Paper given at BSHM Postgraduate Research in Progress, Oxford, February 2005.

1. Embodying the Calculus:
Planimeters and Analogue Computing
Charles Care
Feburary 2005

2. • Planimeters invented and
re-invented throughout the
19th Century.
– Hermann (1814)
– Gonnella (1824)
– Oppikofer (1827)
– Wetli (1849)
– Sang (1851)
– Amsler (1854)
• Principle uses in:
– Land area calculation
– Indicator diagrams

3. Using a planimeter to calculate the area of an indicator diagram

4. A roller can be used to calculate the length S
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S

5. Calculating the area under a two-state function
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h2
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S2
S1

6. Scaling the rotation according to the function’s height

7. The cone provides a different gear for every possible value in the y-axis

8. An Oppikofer planimeter

9. A model of an Oppikofer planimeter

10. The Hermann Planimeter

11. The Wetli Planimeter

12. A differential analyser∗
∗ Crank, J. The Differential Analyser. Longmans, London, 1947.

13. Embodying the Calculus:
Planimeters and Analogue Computing
Charles Care
Feburary 2005