For determining the position in drifting pack-ice, the theodolite proved to be a more generally useful instrument than the sextant.  The ice-floes are quite steady in really thick pack-ice, and the theodolite can be set up and levelled as well as on dry land.  The observations, both for latitude and longitude, consist in measuring altitude of the sun or of a star.  The chief uncertainty in this measurement is that introduced by the refraction of light by the air.  At very low temperatures, the correction to be applied on this account is uncertain, and, if possible, observations should always be made in pairs with a north star and a south star for a latitude, and an east star and a west star for a longitude.  The refraction error will then usually mean out.  This error affects observations both with the theodolite and the sextant, but in the case of the sextant another cause of error occurs.  In using the sextant, the angle between the heavenly body and the visible horizon is measured directly.  Even in dense pack-ice, if the observations are taken from the deck of the ship or from a hummock or a low berg, the apparent horizon is usually sharp enough for the purpose.  In very cold weather, however, and particularly if there are open leads and pools between the observer and the horizon, there is frequently a great deal of mirage, and the visible horizon may be miraged up several minutes.  This will reduce the altitude observed, and corrections on this account are practically impossible to apply.  This error may be counterbalanced to some extent by pairing observations as described above, but it by no means follows that the mirage effect will be the same in the two directions.  Then again, during the summer months, no stars will be visible, and observations for latitude will have to depend on a single noon sight of the sun.  If the sun is visible at midnight its altitude will be too low for accurate observations, and in any case atmospheric conditions will be quite different from those prevailing at noon.  In the Antarctic, therefore, conditions are peculiarly difficult for getting really accurate observations, and it is necessary to reduce the probability of error in a single observation as much as possible.  When possible, observations of the altitude of a star or of the sun should be taken with the theodolite, since the altitude is referred to the spirit-level of the instrument, and is independent of any apparent horizon.  During the drift of the ‘Endurance’ both means of observation were generally employed.  A comparison of the results showed an agreement between sextant and theodolite, within the errors of the instrument if the temperature was above about 20° Fahr.  At lower temperatures there were frequently discrepancies which could generally be attributed to the mirage effects described above.