David Rittenhouse: Logarithms and Leisure

Abstract

The life and times of David Rittenhouse (1732-1796) suggest that leisure and the love of calculation united in early America to stimulate mathematical practice and start, ever so obscurely, our research tradition. Of all the Colonial and Revolutionary natural philosophers, Rittenhouse was the most adept at calculation and mathematics even though his strength and accomplishments lay more in astronomy and the manufacture of precision scientific instruments [2], [3], [4]. Self-taught in mathematics, Rittenhouse read with care Newton's Principia Mathematica. Some intricate calculation or other, always takes up my idle hours, wrote [1, p. 221], [4, III]. William Barton, his early biographer, remarked that he considered all his hours as 'idle' ones which were occupied in some manual employment [1, p. 221]. Frangois-Jean Marquis de Chastellux (1734-1788), member of the Academie Frangaise and American military ally in the Revolution, observed that Rittenhouse was not a mathematician of the class of the Eulers, and the D'Alemberts (almost a self-evident truth, Brooke Hindle notes), yet had many American admirers, of whom Thomas Jefferson was the foremost [3, p. 344]. W. C. Rufus summarizes Rittenhouse's papers in [9]. Rooted in problems of astronomy and measurement of time, they reflect the inchoate, isolated state of mathematics in Colonial and Federal America and the work of good, if undeveloped pragmatic mathematical talent. Rittenhouse's paper of 12 August 1795: Method of raising the common Logarithm of any Number immediately, read when was president of the American Philosophical Society, is a good case in point (see [4], [6]). Printed posthumously in 1799, it approximated in continued fraction form the base-10 logarithm of a positive number. Logarithms were of great use in Colonial surveying; Laplace claimed they doubled the life of the astronomer. Rittenhouse's method in his own spare words is this: