Navigation
It will perhaps interest those readers who have a knowledge of navigation to hear a little more about Sverdrup of the “Maud’s” cleverly calculated but simple methods of navigation in the Arctic Sea. I repeat word by word Sverdrup’s own well-known description:
“One single measuring of the sun’s altitude shows that one stands on one particular spot, in a small circle whose center is the point, where at that moment the sun has reached its zenith, the radius of which is 90° h. (h. indicates the measured height of the sun). This circle shall be called a local circle.”
In order to find the meridian the sun would be in at the exact moment of observation one must read a clock, the agreement of which with Greenwich mean time (G.M.T.) is known. An almanac gives the time level to be added to, or subtracted from, G.M.T.—giving Greenwich true time (G.T.T.). The sun would then be over that meridian, the latitudinal difference of which from Greenwich is equal to the time taken for a clock to strike, according to G.T.T., and would be in its zenith over the point, the breadth of which is equal to the sun’s declination.
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.
Hereby we had the line on which we stood, and must wait until the sun had changed its position to complete our calculations. The cutting point between the local lines would give our position.
According to G.T.T. 5 h 47′ we took an observation in the morning which gave h—d by -33 nautical miles. These observation lines were constructed on the same chart, and the cutting point gave us our position 87° 47′ N. lat. and 13° W. long.
Some days later we used these data as examples and re-calculated the same observations according to the method of St. Hilaire, and thereby found that our landing point lay on N. lat. 87° 43′ 2″ and W. long. 10° 19′ 5″.
After our return our observations were again re-calculated according to absolutely exact astronomical formula by Cand. mag. R. Wesöe, under the guidance of Professor Schroeter. According to their calculations the most northerly point turned out to be N. lat. 87° 43′ and W. long. 10° 37′, the very spot where we had our first camp. During reconnoitering we went further north, but without taking observations. In addition to this Cand. mag. Wesöe calculated the positions as follows. I herewith give four:
| 1925. | 22/5 | N. lat. | 87° 43′ | Long. W. | 10° 37′ |
| 28/5 | „ | 87° 32′ | „ „ | 10° 54′ 6 | |
| 29/5 | „ | 87° 31′ 8 | „ „ | 8° 3′ 9 | |
| 12/6 | „ | 87° 33′ 3 | „ „ | 8° 32′ 6 |
These positions give an idea of the drift of the ice easterly and southerly.