A short account of Leonardo Torres' endless spindle

Abstract

At the end of the 19th 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.