The familiar books on the disaster generally ignore the problem. Others try to fudge a solution and come up with something which only reveals their authors' lack of navigational knowledge. Eaton and Haas (Titanic: Destination Disaster) invoke a change to the ship's clock, which was never made, and an overestimated speed, which is doubtful. Dr Robert Ballard (The Discovery of the Titanic) says Boxhall assumed Titanic was doing 22½ knots, when her real speed was 20½ knots. This is in spite of Boxhall's repeated evidence that he used 22 knots and other people's estimates of at least 21½. Then he makes the extraordinary statement that celestial navigation was "notoriously inaccurate". So inaccurate, good Doctor, that Titanic, at the time of the collision, was exactly on course for the Ambrose Channel, New York. On a large ship and a flat sea, celestial navigation gave positions with an accuracy of a mile or better. Any errors were in the dead reckoning, for reasons discussed elsewhere.
I have given this matter much thought, as one who loves the art of navigation for its own sake. I immediately dismissed the idea that Boxhall overestimated the ship's speed sufficiently to cause the error. Boxhall stated that he used a speed of 22 knots. By my plotting of the ship's track after passing her last turning point of 42° N, 47°W, this is accurate. It also agrees with evidence from Third officer Pitman that Titanic averaged 22.1 knots during her last complete day's run. Boxhall was working from his 7-30 p.m. position, established by celestial navigation. This position would have given him a very accurate starting point. The observations were taken by Second Officer Lightoller and the calculations were done by Pitman and Boxhall. Lightoller had used six stars and Boxhall described his work as "beautiful". Only 4 hours 16 minutes elapsed between the 7-30 position and 11-46 p.m., which was the time for which Boxhall calculated the position. It was generally agreed that the collision took place at 11-40 p.m., so there is room for an overestimate of 2.2 miles or 3' of longitude. From the propeller revolutions some, including Bruce Ismay, estimated the speed at 21½ knots. If so, and I think it doubtful, it would produce an additional overestimate of 2 miles. For a speed error to account for the total error, Boxhall would have had to overestimate the speed by more than three knots, which he plainly did not do. I sought for another source of error and I think have found the answer in the navigational methods of the time. For convenience, I have used the modern compass directions.
He calculated that in 4 hour 16 minutes the ship had sailed 94 miles on a course of 266° True. He probably used GMT taken from a chronometer for this, as this was more accurate than the ship's clock and needed no correction for westward progress. Looking at his tables for this course and distance he saw that the Departure was 93.8 miles. That is to say, his change in Longitude in miles was 93.8 westwards. While on the page, he noted that his change in Latitude (D Lat) was 6.6'.
He then had to convert the Departure to minutes of Longitude. He turned to the page for his Latitude, which was near enough to 42° N. This page also provides data for Latitudes of 48° and the data must be read from the correct columns if mistakes are to be avoided. I think Boxhall looked down a column boldly headed Dep. and found that a Departure of 93.8 miles converts to a change of Longitude of 140' or 2° 20'. The catch is, he was looking in the column for 48°. He should have looked in the column headed Dep. in italics. There he would have found that a Departure of 93.8 gives a change in Longitude of 126' or 2° 06'. His error in Longitude was therefore 14', which equals 10.4 miles at 42° N. Add the 2.2 miles due to the time error and we get 12.6 miles or 17'. This is very close to the known error of 19'. If the speed was overestimated, as some believe, a further 3' can be added, for a total of 20' An error of 17' to 20' is thus accounted for.
It might be added that the 1990/92 collision position is itself an estimation based on limited knowledge of the current running in 1912. It could well be one or two minutes of longitude out.
Boxhall gave evidence that he did not have his calculations checked by another officer. As an Extra Master, why should he?
It is possible to repeat Boxhall's calculation in reverse and obtain a good estimation of his 7-30 p.m. position. Using the Traverse Table, we find that in her run of 4 hr 16 min the ship changed her latitude (D. Lat) by 6.6 '. Applying this to the SOS position we get a starting latitude of 41° 52.6' N. The starting longitude is found by subtracting the sum of the correct D. Long of 126' and the error of 19' from the SOS longitude of 50° 14'W. The 7-30 p.m. position is seen to be 41° 52.6' N, 47° 49' W. This is 5 miles south of the track Titanic would have taken had she been exactly on her originally planned course and agrees with reports that Captain Smith delayed changing course for about 45 minutes after passing his planned turning point at 42° N, 47° W.
If the course is projected eastwards from the 7-30 position until it intersects the previous course of 242° True the resulting plot is consistent with the turning point at 42° N, 47° W being passed at 5-50 p.m. A speed of approximately 22 knots was maintained from there to the collision. This is consistent with her final day's run. It is hard to understand the thinking behind Captain Smith's delayed turn. The extra distance south is purely token. To be clear of the ice as reported by other ships, he needed to come to around 246° True and hold that course until well west of 50° W. The distance added would have been inconsequential, in view of the ship being over 1,200 miles from New York.
It might be added that the delay in turning was to add to the White Star Line's woes in court. Sitting as a Court of Appeal in 1914, Lord Justice Vaughan-Williams found that the delay was proof that Captain Smith was aware of ice ahead and hence was negligent in maintaining his speed and in not increasing his lookouts.
In the morning the results of the error were seen. Mount Temple and Birma arrived on the western side of the ice and searched an area well away from the correct position. The Captain of Mount Temple was one of the few contemporary critics of Boxhall's position. He told him it was about 8 miles out. Californian wasted much time passing through the ice from east to west, only to double back again on sighting Carpathia. Californian took around two and a half hours to reach Carpathia and this time was later used by defenders of Captain Lord to show that he was far distant from Titanic and unable to assist. They neglect to mention that most of the time taken was spent picking a way through the ice in the wrong direction.
The error also gave rise to the legend of Carpathia, a 14 knot ship, racing to the rescue at 17½ knots, which I have discussed in the next article.
The discovery of the wreck was delayed by some years as a result of the error. Had the SOS position been correct, others may have beaten Dr Ballard to it, with results we can only guess at.
Had Titanic been at say, 20° N, Boxhall would have used the page of the tables for 20° and 70°. If the same mistake is made on that page, the error in longitude is 2° 55' and the resulting new position is obviously silly. The tables are to some extent self checking, but not at latitudes close to 45°. It seems that Titanic had nothing going for her on that memorable night, not even nautical mathematics.