September 16, 1912.
When requested this summer to receive the astronomical observations from Roald Amundsen’s South Pole Expedition, for the purpose of working them out, I at once put myself in communication with Mr. A. Alexander (a mathematical master) to get him to undertake this work, while indicating the manner in which the materials could be best dealt with. As Mr. Alexander had in a very efficient manner participated in the working out of the observations from Nansen’s Fram Expedition, and since then had calculated the astronomical observations from Amundsen’s Gjöa Expedition, and from Captain Isachsen’s expeditions to Spitzbergen, I knew by experience that he was not only a reliable and painstaking calculator, but that he also has so full an insight into the theoretical basis, that he is capable of working without being bound down by instructions.
(Signed) H. Geelmuyden,
Professor of Astronomy,
The Observatory of the University,
Captain Roald Amundsen,
At your request I shall here give briefly the result of my examination of the observations from your South Pole Expedition. My calculations are based on the longitude for Framheim given to me by Lieutenant Prestrud, 163° 37’ W. of Greenwich. He describes this longitude as provisional, but only to such an extent that the final result cannot differ appreciably from it. My own results may also be somewhat modified on a final treatment of the material. But these modifications, again, will only be immaterial, and, in any case, will not affect the result of the investigations given below as to the position of the two Polar stations.
At the first Polar station, on December 15, 1911, eighteen altitudes of the sun were taken in all with each of the expedition’s sextants. The latitude calculated from these altitudes is, on an average of both sextants, very near 89° 54’, with a mean error of +-2’. The longitude calculated from the altitudes is about 7t (105°) E.; but, as might be expected in this high latitude, the aberrations are very considerable. We may, however, assume with great certainty that this station lies between lat. 89° 52’ and 89° 56’ S., and between long. 90° and 120° E.
The variation of the compass at the first Polar station was determined by a series of bearings of the sun. This gives us the absolute direction of the last day’s line of route. The length of this line was measured as five and a half geographical miles. With the help of this we are able to construct for Polheim a field of the same form and extent as that within which the first Polar station must lie.
At Polheim, during a period of twenty-four hours (December 16 — 17), observations were taken every hour with one of the sextants. The observations show an upper culmination altitude of 28° 19.2’, and a resulting lower culmination altitude of 23° 174’. These combining the above two altitudes, an equal error on the same side in each will have no influence on the result. The combination gives a latitude of 89° 58.6’. That this result must be nearly correct is confirmed by the considerable displacement of the periods of culmination which is indicated by the series of observations, and which in the immediate neighbourhood of the Pole is caused by the change in the sun’s declination. On the day of the observations this displacement amounted to thirty minutes in 89° 57’, forty-six minutes in 89° 58’, and over an hour and a half in 89° 59’. The upper culmination occurred so much too late, and the lower culmination so much too early. The interval between these two periods was thus diminished by double the amount of the displacements given. Now the series of observations shows that the interval between the upper and the lower culmination amounted at the most to eleven hours; the displacement of the periods of culmination was thus at least half an hour. It results that Polheim must lie south of 89° 57’, while at the same time we may assume that it cannot lie south of 89° 59’. The moments of culmination could, of course, only be determined very approximately, and in the same way the observations as a whole are unserviceable for the determination of longitude. It may, however, be stated with some certainty that the longitude must be between 30° and 75° E. The latitude, as already mentioned, is between 89° 57’ and 89° 59’, and the probable position of Polheim may be given roughly as lat. 89° 58.5’ S., and long. 60° E.
On the accompanying sketch-chart the letters abcd indicate the field within which the first Polar station must lie; ABCD is the field which is thereby assigned to Polheim; EFGH the field within which Polheim must lie according to the observations taken on the spot itself; P the probable position of Polheim, and L the resulting position of the first Polar station. The position thus assigned to the latter agrees as well as could be expected with the average result of the observations of December 15. According to this, Polheim would be assumed to lie one and a half geographical miles, or barely three kilometres, from the South Pole, and certainly not so much as six kilometres from it.
From your verbal statement I learn that Helmer Hanssen and Bjaaland walked four geographical miles from Polheim in the direction taken to be south on the basis of the observations. On the chart the letters efgh give the field within which the termination of their line of route must lie. It will be seen from this that they passed the South Pole at a distance which, on the one hand, can hardly have been so great as two and a half kilometres, and on the other, hardly so great as two kilometres; that, if the assumed position of Polheim be correct, they passed the actual Pole at a distance of between 400 and 600 metres; and that it is very probable that they passed the actual Pole at a distance of a few hundred metres, perhaps even less.
I am, etc.,
(Signed) Anton Alexander.
September 22, 1912.
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