of the circle he was; but he could not determine his position accurately. If, some time after his first measure of the sun's altitude, he should make a second similar measure, he would determine his position on a second circle; and the intersection of those two circles would determine his position completely. The determination, of course, would be more accurate if the circles cut each. other at a high angle, and this could be insured by making the second set of observations on the sun after it had changed its direction (measured on the horizontal plane) by about 90°. Instead of making two sets of observations on the sun, we might, in the evening, observe two stars properly located with respect to each other, and we could then find two circles of position in a few minutes and completely determine our position.
If the sun is due north or south the part of the circle on which the observer is will coincide with his parallel of latitude, which is thus immediately determined; if the sun is due east or west, a part of the circle will correspond with the meridian and the longitude will be found. The old method of determining position at sea, and one still in use, was to observe the sun at noon for latitude, and to accept as local noon the poorly determined time when the sun reached its highest altitude; or to observe also in the morning or evening for time or longitude, guessing at the latitude to work out the observations. But the new method makes it possible to observe altitudes at any time and to get satisfactory results even if the sun were hidden for several hours during the middle of the day. And besides it makes clear just what information regarding our position is yielded by a single observation of the sun's altitude. This beautiful method was first used by Captain Thomas H. Sumner, of Boston, Mass., in 1837; the short parts of the circle which are drawn on the map in finding one's position are called Sumner's lines.
If an explorer were approaching the north pole, and had arrived, let us say within a degree of it, it would be necessary for him to determine his latitude in order to know his distance from the pole, and to determine the direction of the pole in order to know his course. It might be supposed that when approaching the pole he would, by means of his compass, be able to follow his meridian; but the difficulty of keeping a fixed direction when traveling over rough ice, and especially the shifting of his position by the unknown drift of the ice, would soon make a decided change in his longitude in a region where the meridians converge so rapidly.
In the neighborhood of the north pole the compass needle points approximately in the direction of the meridian 155° west of Greenwich, according to Neumayer, but the angle between the needle and the meridian changes considerably for comparatively small variations of position; especially as the distance from the pole becomes smaller.
