I’ve been trying to figure out what went wrong with the plan for Cook’s First Voyage.

Below is the sequence of events that I think happened and how the error played out. It might not have been Cook’s fault/miscalculation at all.

• In England, before the voyage starts, someone takes the four relevant positions from Rembrantse’s extract of Tasman’s 1964 voyage, and converts the longitudes from East of Teneriffe (as used by Tasman) to West of Greenwich (as Cook will use). The four positions are 1. Princes Flag, 2. Van Diemen’s Land departure point, 3. Murderer’s Bay and 4. Cape Maria Van Diemen.
• The conversion of the longitude of one of the points – Cape Maria Van Diemen is incorrect. The converted point is one degree too far east. It is pretty easy to make such a mistake – especially when manually converting longitudes from East to West. (I no longer think it was a subtraction “carry” error as I wrote previously, because of the way the one degree error popped up again later on 18th April with Cook failing to catch it at that time).
• Cook successfully locates Cape Maria Van Diemen. He calculates the offset between his value of Cape Maria Van Diemen and Tasman’s value as 49 minutes in latitude, when it is – in fact – 1 degree, 49 minutes. This error is due to the earlier mis-conversion of the Cape Maria Van Diemen point.
• Cook takes Tasman’s value of Murderer’s Bay, then calculates a point 49 minutes to the west. He searches this area for Murderer’s Bay. This is in Queen Charlotte Sound – around Ship Cove. Cook is searching one degree too far east due to the error.
• Cook spends several days in this area of Queen Charlotte Sound, taking his time – exploring and charting it well. His astronomer is busy determining the precise longitude by repeated astronomical observations during this time. However Cook has some doubts he is in the correct spot because the latitude is too far south.
• This hunting for the precise bay by pure longitude is – in a practical sense; a waste of time. Abel Tasman used dead-reckoning and an hour glass to measure his longitude of Murderer’s Bay. For Cook’s men to try to find this arbitrary longitude that was imprecisely measured in the first place is pointless – UNLESS the goal is to show off the technology Cook’s party is using. This is why I think ultimately – the goal was not to find the exact bay Tasman got attacked, it was to show off to the world that the British have solved the longitude problem.
• After leaving Queen Charlotte Sound, then doing a complete anti-clockwise round of the south island, Cook finds there is more land further to the west of Queen Charlotte Sound (at the top of the south island). He searches for Murderer’s Bay again – this time using it’s recorded latitude. This is when he goes into Admiralty Bay
• Cook (wrongly) realises that Murderer’s Bay must lie somewhere inside a large labyrinth of coves. He needs more information to correctly identify it. He has top-secret instructions to take his departure directly from Murderer’s Bay – but he doesn’t know where Murderer’s Bay is – so he has a problem. He solves this problem by inventing “Cape Farewell”. At time of departure, “Cape Farewell” is not a geographical feature – it is a “label” for a theoretical cape that lies at the same longitude of Murderer’s Bay (which he can’t find). At the time of departure – Cook gives the longitude of “Cape Farewell” as the same real-life longitude of Whareatea Bay (a cove inside Admiralty Bay). Whareartea Bay is a good candidate for Murderer’s Bay as it lies at the expected latitude of 40 degrees 50 minutes South. It’s clever to call the label “Cape Farewell” – as it is also a self-cue to Cook – “the place I was supposed to take my departure from”.
• On the 17th April, Cook is transiting the Tasman Sea and is close to New Holland. He indicates that some astronomical calculations have been done, and that there may be an error of up to 22 minutes in his ship log position. This 22 minutes error range – backtracked and superimposed on NZ, is enough to encompass Ship Cove as a possible location of Murderer’s Bay. He is allowing himself a possibility to shift “Cape Farewell” to the top of Queen Charlotte Sound at a latter date. He thinks Murderer’s Bay should lie within this 22 minute longitude range that encompasses both Admiralty Bay (Whareatea Bay) and Queen Charlotte Sound (Ship Cove).
• On the 18th April, Cook states “By our Longitude we are a degree to the Westward of the East side of Van Diemen’s Land”. Doing the sums here – it is clear he has used the erroneous 49 minute offset value, and added this to the value of Tasman’s departure point from Rembrantse – rather than use the correct value of 1 degree, 49 minutes.
• At the arrival in New Holland, Cook has a slight problem. He doesn’t know where he is supposed to land. He makes-do. His first successful landing is at Botany Bay. He gives the Longitude of Botany Bay as being “Latitude of 34 degrees 0 minutes South, Longitude 208 degrees 37 minutes West”. This is EXACTLY the longitude Rembrantse’s extract has given for the Prince Flag (167 degrees 55 minutes east of Teneriffe) – converted to west of Greenwich Observatory using Cook’s longitude for Teneriffe that he has in his journal on 24th September 1768 “<The Peak of Teneriff>… lies in the Latitude of 28 degrees 13 minutes North, and Longitude 16 degrees 32 minutes from Greenwich.”.
• Cook has actually landed 10 minutes to the east of this stated longitude. This lies within the expected 1/2 degree error range for using the lunar distances method. But it could also be that Cook has a chronometer at-hand, and has (secretly) adjusted for the true position of Teneriffe relative to Greenwich. The standard conversion number used at the time (Teneriffe to Greenwich) was off by about 6 minutes of longitude. If it is the case, and Cook has adjusted for this 6 minute error (he swung by Teneriffe earlier on this journey and had the opportunity to measure it’s position with a stealth chronometer) – then he has landed in Botany Bay within 3 minutes of longitude of this adjusted goal – very precise. The adjusted goal is the red line in the map below.

• It would not surprise me if Cook also sailed into Port Jackson/Sydney – firstly because it lies at the same longitude as the Botany Bay landing site, and secondly – it lies right on this red line. If Cook got the landing spot-on (without the 3 minute error), Port Jackson would have been the real target. If he was combining lunar distances and the chronometer, and also using lunar distances to periodically re-calibrate the chronometer, he may have been able to pinpoint to-the-minute precision. It certainly seems like he already achieved this INSANE level of precision at Cape Maria Van Diemen and at Ship Cove. I suspect there exists a drawing or chart of Port Jackson from 1770 that will be revealed sometime in the future – a drawing without depth sounding information (water depths taken by holding a string with a weight off the side of the boat to see how deep the water is). This is the reason Margaret Cameron-Ash has speculated that Cook walked overland from Botany Bay to Port Jackson – I think this story is to ‘prime’ people with an explanation when the drawing is eventually revealed. Cameron-Ash seems to already know there is no depth sounding data on this sketch/chart. It would make sense strategically to keep Sydney Harbour secret. Also Botany Bay lies at exactly latitude 34 degrees south – so it’s easy to find by low-tech methods, and makes a good ‘decoy’ for Sydney Harbour. Perhaps this is why La Perouse also found Botany Bay so easily in 1788.
• Back to the NZ situation. Short of taking a long detour for further exploration, I don’t think Cook could have much else during the voyage to ‘solve’ the problem of not finding Murderer’s Bay, and therefore salvage one of the key missions – to showcase British technical ingenuity in solving the longitude problem. But Cook was genius in leaving as many options open to later place Murderer’s Bay through his “Cape Farewell” idea. On return to England, more information was sourced – namely – Abel Tasman’s journal and charts. Through this – Blind Bay was revealed as the location of Murderer’s Bay. “Cape Farewell” was stuck on the top of Blind Bay.
• The rest of the chart of New Zealand was then moulded around this – into a creative fiction to place other key places at the “correct” location. This has no bearing on actual location of places. Cook had a habit of leaving spaces in his journal for latitudes and longitudes to be filled in afterwards (you can see this in the holograph scans). In practice, coordinates would have been kept track of inside tables in a dedicated navigation log (far more convenient). Cook filled in his journal coordinates based on the ‘creative’ chart that was made afterwards – not from the original navigation logs. It was probably filled-in after he got back to England and found where Murderer’s Bay really is. And at whatever time it was filled in, the original one degree error had still not been discovered – otherwise the chart would not have been distorted, as there would have been no need to.
• The problem with this – while a chart and a ship’s journal can lie, the actual coastline of New Zealand will never mould itself to conform to the chart. The British (and Cook) must keep their mouths shut about the achievement (and I acknowledge – the longitudinal precision achieved on this voyage was groundbreaking) and try again. If they use this voyage as proof of solving the longitude problem using fraudulent charts and an embarrassing high-school level math error, the fraud will be eventually revealed by the New Zealand coastline itself. Instead – Cook openly takes chronometers on his second voyage.