Methodology:

The key data sources underlying this study are daily journals and logbooks from the voyages of Cook and Bellingshausen. For Cook's expedition (1772-1775) those used include the post-voyage journals of Cook (Cook, 1775) and Johann Reinhold Forster (1981), both of whom were on board the Resolution, and the logbook of Tobias Furneaux (1774), captain of the Adventure. From Forster (1981), it is Volumes II-IV that are relevant to the Southern Ocean part of the expedition. For Bellingshausen's voyage (1819-1821) they include a translation of the journal of Bellingshausen (Bellingshausen, 2016), where Volume II contains the Southern Ocean component. Note that the separate voyage of the Mirny in the Indian Ocean sector is included within this journal.

All journals and logs were read and where sea ice or icebergs were mentioned a set of data were recorded in a spreadsheet. These entries also include days at high latitude before and after the last ice encounters. The positional data recorded were the day, month and year of the record, the latitude and (where recorded) the longitude at noon on the day. Very occasionally, the position was given at a different time of the day, presumably through lunar rather than solar observations, but for the purposes of this study this time difference was ignored. Very occasionally, either the latitude or longitude was not given and this was linearly interpolated from values found on neighbouring days. Bellingshausen used the Russian "Old Style" calendar, so his observations are 12 days earlier than dates given by the contemporary calendar; in the spreadsheet all his data has therefore been adjusted forward 12 days for consistency.

Cook and Furneaux's voyage took place early in the age of using chronometers to determine longitude (Sobel, 1996). Both captains had a copy of Harrison's K2 chronometer on board their respective ships for time-keeping relative to known meridians. These chronometers gradually lost time so during sections of their voyages with no sight of known land longitude values derived purely from the chronometer accumulated error. Cook and Forster had corrected this on return to Britain, to standardize the daily longitude measurements in their journals. However, Furneaux's log records longitude as given by the time difference between the chronometer and observed noon. The chronometer was re-set at the known positions of Cape Town, before any southern excursions began, and again at Queen Charlotte's Sound in New Zealand, where the Resolution and Adventure rendezvoused. Any difference between real and calculated longitude during the time Furneaux and Cook were separated in the Indian Ocean appeared small when positions were calculated, and so this drift was ignored for this segment. However, over Adventure's final journey in late 1773-early 1774, from New Zealand across the Pacific and Atlantic to reach Cape Town, when the chronometer had aged by almost 2 years and no land was seen for some 3 months, the timepiece had drifted so that the log's recorded longitude was ~ 17° out by the time Adventure reached Cape Town on 3 March 1774. Presumably lunar observations had helped Furneaux identify his real longitude roughly as some 10 days earlier he had changed course from tracking near the 50th parallel of latitude to head essentially due northwards towards Cape Town. The data used here for this part of the Adventure's voyage have therefore had the longitude corrected assuming the chronometer slowed uniformly over the 81 days it took to sail from New Zealand to Cape Town. This only affects iceberg observations, as no sea ice was observed by the Adventure whenever it was separated from the Resolution.

For each day iceberg density as noted in the journals and logs was recorded, with '0' denoting no "islands of ice", '1' if 1 "island of ice" was noted, '2' if a f...(13)