Taking an observation of the sun’s altitude, with a simultaneous noting of the clock’s striking, can be done most rationally by describing a tangent from a local circle in the neighborhood of the place where one believes oneself to be. Such a tangent should be called a local line. In the neighborhood of the Pole it is easy to find local lines without scientific calculations. The meridian the sun is in can be found directly one has calculated the clock’s stroke by G.T.T. The local circle cuts the meridian in the distance h--d from the Pole, where d signifies the sun’s declination. This cutting-point we will call the local circle’s Pole point. If the difference h--d is positive, this point will be on the same side of the Pole as the sun, should it be negative it will be on the opposite side. A line dropped on the meridian which the sun is in, through the local circle’s Pole point, describes a tangent from the local circle. We will call this tangent the “Pole tangent.” At a distance from the Pole point equal to 5° of latitude, the Pole point will represent the local circle with sufficient exactitude, and can be considered as a local line. But if the distance increases, the tangent’s divergence from the circle will be noticeable. Sverdrup explains how, by an easy method, one can calculate the corrections which have to be made, should one find oneself within the above-mentioned limits from the Pole. During our observations in the ice region we were always within the limit, and had therefore no need for corrections. The method is of course particularly simple and sufficiently exact because there is so little difference between the hour-angle and azimuth. I here give a table of our observations on the night of the 22nd immediately after landing: Clock readings: 3 h 23′ 3″ Error -1 h 0′ 19″ ------------------------------ G.M.T. 2 h 22′ 44″ Time level + 3′ 33″ ------------------------------ G.T.T. 2 h 25′ 17″ Converted into degrees: 36° 3′ Sun’s lower rim from the imaginary horizon measured 35° 58′ 2″ Half of this 17° 59′ Mistakes: 0 Corrections + 13′ ----------- Sun’s center correct altitude 18° 12′ Sun’s declination 20° 15′ 4″ ----------- h--d: - 2° 3′ 4″ Converted into nautical miles 123.4 On a chart we drew a line representing Greenwich meridian, and a point on that was selected as the North Pole. The angle 36° 3′ was set from north to east and the sun’s meridian drawn through the North Pole. From the last named point towards the southwest we marked out 123.4 nautical miles, as the h--d was negative we drew the local line straight up to the sun’s meridian.