Archaeology · toxicology · a verdict that depends on its yardstick

Compared With Whom

The Franklin crew's bones carry about twenty times the lead of 19th-century Inuit, and that comparison made lead poisoning famous. Set the same nine bones against 23 men buried at the Royal Navy's hospital in Antigua, measured by the same method, and they carry only about a quarter more: of the 28,048,800 ways to pick nine of those 32 men, 18.5% carry at least as much. Pick the yardstick yourself and watch the verdict change.

In 1845 HMS Erebus and HMS Terror sailed into the Canadian Arctic under Sir John Franklin to finish the Northwest Passage. Both ships were beset in ice off King William Island in September 1846. In April 1848 the 105 men still alive left them and walked south, and none of the 129 who had sailed on from Greenland came home. In the 1980s Owen Beattie's team found high lead in the crew's bones and tissues, by 1991 had found its isotope ratios similar to those of the lead in the expedition's food tins, and lead poisoning became the famous answer to what went wrong.

"High" is a comparison. Every one of those papers had to say high compared with whom, and the answer they had in the 1980s was the Inuit who lived on the same island and modern Canadians. Below are nine Franklin bones from one site, each measured by the same method, and every group they have been held against. Choose one.

What the yardstick changes

Against the Inuit of King William Island as Kowal's team measured them (1 to 14 ppm, mean 5.1), the nine Franklin bones average 103.1 ppm, about 20 times more, and Welch's t-test gives t = 5.91. That is the test Anne Keenleyside, Margaret Bertulli and Henry Fricke reported in 1997 (t = 5.90) for these same nine bones; recomputed here from the printed summaries, it comes out the same to rounding, which also tells you which test they ran. Every one of the nine sits above the Inuit range. Against a yardstick like that, the crew look poisoned.

The yardstick those papers did not have is the Royal Navy's own dead. In 2017 Karen Giffin and colleagues published their measurements of the fibulae of 23 men buried at the Royal Naval Hospital cemetery at English Harbour, Antigua, between 1793 and 1822, made by the same method as the nine, inductively coupled plasma mass spectrometry, and printed every value. The cemetery, their paper says, likely held low-ranking naval personnel and enslaved men owned by the navy; six of the 23 are of African ancestry. Their mean is 80.76 ppm. The Franklin nine average 1.28 times that. Six of the 23 navy men carry more lead than the Franklin average, and two carry more than the highest Franklin bone (204 ppm): a boy of 14 or 15 at 214.77, and a man of 35 to 39 at 251.49.

Draw nine men at random

Here is the test that needs no formula. Put all 32 men, Franklin's nine and the navy's 23, in one pool. If being on Franklin's expedition made no difference to a man's lead, then the nine are just nine of the 32, and any nine would do as well. So draw nine at random and see how often they carry as much lead as the real nine did.

You do not have to sample. There are exactly 28,048,800 ways to choose nine of 32, few enough to count, and this page counts all of them in your browser (it tallies how many nine-man groups reach each possible total, in hundredths of a ppm, so the count is exact). Of those 28,048,800 groups, 5,182,006 carry a mean of 103.1 ppm or more. That is 18.5%, the exact one-sided permutation p-value. Pairs tell the same story: of the 207 ways to pair one Franklin bone with one navy man, the Franklin bone is higher in 138, two thirds.

Restrict the navy to the seven men Giffin's team could assign European ancestry, the closest thing in the cemetery to Franklin's crew, and the gap shrinks again: their mean is 87.67 ppm, and of the 11,440 ways to pick nine of those sixteen men, 3,724 (32.6%) carry as much as the real nine.

Could this test have seen a difference at all?

Eighteen percent is not "the same". A test on nine bones and 23 can miss a real difference, and a negative result is only evidence if the test could have come out positive. So ask the counting machine what it would have taken. Multiply every Franklin bone by the same factor and recount all 28,048,800 groups:

At about 1.22 times the real values, a Franklin mean near 126 ppm, the count drops under 5% and the test would have called it. So the honest reading is narrower than either side of the old argument: measured like with like, the Franklin nine cannot be told apart from the Royal Navy's own dead, and on these data the same count would have crossed the 5% line had every Franklin value been about a fifth higher. That is a rescaling, not a power calculation: a true difference of that size would cross the line only about half the time with samples this small. It does not show the crew were unharmed by lead. The navy men in Antigua had plenty of it too.

The larger Franklin series says more

The nine are not the only Franklin bones ever measured. Kowal's team reported 27 bone samples from King William Island at 87 to 223 ppm, a mean of 138.1 (standard deviation 35), measured by a different method, graphite furnace atomic absorption. Choose that series in the chart above and the gap over the navy is 1.71 times. Welch's test from the printed summary gives t = 3.72 if the 27 samples are 27 men, and t = 3.08 if they are 8, the smallest number of individuals Swanston's table gives for them. That table gives the mean for 24 elements, not 27 samples; counted as 24, t = 3.67. Either way that series does stand above the Antigua dead, by about as much as the slider says the nine would have needed.

So the evidence splits by series. The two series come from the same island; they differ by site, by bones, by laboratory and by method, and Welch's test between them gives t = 1.96, close to the line by itself. The papers that compare these numbers warn that values from different analytical methods should be compared cautiously, and that is the whole difficulty in one sentence: the like-for-like comparison is the small one, and the big Franklin series has no navy series measured its way.

Two numbers that do not agree with their sources

Building this page meant typing every number in from the papers, and two of them would not reproduce.

The modern yardstick. Table 1 of Treena Swanston and colleagues' 2018 PLOS ONE paper, the review that tabulates every comparison, gives the modern Vancouver cadavers as 1 to 8 ppm. The same paper's text gives modern Western Canadian cadavers as 18 to 50 ppm, and the abstract of the 1989 paper both cite gives 18 to 50 for "a modern population". The arithmetic can settle which series Keenleyside's 1997 t = 4.17 was run against, if that test was Welch's, the only one that reproduces the paper's 5.90 against the Inuit. Five values between 1 and 8 can have a standard deviation of at most 3.83, and with any such values the test gives t of at least 5.71, never 4.17. To get 4.17 the cadaver mean has to sit between about 27 and 34 ppm, inside 18 to 50. The 1-to-8 row is not the series that test used. With Student's pooled test instead, the conclusion would reverse (1 to 8 gives at least 4.20, and 18 to 50 at most 3.76), so this rests on the paper using one test throughout; the paper names neither.

The navy's mean. The same Table 1 gives the Antigua sample as mean 79.6, standard deviation 65.39. The 23 values Giffin's paper prints give 80.76 and 66.58, and 80.76 is the mean Giffin's own text states. Neither figure changes anything above. Both are the kind of slip a table copied from other tables collects, and both are checkable only because the papers printed their raw values.

What the bones say instead

Swanston's team did not stop at bulk numbers. They mapped where the lead sits inside bone, osteon by osteon, with a synchrotron, and tested three predictions of the poisoning story. If the expedition poisoned its men, those who lived longer should carry more:

The data did not support our first hypothesis as Pb distribution within the samples from the two different sites was similar.

Swanston et al. 2018, abstract (Beechey Island, the first winter, against King William Island, up to two years later)

The men buried on Beechey Island died within the expedition's first year, yet lead runs all through bone that formed long before they sailed, which the authors read as exposure before the voyage. Bone laid down near death does show lead, so the crew were taking some in during the expedition, but not the marked rise the poisoning story needs. Their conclusion:

Taken all together our skeletal microstructural results do not support the conclusion that Pb played a pivotal role in the loss of Franklin and his crew.

Swanston et al. 2018, abstract

None of this shows what did kill them, and no one has shown that yet. Inuit accounts gathered from the 1850s onward describe starving men, and some describe cannibalism. The same 1997 paper whose nine bones are on this page found cut marks on 92 of the bones at that site, about a quarter of them, made by metal blades, and read them as support for those accounts. Scurvy has been argued for and against. What a yardstick can do is narrower and firmer: the lead in these nine bones is within what the Royal Navy's hospital dead in Antigua carried a generation or two earlier, and something the navy's own dead carried too cannot by itself explain why this one crew, of all the navy's crews, never came back.

curl -sO https://artwaste.land/checks/verify-did-lead-kill-the-franklin-expedition.mjs
node verify-did-lead-kill-the-franklin-expedition.mjs