ALTITUDE AND AZIMUTH OF POLARIS.—It is a matter of common knowledge that the Pole star is about a degree and a quarter from the true pole, so that azimuths and latitudes cannot be directly determined by observations of this star. The usual mode of procedure is to employ tables reducing the observations to the true pole; a graphical method of performing this rather tedious reduction, with an accuracy sufficient for most purposes, has been devised by A. Tanakadate, of Tokio (Sũgakub.-Kizi.) It is shown that the usual formula for the calculation of azimuth corresponds very nearly with the equation of a circle of radius p sec Φ (p being the polar distance of Polaris, and Φ the latitude of the place of observation), and the centre of which is displaced above the origin by an amount equal to . An origin being chosen near the middle of a sheet of squared paper, degrees and minutes are marked off along the axes in both directions, and a circle is drawn on the same scale with radius and displacement of centre adapted to the latitude as defined above. Radiating straight lines drawn from the origin correspond to different hour angles, the line t = o being that along which the centre of the circle is displaced. The abscissa of the point where the line corresponding to the hour angle at which an observation is made cuts the circle, gives directly the azimuth of Polaris, the star being east or west of the true north according as the point lies to the right or left of the origin in the diagram. Neglecting errors of construction, the readings will only differ by a few seconds from the calculated results, and it is shown that even these errors can be reduced by slightly enlarging the radius of the circle.