According to Spirits & Distilling, it began life as the Argentinean version of the Martini. And back then, in the early twentieth century, it was called the San Martin, after Don Jose de San Martin, a liberator of Argentina, Chile and Peru. There are Argentinean cocktail manuals that specify dry vermouth and others that specify sweet vermouth. By the time of Craddock's Savoy Cocktail Book, the drink had become equal parts dry and sweet vermouth and gin and the editors had mangled its name as Sand Martin. Quite a history.
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