Conquering carries: Genaille–Lucas rulers | Tangente

Conquering carries

Napier's rods had simplified multiplication, but handling carries remained an unsolved problem. The obstacle they posed remained insurmountable for three and a half centuries, until Genaille and Lucas finally found a solution.

Written by

Jean-Jacques Dupas

PublishedAugust 22, 2025UpdatedMay 16, 20261 min read

At a conference of the French Association for the Advancement of Science, Édouard Lucas (1842–1891) wondered whether Napier's rods could be improved so that multiplication results could be read from them directly. With his deep knowledge of arithmetic, he sensed that since the carries were known and fixed, something could be done. Henri Genaille (1856–1903), "an engineer with the state railways in Tours, obscure yesterday, illustrious tomorrow", as Lucas put it, found the solution. The rulers invented by Genaille were undoubtedly improved by Lucas, which is why they now bear both their names.

They were presented in 1884 at the 7^th conference of the French Association for the Advancement of Science in Blois.

A complete set of Genaille–Lucas multiplication rulers.

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