONDARY MINIMUM, 9.76. PERIOD, 9 HOURS.] The difference of these minima, 0m. 14, is less than the errors which really ordinarily affect measures of a star’s magnitude with the best photometers. Some skepticism has, therefore, been felt as to the reality of the difference which, if it does not exist, would reduce the periodic time below four and one-half hours, the shortest yet known. But Pickering maintains that, in observations of this kind upon a single star, the precision is such that the reality of the difference, small though it be, is beyond reasonable doubt. Taking Pickering’s law of change as a basis, Myers has represented the light-curve of _U_ Pegasi on a theory similar to that which he constructed for Beta Lyræ. His conclusion is that, in the present case, the two bodies which form the visible star are in actual contact. A remarkable historic feature of the case is that Poincaré has recently investigated, by purely mathematical methods, the possible forms of revolving fluid masses in a condition of equilibrium, bringing out a number of such forms previously unknown. One of these, which he calls the apiodal form, consists of two bodies joined into one, and it is this which Myers finds for _U_ Pegasi.