Pierre Varignon and the measurement of time

Ronald Gowing (*)

The work of Pierre Varignon (1654-1722), priest and scientist, géomètre in the Académie royale des sciences de Paris, correspondent of Leibniz, Newton, the Bernoullis and many others, deserves wider attention. He was one of those mathematicians who, in an age of slower communication, were so important in the diffusion of new ideas. He learned the differential and (some) integral calculus from Jean I Bernoulli, initially during the latter's youthful visit to Paris in 1698, and thereafter in the course of a lifelong and fruitful correspondence (1). Varignon' s importance in the diffusion of the differential calculus in France has been discussed by Pierre Costabel (2) and the importance of his influence in the spread of Newtonian ideas on the continent of Europe has been recognized by Henry Guerlac (3). He contributed papers, often of major significance, to every volume of the Mémoires of the Paris Academy from 1699 to 1721.

I have chosen to illustrate Varignon' s work by discussing what, on the face of it, is a modest little paper dealing with a minor technical problem, but which, like so much of Varignon's work, is related to a major problem of the day. The major problem of the day is that of finding longitude at sea, in particular by improving the accuracy of spring- driven portable clocks; and the technical problem is to find the correct shape for the fusee — part of the regulating mechanism. The mathematical interest, is in deriving and solving differential equations with separated variables, and in the integration of binomial differentials.

The fusee is a device for compensating the declining power of a coiled