REFRACTION AND THE APPARENT DIURNAL MOVEMENTS OF STARS.—The question of the apparent change of positions of stars due to refraction as the hour angle varies, becomes of importance when long intervals of time are taken into account. In photographing the stars, it is generally usual to “stand by” and make all the necessary small adjustments, due to atmospheric refraction, with the hand. A method has, however, been recently suggested and worked out by Dr. A. A. Rambaut, by which the rate of the driving clock may be so adjusted as to take into account these minor discrepancies when a high state of accuracy is desired for stars, at large hour angles (Monthly Notices, vol. lvii. No. 2). This method does not, of course, take into consideration local or temporary changes in the refraction, but the perfectly regular and systematic change as the star increases or decreases its altitude. For a telescope to follow a star with absolute precision, a clockwork must be constructed which would drive the instrument at an ever-varying rate according to the formula given by Dr. Rambaut. This, however, cannot be practically achieved, and would, further, be unnecessary, as a close approximation is all that is needed in practice. By a system of curves obtained from the above-mentioned formula, and treated graphically, it has been found that a uniform rate, if suitably chosen, will not in ten minutes introduce an error amounting to one-twentieth of a second, which is within the limits of the accidental errors of a good equatorial clock. By prolonging the exposure beyond the period for which a uniform rate is admissible, the rate must be altered to one now more suitable. A series of weights, skilfully employed in controlling the action of a pendulum in connection with the driving clock, will allow the different rates to be easily produced. Dr. Rambaut describes a graphical method for obtaining the length of exposure during which a uniform rate may be used. This he finds most convenient in practice for short exposures, and he relates that he can turn his telescope, with the greatest confidence, from a star at its upper culmination, to follow which a star must lose at the rate of from 18 to 100 seconds or more a day, and one at its lower culmination, gaining at the rate of 70 or 80 seconds a day, and he finds “the telescope will follow both with equal accuracy.” It may be remarked that this method is practically intended to be utilised when photographs for the detection of stellar parallax are in question, as it is only then that they must be obtained when the stars have a considerable hour angle.