this is about 22 minutes, or about 25 English miles, from the pole, and nearly on the 90th meridian. He now knows his position, and by the Greenwich time and the position of the sun he knows the direction of the 90th meridian, and therefore of the pole.
He then travels in the direction of the pole, keeping this direction by means of his compass or by the sun and his chronometer. Knowing about how fast he travels, he knows when he is in the immediate neighborhood of the pole, and he checks his position again by another pair of observations similar to the last.
Suppose, however, the drift of the ice has been quite strong; it may have carried him several miles from the line AA′ during the six hours between his observations; at the time of the second observation he would, indeed, be on the line BB′, but he would no longer be on the line AA′. If he should wait another six hours and observe the sun when on the 210th meridian, he would then find himself, let us say, on the line CC′; and, assuming a uniform drift of the ice, his position at the time of the second observation would have been on the line BB′ half way between the lines AA′ and CC′—that is, at B″; but he has drifted away from the line BB' during the six hours since he determined his position on that line, and he does not know exactly where he is on the line CC′. If he waits six hours longer, and observes the sun when on the 300th meridian, and then finds himself on the line DD', his true position at that time will be at D, and the drift of the ice during the twelve hours between his second and fourth observations will have been in the direction B″D, and it will have drifted a distance equal to the length of the line B″D on the scale of the figure.
An explorer may find his position by pure calculation, and may not use the graphic method described, but the principle in the two methods is exactly the same, and the graphic method shows more clearly what the observations mean.
An important source of error enters all these observations, namely, atmospheric refraction, or the bending down of the light rays as they pass through the atmosphere. The amount of this bending increases rapidly as the sun is nearer the horizon; it also varies with the barometric pressure, and with the temperature. On April 21, 1908, the sun was only about 113 degrees, and on April 6, 1909, only about 61 degrees above the horizon at the north pole; on both dates the refraction was considerable, and it is hardly well enough known to prevent errors of several minutes of arc in the determinations of position. If, however, the observer should wait for twenty-four hours after his first observation and should measure a fifth altitude of the sun, he could find a fair correction for the refraction and greatly improve the determination of his position.
It would be unreasonable to expect an explorer, making a dash for