The South Pole; an account of the Norwegian antarctic expedition in the "Fram," 1910-1912 — Volume 2

CHAPTER IV

The As­tro­nom­ical Ob­ser­va­tions at the Pole

Note by Pro­fes­sor H. Geel­muy­den

Chris­tia­nia,

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,

Chris­tia­nia.

Mr. Alexan­der’s Re­port.

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.

Chris­tia­nia,

Septem­ber 22, 1912.