It was Robert Hooke who discovered that the line of an
arch, for supporting any weight assigned, should be the inversion of the
shape of a catenary, or hanging chain, which is bearing that weight. He
apparently announced that he had made the discovery to the Royal Society
of London around 1671, but he did not provide any details until 1675, and
then the details were encrypted. In an appendix to his Description of
Helioscopes, he stated that he had found "a true mathematical and
mechanical form of all manner of Arches for Building," and the
solution was: "abcccddeeeeeefggiiiiiiii-illmmmmnnnnnooprrsssttttttuuuuuuuux."
Unlike Hooke’s law of the spring, which he announced with a similar
anagram, Hooke did not provide a translation in his lifetime, but it was
provided by his executor in 1705: "Ut pendet continuum flexile, sic
stabit contiguum rigidum inversum--As hangs a flexible cable, so inverted,
stand the touching pieces of an arch."
We display the page showing Hooke’s announcement; the
"law of the arch" anagram is in paragraph 2. Paragraph 3, which
follows immediately, contains the much more succinct anagram for Hookes’
law of springs: "ceiiinossssttuu," or "ut tensio, sic vis—as
the deflection, so is the force."
