Variations of Polar Planimeters

Improved Willis Planimeter with 3 patent dates ranging from 1896-1901.
Manufactured by James L. Robertson & Sons Inc., New York.

Instead of having a wheel with its axis parallel to the tracer arm, this type of planimeter has a wheel with its axis perpendicular to the tracer arm. The wheel slides sideways along its axis. The distance it slides is proportional to area, and can be read from the scale.



Amsler's Spherical Polar Planimeter, 1884

This was never manufactured, but at least one prototype was built. It is in the Musée des Arts et Métiers (lit. Museum of Arts and Trades, but it's a science and technology museum) in Paris, donated by Amsler in 1889.