Theory of the hatchet planimeter

Abstract

The remarkable area measurement property of the hatchet planimeter is proved directly and easily by a series expansion. The previously known correction terms are readily generated and extended by a new analysis which now easily shows any blade misalignment to be of minor effect. This allows rationalizing the design for adjustment to give the best precision for the size of the figure. A new operating scheme, illustrated by an example, attempts to ensure accuracy at the minimum of user sophistication and calculation, to realize the hatchet planimeter’s enormous advantage in cost, mechanical simplicity and ruggedness over the Amsler planimeter. This is the background to an attempt to popularize this planimeter for rural engineering (Farthinget al 1985).