Prytz (Hatchet) Planimeter

Planimeters can measure the area of any drawn shape. The Prytz planimeter is undoubtedly the simplest of these. It consists of

a rod with its ends bent at right angles. One end, the tracer point T, is sharpened to a point, while the other end, C, is sharpened to a chisel edge parallel to the rod. The chisel edge is usually slightly rounded, making it look similar to a hatchet, and consequently the device is also known as a "hatchet planimeter."

Compared to more complicated planimeters, it has a poor accuracy. The accuracy improves with longer planimeters.

Prytz Planimeter Links:

Introductory page.

When the tracer point T moves along a line, the chisel edge C follows a tractrix.

Pictures of old ones, new ones, and in-use ones.

Here is one that was probably manufactured in Holland (it came with instructions in Dutch) in the late 1800's or early 1900's.

The Geometry of the Prytz Planimeter (Technical paper from arxiv.org).

The Prytz planimeter is a simple example of a system governed by a non-holonomic constraint. It is unique among planimeters in that it measures something more subtle than area, combining the area, centroid and other moments of the region being measured, with weights depending on the length of the planimeter.

Do-it-yourself model made of an exacto blade, pennies, pins and wood.