Planimeter

Planimeter, a machine for measuring areas on a plane. The best-known form is that of Professor J. Amsler-Laffon of Schaffhausen, the theory of which will be found discussed in Williamson's Integral Calculus, and in Minchin's Uniplanar Kinematics. It consists of two rods hinged together. The extremity of the one rod is fixed, so that the free extremity of the other is able to trace out any form of curve limited only in size by the dimensions of the apparatus. The theory of the instrument depends upon the fact that, as the free end is made to trace out the boundary of any closed area, the hinged end oscillates to and fro along a curve, but traces out no area. Rigidly attached to the rod whose one end traces out the plane area is a graduated roller fixed with its axis of rotation parallel to the line joining the hinge and the tracing point. As the closed curve is being described the roller rotates because of the lateral movement of the rod; and the difference of the readings before and after the tracing has been accomplished gives a number proportional to the area that has been gone round. To Amsler-Laffon also is due a more elaborate form of integrator capable of measuring moments of inertia of areas. It greatly facilitates the calculation of displacements, metacentres, and curves of stability in naval designing.