This sketch shows a Prytz-type planimeter as built by Weston Farmer.
Posted by: Paul Browne - website: http://www.geocities.com/geezerboat
These cheap planimeters work with amazing accuracy.
I've just built one, using this pic as my model. It is surprisingly accurate (certainly good enough for my modest needs). I used scraps that were lying around the shop --walnut rods, small finishing brads, and an Xacto chisel blade. I put about twenty minutes' work into it, and spent precisely nothing.
In my tests on known areas (circles and rectangles) error levels hovered around 1%. I ran the device over my drawings for Blackfly (a small sailboat), and results were quite consonant with those I arrived at by superimposing 1/8" grids on sectional areas, curve of areas, submerged lateral plane, and so forth.
A great little tool!