The North Star, so closely associated in our minds with the pole, would be of no use to the explorer, for it is about a degree and a quarter from the pole, and, like the other stars, it would circle around the observer, and at times even be directly south of him. To determine its direction the explorer would have to know his own latitude and local time; moreover, it would be invisible if the sun were above the horizon.
By means of his chronometer, keeping Greenwich mean time, the explorer could determine the direction of any meridian, for the sun would be on the meridian of Greenwich at Greenwich noon, and would move 15 degrees in longitude for every hour thereafter; this knowledge would be very valuable to enable him to lay out his return course from the pole to his base of supplies, but it would not, in ignorance of his meridian, help him to find the pole; for the direction of the pole in relation to the direction of the sun, or of the compass needle, does not depend upon the general direction of the meridians, but upon the particular meridian on which he happens to be.
We have thus the apparent anomaly that the same observations would enable a person to set a satisfactory course away from the pole, but not toward it. But the anomaly is only apparent; for, suppose the base of supplies were on the 70th meridian and in latitude 83°; and suppose the explorer were near the pole and twenty miles from the 70th meridian, on one side or the other; he could lay a course parallel with the 70th meridian and this direction would only differ by about a third of a degree from the most direct line to his base of supplies; but if he kept this course accurately, he would miss his base by twenty miles. This, however, would be less important than missing the pole by the same distance.
The very simple method of determining latitude by the altitude of the sun when on the meridian would not be available to the explorer, for his meridian would not be known; and it would require a set of observations extending over several hours to learn when the sun was on his meridian. On the sixth of April the sun would circle around the horizon, at an average altitude of about 614 degrees, and would only be two degrees higher at midday than at midnight, as seen by an explorer one degree from the north pole, provided its declination were constant; this, however, is not so; but on the date mentioned we should find, superposed on the variation in altitude due to the rotation of the earth, a steady increase in altitude amounting to a little more than a third of a degree in a day. On April 21 the sun's altitude would be about ll34 degrees above the horizon, and the variations in altitude during the day would be almost the same as on the earlier date.
To determine his position, and the direction of the pole, the ex-
