I think I have just found a smoking-gun, mathematical proof that it was always planned for Cook to claim the east coast of New Holland. Cook made a very simple mathematical error that gives it away.

The Strategy

One of the secret goals of Cook’s first voyage was to claim parts of New Holland that lay to the east of the western-most parts charted by the Dutch (what I have dubbed the Orange line).

The challenge is to do this without having to actually locate the section of east coast of Van Diemen’s Land that Abel Tasman charted. This can be done mathematically.

In 1642, Abel Tasman sailed directly from the east coast of Van Diemen’s Land to New Zealand. In his journals, he recorded longitudes on both sides of the Tasman sea. With these longitudes in hand – anyone can calculate the longitudinal difference between the two coasts.

The difference is 23 degrees and 46 minutes longitude between the location where Tasman planted the Prince Flag (Van Diemen’s Land) and Moorderaers Bay (New Zealand).

So for Cook to sail in the OPPOSITE direction – all he has to do is locate Moorderaers/Murderer’s Bay and count the ~24 degrees of longitude back to the Prince Flag. This is what Cook attempted to do – but he made a simple miscalculation and didn’t find Murderer’s Bay correctly – which I will show proof of here.

One result of this – is that the First Fleet went to Botany Bay instead of somewhere else. This simple calculation error changed history.

Locating Murderer’s Bay

Cook had with him a small booklet by Dirk Rembrantszoon van Nierop, translated to English by Robert Hooke (the famous scientist??). You can access the booklet online CLICK HERE.

 but it is necessary to observe that I do not take the Situation of Vandiemen’s from the Printed Charts, but from the extract of Tasman’s Journal, published by Dirk Rembrantse.

Cook’s Journal 19th April 1770

This book contained some coordinates from Abel Tasman’s Voyage. This helps my investigation as the booklet only has a handful of coordinate sets. It means Cook only had a few points to work with – so there isn’t much “hay” in which I must search for the needle. Tasman’s full journal and charts – which have much more information – were not widely available in the anglosphere at this time.

In the Rembrantse extract, there are only two sets of coordinates given on the New Zealand side. These are;

• #R_CMVD – Rembrantse Cape Maria Van Diemen.
• #R_MB – Rembrantse Murderer’s Bay

I’m putting #’s in front because they are variables that I will show later in calculations. Also keep in mind – I am concentrating on Longitudes here – not Latitude, as Latitudes are straightforward and irrelevant in these calculations.

Cook can use either of these two points as the “starting line”. Murderer’s Bay is probably preferable because Abel Tasman arrived there first – theoretically there will be less chance of error. Ideally, Cook will find both of these points.

On the other side of The Ditch, there are two points in Van Diemen’s Land given in Rembrantse’s extract.

During this voyage, Cook had some basic “second-hand” charts of New Zealand – charts that were widely available in publications, but not the highly detailed “original” (I’ll show proof of why I think this later). An example of available chart is the Thevenot chart – which was published in English 1705 in Navigantium atque itinerantium bibliotheca (example of an original copy).

So Cook’s task is first to find both of these points in N.Z.. Let’s follow how that goes.

Locating Cape Maria Van Diemen

Cook approaches New Zealand from Tahiti – sights the east coast of the north island first. He initially heads south along the east coast, but then turns around and follows the coast north. He ends up rounding the north island coast at the North West Cape – Cape Maria Van Diemen. He verifies the correct location by also finding the nearby Three Kings Island – an island that Tasman also identified there.

Tuesday, 2nd. Fresh breezes at South-South-West and West accompanied with a rowling Sea from the South-West. At 5 p.m. the wind Veering to the Westward we Tack’d and Stood to the Southward. At this time the North Cape bore East 3/4 North and was just open of a point that lies 3 Leagues West by South from it, being now well assured that it is the Northermost Extremity of this Country and is the East point of a Peninsula which Stretches out North-West and North-West by North 17 or 18 Leagues, and as I have before observed is for the most part low and narrow except its Extremity where the land is Tollerable high and Extends 4 or 5 Leagues every way. Cape Maria Van Diemen is the West point of the Peninsula and lies in the Latitude of 34 degrees 30 minutes South; Longitude 187 degrees 18 minutes West from Greenwich.

…

At 1/2 past 7 p.m. the Island of the 3 Kings bore North-West by North and Cape Maria Van Diemen North-East by East, distant 4 Leagues.

Cook’s Journal 2 January 1770

So far, so good. Cook now has the longitude of Cape Maria Van Diemen. This is another variable for our calculations.

• #C_CMVD Cook Cape Maria Van Diemen

From this, Cook can use Rembrantse’s extract to calculate the Longitude where Murderer’s Bay should be. This is fairly simple to do. Just looking at a modern map, you can see that Murderer’s Bay and Cape Maria Van Diemen are almost in a north-south line with each other – so the offset shouldn’t be that much.

Note: You don’t have to worry that Cook and Tasman reckon longitude from different meridians (Greenwich and Teneriffe) because we are calculating relative/offsets longitudes, and we aren’t spanning any anti-meridians. It just means you can’t just look these numbers up directly on a modern map.

Mathematically:

#R_CMVD	Rembrantse Cape Maria Van Diemen.	191d 9m
#R_MB	Rembrantse Murderer’s Bay	191d 41m
#C_CMVD	Cook Cape Maria Van Diemen	187d 18m
#R_OFFSET	Tasman difference = #R_MB minus #R_CMVD	32m
#C_MB	Expected longitude of Murderer’s Bay = #C_CMVD minus #R_OFFSET	186d 46m

Now – all Cook has to do is follow the east coast down, south to Latitude 40d 50m South (also from Rembrantse) where there should be Murderer’s Bay sitting there at Longitude 186d 46m. Then he has his starting point to New Holland.

Easy peasy…

Just FYI – 186d 46m is West of Greenwich. When converted to East of Greenwich, you can look where this is on a “normal” map – it is 173d 14m EAST. (the international prime meridian is not exactly Greenwich, but it’s precise enough for our purposes). So on our modern maps, Murderer’s Bay should be at Latitude 40d 50m South, 173d 14m East.

Cook heads south following the coast…

Ship Cove

When he gets down towards our target zone, on 16 January 1770, Cook navigates his way into a place called Ship Cove. If we look on our modern map where this is (it’s still called by that name, and Cook gives a description that matches) we will see that Ship Cove is EXACTLY one degree east of where our calculations place Murderer’s Bay – it’s at 174d 14m East.

Reading Cook’s journal is very insightful here.

These people declared to us this morning, that they never either saw or heard of a Ship like ours being upon this Coast before. From this it appears that they have no Tradition among them of Tasman being here, for I believe Murtherers bay, the place where he anchor’d, not to be far from this place; but this cannot be it from the Latitude, for I find by an Observation made this day at Noon that we are at an Anchor in 41 degrees 5 minutes 32 seconds South, which is 15 miles to the Southward of Murtherers Bay.

Cook’s Journal, 16 January 1770

Clearly he thinks he is DIRECTLY SOUTH of Murderer’s Bay. This indicates he believes is at the correct Longitude. But 15 miles northward of his position there is no bay, just water. And using Google Earth’s measure tool, latitude 40d 50m South lies about 15 “Seemeilen” (I’m using a German language install) north of Ship Cove. I don’t know what units Cook used for a mile or what a “Seemeile” is (maybe a nautical mile?), but it checks out.

He asks the locals if they have ever seen white-man ships before – so he is trying to verify if the place is Murderer’s Bay.

Cook has done a simple miscalculation. In our earlier calculations here of the variable #C_MB we came up with a value of 186d 46m. Cook has calculated 185d 46m – he is one degree too far east. This can happen by a subtraction “borrow” error when calculating #C_MB = #C_CMVD minus #R_OFFSET (187d 18m minus 32m)

*** EDIT.. I don’t think it was a subtraction borrow error anymore, but there was a one degree error.

Cook’s confirmation bias might be setting in – the next day in his journal, Cook unconvincingly writes that the locals are feasting on human flesh (like the cannibal “murderers” of Tasman’s crew)

Soon after we landed we meet with 2 or 3 of the Natives who not long before must have been regaling themselves upon human flesh, for I got from one of them the bone of the Fore arm of a Man or Woman which was quite fresh, and the flesh had been but lately picked off, which they told us they had eat; they gave us to understand that but a few days before they had taken, Kill’d, and Eat a Boats Crew of their Enemies or strangers, for I believe they look upon all strangers as Enemies.

Cook’s Journal, 17 January 1770h

I admit – I laughed at the mental-image of Cook’s party landing, finding locals sitting around under a tree – nonchalantly nibbling on a human forearm. “Hey how’s it going there white strangers! We are just eating the people from that other strange boat parked over there. Look, here is a forearm – wanna try some?”. It sounds absurd.

If the locals routinely eat strangers – why doesn’t Cook seem concerned for his own party’s safety? He hangs around the area for some days in total, seemingly unconcerned.

A few days after further exploring the area, verifying the separation of North and South Islands, and claiming possession, Cook has an interesting conversation with an old man;

The old man, seeing us under sail, came on board to take his leave of us. Amongst other conversation that passed between him and Tupia, he was asked if either he or any of his Ancestors had ever seen or heard of any Ship like this being in these parts; to which question he answer’d in the Negative, but said that his Ancestors had told him that there came once to this place a small Vessel from a distant part, wherein were 4 Men that were all kill’d upon their landing; and being asked where this distant land lay, he pointed to the North, intimating that it would take up a great many days to go thither. 

Cook’s Journal, 6 February 1770

I suspect that Cook has made this story up, trying to “prove” this is Murderer’s Bay. There are elements of this story that don’t make sense. Like how do the people know the vessel sailed very far away north? They are inside a maze of coves with only so-many ways out. Also – Tasman’s men were killed in their dinghy – they didn’t land. But from the way Rembrantse’s extract reads, one would get the impression they landed. I think this fiction is for the benefit of Cook’s superiors – because Cook is supposed to locate Murderer’s Bay, this story is confirmation that he must have the right place.

Anyway – fast forward the voyage a bit…. Cook then does a clockwise-lap around the south island, then comes back to the same area.

Blind Bay

On the 24th March, Cook rounds the northern point of the south island (Farewell Spit), then sails straight past Murderer’s Bay in good weather without exploring it. He obviously has no idea that he is sailing past his goal;

Saturday, 24th. In the P.M. had a Gentle breeze at South-West, which by Dark run us the length of the Eastern Point set at Noon, and not knowing what Course the land took on the other side, we brought too in 34 fathoms about one League from the land. At 8, it falling little wind, we fill’d and stood on until 12, at which time we brought too until 4 a.m., then made Sail. At daylight we saw low land extending from the above point to the East-South-East as far as the Eye could reach, the Eastern Extremity of which appear’d in round Hillocks; by this time the wind had veer’d to the Eastward, which obliged us to ply to windward. At Noon the point above mention’d bore South-West by South, distant 16 miles; Latitude observ’d 40 degrees 19 minutes South. This point I afterwards named Cape Farewell, for reasons which will be given in their proper place

Cook’s Journal 24 March 1770

He heads further west to fully complete his lap of the south island, and from about the 27th till the 31st of March, does daily non-descript “wooding and watering” excursions in the labyrinth of islands and inlets around Admiralty Bay. To me, that sounds like an alibi for a 4-day-last-ditch attempt to find Murderer’s Bay in the maze – this time trying to find it by Latitude, as Admiralty Bay lies at the expected latitude.

Now back to something I mentioned before, that I think Cook was using second-hand charts. Below are two charts showing Murderer’s Bay in context- one is an “original” chart from Tasman, the next is a typical low-res version that was in books in Cook’s era. As you can see – it’s hard to find the exact Murderer’s Bay with the poor-man’s chart. But the poor-man’s chart would be enough to eliminate the maze where Cook is searching. Note also – the poor-man’s chart includes the 3 Kings Island (Het Eylandt drie Koningen) which Cook used to identify Cape Maria Van Diemen.

Cook’s first voyage charts has Murderer’s Bay marked as “Blind Bay” – a mysterious, uncharted area. I think some time later after he already left New Zealand, he realised from revising his poor-man’s charts that Blind Bay is a possible location for Murderer’s Bay. But it’s too late to explore because he has already left. He scrawls his suspicions on the bottom of one of the pages of his journal… don’t know if you can tell from the image below, but on better quality image you can clearly see that the last 1.5 lines are in a slightly different ink or pen. (source – https://nla.gov.au/nla.obj-229033436/view navigate to image number 427, very bottom of page). There are quite a few scribbles and alterations around this section of the journal that tell the story of Cook’s confusion. It was at this moment that he knew… he f**ked up.

A slight tangent – but Cook came back to this area on his second voyage. And when he did, he immediately identified the correct Murderer’s Bay. So sometime between the first and second voyages, he had sourced the “original” charts. This is very important because the original accounts were the secret weapon of Furneaux’s side-expedition. If Cook had the original charts during the second voyage, then Furneaux would have had a copy too. When Joseph Banks died, in his library there was a Dutch version of the full Tasman’s account, complete with the charts and drawings, and a English translation with a handwritten-note from the translator. I’m guessing that money-bags-Banks sourced it sometime between Cook’s first and second voyage.

Kook Kardashian chart

There is something very wrong with Cook’s charts of New Zealand – and it is due to Cook’s error.

If you eyeball the north-west point of the north island, then draw your eye directly south, with most maps and charts you should hit Farewell Spit, roughly on the northern-most point of the south island. But on Cook’s charts, you will instead hit somewhere along the east coast of the south island.

Cook was so certain about his Murderer’s Bay calculation that he warped his entire chart to put the geographical features of Cape Farewell at that longitude.

Everyone knows about Cook wrongly depicting Stewert Island as a peninsular – but few notice that the entire chart is distorted like a Kardashian on Instagram.

Landing in Botany Bay

Cook then proceeds across the Tasman Sea in an attempt to measure 23 degrees 46 minutes longitude from Murderer’s Bay. Then he plans to land just east of that line. Problem is – he doesn’t know where Murderer’s Bay is.

As Cook tracks across the Tasman Sea, he is reckoning his longitudes from “Cape Farewell”.

I think “Cape Farewell” is just code for the arbitrary zero starting point, and it is not tied to any geographical feature until afterwards. By the raw coordinates, it’s actually at Admiralty Bay.

Noon on the 17th of April, Cook makes some more detailed lunar/solar calculations from Greenwich. This was just before landfall in New Holland. These numbers are very interesting. It appears that Cook was reckoning his longitude from zero-point “Cape Farewell”, but on the 17th he used a fake lunar/solar calculation to covertly reset that zero point longitude from Admiralty Bay to Ship Cove (Ship Cove is #C_MB_Error, what he thinks is the true longitude of Murderer’s Bay).

#C_CF	Cook Cape Farewell (nowhere near today’s Cape Farewell, 174d 2m East)	185d 58m
#C_MB_Error	Cook Murderer’s Bay calculation with his 1 degree error	185d 46m
#C_17Offset	Cook 17th April offset from Zero Point	22d 22m
#C_17Log	Cook 17th April position by ship log	208d 20m
#C_17Astro	Cook 17th April position by Solar/Lunar measurements	207d 58m
	Zero Point (log) = #C17_Log minus #C_17Offset (should be same as #C_CF, yes it is)	185d 58m
	Zero Point (Astro) = #C_17Astro minus #C_17Offset	185d 36m
#C_17Average	Average of #C_17Log and #C17_Astro	208d 09m
#C_ZeroPoint	Zero Point (Average) = #C_17Average minus #C_17Offset	185d 47m

In light of these new findings, that there are several different zero points – I will re-evaluate the landings on the east coast of New Holland in another post. The first landing attempt in Bulli appears to have been calculated from Admiralty Bay. Botany Bay seems to have been calculated from longitude 175 degrees 0 minutes – a round number and conservatively placed far to the east, as if Cook had given up on finding Murderer’s Bay.

The proof of the deception of Cook’s first voyage lay in the numbers – waiting for someone to discover the conspiracy through crunching numbers.

I still have one question for my own curiosity. Did Cook lie for the Admiralty, or did he lie to the Admiralty to cover-up his failure? If the latter – did he ever get caught?