Mendeleev leaves holes and fills them

Mendeleev was not looking for a law of nature. He was trying to finish a textbook. He had been appointed to a chair at St Petersburg and there was no adequate Russian textbook of inorganic chemistry, so he wrote one: Principles of Chemistry. The first volume dealt with the halogens and the alkali metals, and it went well. The second had to cover everything else, and that meant deciding what order to take the elements in — which is an entirely practical question, and the sort of practical question that forces you to work out what you actually believe. There is a pattern here worth noticing, because it recurs. The people who systematise a subject are very often the people who have had to teach it. A researcher can leave an awkward corner alone. A textbook has to have a next chapter.

On 17 February 1869 by the Russian calendar — 1 March in ours — he laid out the 63 known elements by atomic weight, in rows arranged so that chemically similar elements fell underneath one another. So far this is what de Chancourtois, Odling, Newlands and Lothar Meyer had all done. The next decision is the entire lesson. Where the chemistry refused to line up — where the next element by weight plainly did not belong in the family the column called for — everyone before him had shuffled something into the space to keep the table full. Mendeleev left the space empty, and said an element would be found to fill it. And then, in a longer paper in 1871, he did something considerably more exposed than that. He published what the missing elements would weigh, how dense they would be, how they would melt, what their oxides and chlorides would look like, and in one case how they would be discovered.

Where do numbers for an element nobody has ever seen come from? From the neighbours. Atomic weight climbs smoothly as you move along a row and down a column, so the value in an empty box is close to the average of the four boxes around it. For the eka-silicon slot that is silicon above, tin below, gallium to the left and arsenic to the right. Density comes the same way. So do melting points, roughly. The formula of the oxide does not need interpolation at all — it comes from the group, because that is what a group is: eka-silicon sits in the column of carbon, silicon and tin, all of which form RO₂, so eka-silicon forms EsO₂. None of this is difficult. What is difficult is being willing to print it. He used the same reasoning in the other direction too, and this is less often mentioned: where an element’s accepted weight put it in the wrong place, he changed the weight. Indium had been assigned 75.6; he reassigned it to about 113 on the grounds that its chemistry demanded a different valency. Uranium he roughly doubled, from 120 to 240. Beryllium, cerium, yttrium and titanium all moved. Every one of those corrections turned out to be right.

And then the moment the whole history of chemistry keeps coming back to. Mendeleev, in St Petersburg, read Lecoq’s announcement and wrote to say that the density of 4.7 was wrong. It should be about 5.9, and the sample was probably still contaminated with sodium from the preparation. Lecoq — who owned the world’s only gallium — repurified it and measured it again. 5.904. It is worth being precise about why this is impressive, because it is not the accuracy. It is that the correction came from the table. Mendeleev had no gallium, no spectroscope pointed at any, and no information about Lecoq’s procedure. He had a position in a grid, four neighbours, and enough confidence in the arrangement to tell a specialist that his own measurement of his own element was out by a quarter.

There is one more thing he did, and at the time it looked far worse than leaving gaps. Tellurium weighs 127.6. Iodine weighs 126.9. By weight, iodine comes first. But tellurium behaves like sulphur and selenium, and iodine behaves like chlorine and bromine, so putting iodine first destroys two columns at once. Mendeleev put tellurium first, against the weights. He did the same with cobalt and nickel, where cobalt is the heavier and belongs first. His stated reason was that the accepted weight of tellurium must be wrong, and that a better determination would put it below 126.9. It was measured again, and again, and again over the following thirty years. It is 127.6. He was wrong about that. To his critics this was exactly the move that makes a theory unfalsifiable: when the data agrees with you it is evidence, and when it disagrees you declare it faulty. That criticism was fair. He had no principled way to say which weights to trust and which to overrule beyond his own judgement about what the chemistry demanded — and judgement is what everyone claims to have. He was right anyway. Proving it took another twenty-seven years and an entirely different kind of measurement, and it is the last lesson of this act.

Before the promulgation of this law the chemical elements were mere fragmentary incidental facts in Nature; there was no special reason to expect the discovery of new elements.

1. 1869The first table: 63 elements, arranged by weight, with question marks where nothing fits.
2. 1870Lothar Meyer publishes the atomic-volume curve, and periodicity becomes something you can look at.
3. 1871The long paper: eka-boron, eka-aluminium, eka-silicon and eka-manganese, with weights, densities and formulae.
4. 1875Lecoq de Boisbaudran finds gallium by two violet lines, and is corrected on its density by post.
5. 1879Nilson isolates scandium in Uppsala; Cleve recognises it as eka-boron.
6. 1882The Royal Society awards the Davy Medal to Mendeleev and Lothar Meyer jointly.
7. 1886Winkler tracks down the missing seven per cent of argyrodite and it is eka-silicon.
8. 1894Argon, which fits nowhere at all, and briefly looks like a refutation.
9. 1937Perrier and Segrè make eka-manganese in Palermo from a foil irradiated in Berkeley. Technetium: sixty-six years late.