Nineteen Hours Late

Where did Shackleton's Endurance sink? Her captain, Frank Worsley, wrote it in the log: 68°39′30″ south, 52°26′30″ west. But no sight of the sun is recorded for the three days up to the sinking, and the sun sight behind that position was taken 19 hours after she went down, from a camp on drifting ice a mile and a half away. In March 2022 the wreck was found 3,008 metres down, 10.1 km from the log's X. Here are his own numbers from the log, to be added up again, the three things he could not know, and the predictions people made before the find, scored against where the ship actually lies.

1. The afternoon she went

Endurance was beset in the Weddell Sea in January 1915 and carried by the pack for ten months. On 27 October, crushed by the ice, she was abandoned and the crew moved onto the floe. They made a camp, Ocean Camp, “one and a half miles from the wreck”, and watched her. On 21 November, in the words of a diary quoted in Shackleton's South:

“there was our poor ship a mile and a half away struggling in her death-agony. She went down bows first, her stern raised in the air.”Shackleton, South (1919), chapter V

Shackleton's own diary, as Bergman and Stuart quote it, gives the hour: “at 5pm she went down by the head.” No sight of the sun is recorded in the log for the 19th, the 20th or the 21st (South says the sun came out at 9 p.m. on the 21st, four hours after she sank). His first sight after the sinking was the next morning, and the one he used for latitude was the noon sight of 22 November, 19 hours after she went down. The position he entered for the sinking is underlined once in the log, which is his mark for an estimate. Observed fixes are underlined twice.

Every number below from the log comes from Worsley's workbook, now in the Canterbury Museum in Christchurch, as Lars Bergman and Robin Stuart transcribed it in the appendix of a paper in the Journal of Navigation, published online on 5 September 2018. Their paper is the reason there is anything to check here. It printed the log's numbers in full so that others could “interpret this content differently”, and it made a prediction, three and a half years before anyone saw the wreck.

2. Add up the noon sight

At local noon the sun is due north (from 68° south in November). Measure its height above the horizon, correct it, and the latitude falls out of one subtraction and one addition: ninety degrees minus the sun's altitude is its distance from the point overhead, and adding the sun's declination from the Nautical Almanac gives the latitude. These are the lines Worsley wrote on 22 November 1915.

Bergman and Stuart found this slip, and on the page it is small: “a few of the relevant digits were jotted down before the final result was incorrectly recorded”. The declination is not the problem. Worsley's 19°59′54″, interpolated from the Nautical Almanac, agrees with a modern solar ephemeris to within two seconds of arc at that moment (the check is described at the end). Every other line of the reduction is right. So is almost every other day. Here are the six noon sights in the paper's table, added up again:

Two slips, twenty seconds of arc on the 18th and a full minute on the 22nd: the two days on either side of the sinking. Bergman and Stuart: “In general, arithmetic errors are very rare in the log and it is particularly unfortunate that there are two on the dates that bracket the sinking.”

3. How a latitude slip leaks into longitude

Longitude came from time sights: the sun's height in mid-morning and mid-afternoon, compared with Greenwich time on the chronometer. Working one out needs a latitude, and the navigator uses the best one he has. When the sun is due east or west the answer barely depends on it. On 22 November it was nowhere near: each minute of assumed latitude moves the morning and the afternoon sights by 130″ and 70″ of longitude. Move the assumed latitude and watch the two sights pull apart.

4. Three days without a sight

So the noon fix of 22 November is a good fix, once the sum is added. The trouble is that it is a fix of the camp, 19 hours after the ship went down. To get from it back to the ship, Worsley needed three things he did not have: how the ice had moved in those 19 hours, which way the ship lay from the camp, and how far his chronometer had wandered since it was last checked against the sky. Bergman and Stuart's reading of the log is that he took the noon fix and simply stepped from it “1·2 NM at a bearing of S33°E”. From his logged fix that reproduces the X to within three seconds of arc (seven, from the fix as recomputed here). Now take each unknown in turn.

The drift. The logged noon latitudes show the camp barely moving from 15 to 18 November (a little south, if anything), then heading north fast after the gap. Shackleton's diary for the 21st, as the paper quotes it, has “a SSE fair wind all day”. Bergman and Stuart took the northward drift between the corrected noon latitude of the 22nd and the noon latitude of the 24th, 11.5 nautical miles in 48 hours, and carried it back 19 hours. At 0.24 knots that is 4.55 nautical miles. Their own words for the assumption are careful: “If it is assumed that the wind and northerly drift speed of the ice remained relatively constant from 21 to 24 November”. If it did, the ship went down well south of the fix, further south than the one nautical mile Worsley's step allows. Bergman and Stuart also note that Worsley's own judgement on the spot “may incorporate information not recorded in the log.” “Allowing an additional 1 NM to account for the distance from Ocean Camp gives 68°45′S as a southern limit” for where the wreck could lie. The corrected sum, with Worsley's own step to the ship, gives the northern one. That is their 2018 band, 4.5 nautical miles tall, “but not as far north as Worsley placed it.”

The clock. Longitude is time. One second of error on the chronometer is fifteen seconds of arc of longitude, 169 metres east or west at this latitude. The chronometers were last checked against the sky on 15 September, by timing stars as the Moon covered them, using the Nautical Almanac's predictions. The working chronometer after the ship was abandoned was a Smith pocket chronometer, which took over from the Mercer that had been rated against the Moon, so its error was carried across by comparison. In 2018 Bergman and Stuart judged the longitude “not known to an accuracy of better than about 16′ or 6 NM” and, because Worsley appeared to underestimate how slow his watch was running, leaned west, with a hedge: the tendency “would favour a search area to the west which might be reduced by a westward component of the ice drift between the sinking and the first celestial sights.” Then, in February 2022, with the search ship already on its way, they released a preprint with David Mearns that re-reduced those 1915 occultations using modern lunar ephemerides and star catalogues. As the BBC reported it on 13 February 2022, the clocks were “running 22 seconds faster than they were accounting for”, which “would have put the Endurance more than 3km east of Worsley's log coordinates.” The published paper gives the difference as “an average of 20 s”. We could read only its abstract, and the BBC's account of the preprint; the clock dial here uses the BBC's figure of 22 seconds.

The bearing. Nobody wrote down which way the ship lay from Ocean Camp. South has the party's first march from the wreck going a mile “in a north-north-westerly direction”, and a second toward the north-west, before they gave up and moved to Ocean Camp, “about one and a half miles from the wreck”, in no stated direction. That hints the ship lay somewhere to the south or south-east of the camp, and no more than hints. (Worsley's S33°E, on the paper's reading, is a step from the noon fix, not a recorded bearing.) The ring on the chart is what that silence costs: at a mile and a half it is 2.6 nautical miles across, and no sight can shrink it.

5. The predictions, scored

On 9 March 2022 the Falklands Maritime Heritage Trust announced that Endurance22 had found the wreck at a depth of 3,008 metres, “within the search area defined by the expedition team before its departure from Cape Town”. The wreck is Antarctic Historic Site and Monument 93, whose listing was updated in 2022 with the position 68°44′21″ S, 52°19′47″ W. Here is everything above, set against that:

The latitude band held: the wreck is inside it, near the southern edge that the carried-back drift set, and the wreck is indeed south of the X, by 4.9 nautical miles. The 2018 lean in longitude was the wrong way, though it came hedged with the drift, which could have pulled it back. The February 2022 clock correction turned it round before the ship was found, and accounts for about four fifths of the 4.5 km the wreck lies east of the X.

The last row is ours, and it needs a warning. Stacking the three published corrections (the sum, the drift, the clock) lands 2.1 km from the wreck. But the choices inside it (1 NM due south to the ship, the drift due north, the full 22 seconds) are ours, made after we knew the answer, and a different defensible choice for the unrecorded bearing alone moves the point anywhere on the ring. The preprint may contain its own best point; we have not seen it. What the stack shows is narrower: each correction was argued from the log before the find, and each moved the estimate toward where the ship turned out to be.

Worsley's X was 10.1 km off, and that is not a failure of navigation. It is a fix of a drifting camp, taken 19 hours late, with an unrecorded bearing to the ship and a clock last checked two months earlier. Every noon sum we can check adds up but two, and his two printed longitudes agree with a fresh reduction to within eight seconds of arc.

6. What the retellings say

“Four miles south.” The Trust's press release put the wreck “approximately four miles south of the position originally recorded by Captain Worsley”, and it was reported that way around the world. From the two published coordinates the wreck is 4.9 nautical miles (5.6 statute miles, 9.0 km) south of the X and 4.5 km east, 10.1 km in a straight line. We could not find what the four miles was measured from. Wikipedia's article on the ship already sets out similar arithmetic (9.1 km south and 4.4 km east, by its figures).

The drift line. Under the sinking position the log sums up the whole drift, as Bergman and Stuart transcribe it: “Endurance sank after drifting in 306 days N38°E 605 miles”. 306 days before 21 November is 19 January 1915, when South puts the beset ship at 76°34′ S, 31°30′ W. (South's scientific appendix gives the same day's position as 76°34′ S, 37°30′ W, which would make the line 543 miles on N29°W; the narrative's 31°30′ is the one that matches the log; which of the two is right we cannot say.) From there to the X is a rhumb line of 601 nautical miles on a course of N38°W. The angle and the distance agree with the log. The direction cannot be east: the ship went from 31° west to 52° west. Whether the E is Worsley's pen or the transcription we cannot tell without the page.

Where she was lost. South gives one position for the day the ship was abandoned: “Wednesday, October 27. The position was lat. 69° 5´ S., long. 51° 30´ W.” That is where the crew left her, not where she sank. The log's two positions, abandonment and the X, are 32.8 nautical miles apart: the wrecked hull rode the ice for 25 more days.