402 APPENDIX IV 



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 displace- 

 ments 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 culmina- 

 tion 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 He 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 determina- 

 tion 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 abed 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 



