A short account of Leonardo Torres' endless spindle

Abstract

At the end of the nineteenth century, several analog machines had been proposed for solving algebraic equations. These machines —based not only on kinematics principles but also on dynamic or hydrostatic balances, electric or electromagnetic devices, etc.— had one important drawback: lack of accuracy. Leonardo Torres was the first to beat the challenge of designing and implementing a machine able to compute the roots of algebraic equations that, in the case of polynomials of degree eight, attained a precision down to 1/1000. The key element of Torres’ machine was the endless spindle, an analog mechanical device designed to compute log(a + b) from log(a) and log(b). This short account gives a detailed description of this mechanism.