Tin has the thinnest symbolic literature of the seven, and the reason is geological. Workable tin ore is rare and very unevenly distributed, so tin was almost never a local metal. It was a traded one, moving from Cornwall, Brittany, Iberia and Central Asia to bronze-working centres that could not manage without it. Herodotus writes of the Cassiterides, the tin islands, as somewhere at the edge of the known world that he cannot place, and their identification is still unsettled.
That trade is the substance of tin's importance. Bronze is copper with roughly a tenth part tin, an entire age is named after the alloy, and so the metal hardest to obtain was the one that decided whether a society could arm and equip itself. The routes that carried it are among the earliest evidence for organised long-distance exchange in Europe.
Its own attributes in the tradition are mostly borrowed from Jupiter rather than observed in the metal. Tin is soft, light, low-melting and dull. The one property the alchemical writers reliably single out is the cry of tin, the audible creak a bar gives when it is bent, caused by the crystal structure deforming. Where a working tradition uses tin directly it is usually as a substitute: tin foil standing in for silver, pewter for the plate of a household that could not afford better.
The atlas records the Jupiter pairing because the sources are unanimous on it, and notes that the unanimity reflects the tidiness of a seven-and-seven scheme rather than a strong independent tradition attached to the metal.
Sources HistoriesHerodotus with The Secrets of AlchemyLawrence M. Principe