Les instruments du calcul savant > Instruments d'intégration conservés au musée des arts et métiers

Spherical Planimeter

Spherical planimeter, according to Jakob Amsler
Maker: Amsler, Schaffhausen/Switzerland; instrument no.: none; pre-1889
Inventory: CNAM, inventory no. 11617-0000-
Details: Not signed. Entry CNAM: 1889
References: Amsler 1884 (= Zeitschrift für Instrumentenkunde 4, 1884, 11-24) 23. Mentioned in Cat. CNAM 1905, 156 and Cat. CNAM 1942, 128

Spherical planimeter, from Amsler 1884, 23

In 1884 Jakob Amsler (1823-1912) published his second important contribution to theory and practice of mechanical integration, the first being his fundamental publication of 1856. In his 1884 publication he dealt mainly with two topics: on the one hand, he looked at possibilities of generalising the theory of the integration mechanism wheel-and-plane into three dimensions; on the other hand he investigated the circumstances under which gliding of and in the integrating mechanisms can be suppressed or at least minimised.

Amsler was able to show that the operation of a usual polar planimeter could be transferred to the surface of a sphere without any problems; only the pole and tracer arms had to follow great circles. By adding a horizontal joint on each of the arms of a common polar planimeter this requirement was fulfilled and a spherical planimeter realised.

Amsler's spherical planimeter, c1889, CNAM 11617-0000

It seems that only one instrument of this kind was ever built or has survived. It was shown at the Great Exhibition which took place in Paris in 1889, and was subsequently donated to the CNAM by Jakob Amsler.

Amsler's spherical planimeter on a globe