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2010/1/298 Planimeter with Amlser integrator and case, Special Purpose, wood / metal, made by Stanley of London, England, 1880-1900. Click to enlarge.

Planimeter, Special Purpose

  • 1880-1900
This object is part of a collection relating to the history and development of calculating devices assembled by Assoc Professor Allan Bromley of Sydney University, comprising mathematical instruments, slide-rules, mechanical and electronic calculators, electronic analogue computers, computer components, kit computers, education computers, and associated ephemera.

Allan Bromley was a lecturer and researcher at the University of Sydney Basser Department of Computer Science from 1978 until his …


Object No.


Object Statement

Planimeter with Amlser integrator and case, Special Purpose, wood / metal, made by Stanley of London, England, 1880-1900

Physical Description

Naval architects favour this instrument for measuring area, moment, moment of inertia, centre of gravity, and volume. Area, moment and moment of inertia are measured upon any diagram by moving a tracing point around the outline of the item. It includes an assembly of three disc integrators mounted in a cast brass framework.



  • 1880-1900


Bromley: Presumably by Coradi of Zurich. French style lacquer finish. French dovetailing of box. Blued screws.



In its basic form the Planimeter is a mechanical integrating instrument, based on the intuitive notion of a line segment sweeping an area bounded by a curve drawn on a piece of paper, for example on a map, thereby measuring the size of the area.

The Linear Planimeter consists of two metal arms hinged together in an elbow joint, which bends and slides freely; one arm is free to rotate about a fixed point, while the other arm traces the perimeter of the area to be measured. A small wheel is placed beneath the second arm, resting on the paper surface; it is free to rotate around a fixed axis parallel with the second arm. The two arms are held in a horizontal position above the paper surface. When there is a movement of the second arm perpendicular to the arm, the wheel rotates; when the movement is parallel to the arm, the wheel does not rotate. A simple counter is attached to the wheel to record its rotations. It can be shown mathematically that the amount the wheel rolls is proportional to the area which has been traced.

The Polar Planimeter is based on polar coordinates; in mathematics it was useful for determining static and inertial moments and the coefficients of Fourier Series.

The invention of the Planimeter appears to have been due to the inventive skills of a number of people. The method of rolling a wheel of known circumference along a curved line to determine its length was used by ancient Egyptian mathematicians, and the development of this method for the measurement of an area was carried out early in the 19th century. The first complete Polar Planimeter was exhibited in Paris in 1836, and a patent was published in 1836. The Linear Planimeter did not appear till 1912; it has been attributed to a German engineer, J.H.Hermann. A Swiss mathematician Jacob Amsler was a major contributor to the Linear Planimeter. It was used particularly by railway engineers and shipbuilders. During Amsler's lifetime, his workshop in Schaffhausen, Switzerland, produced 50,000 Polar Planimeters.

In this age of computer-aided design and digital images, while the Planimeter is still being manufactured, it is undoubtedly heading toward obsolescence.


Credit Line

Donated through the Australian Government's Cultural Gifts Program in memory of Associate Professor Allan Bromley, 2010

Acquisition Date

19 January 2010

Cite this Object


Planimeter, Special Purpose 2021, Museum of Applied Arts & Sciences, accessed 4 October 2022, <>


{{cite web |url= |title=Planimeter, Special Purpose |author=Museum of Applied Arts & Sciences |access-date=4 October 2022 |publisher=Museum of Applied Arts & Sciences, Australia}}