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# The Road to Nordsieck’s Machine

###### Kelvin's Harmonic Analyser

Lord Kelvin used calculating machines to predict tides in harbors—critical for an island nation! Integrators enabled him to solve differential equations, but their limited torque curtailed the machine’s utility.

###### The Road to Nordsieck’s Machine

The differential analyzer was an important milestone on a path that began much earlier with the integrator, a key component of measuring tools called planimeters.

Johann Martin Hermann, the Royal Bavarian Trigononometer, built an early planimeter in 1814. Planimeters didn’t gain wide use, however, until Casper Wetli’s better-known 1849 version, based on a refined wheel-and-disk integrator.

In 1876, Scottish engineer James Thomson introduced a simplified integrator. He also introduced the term “integrator.” Thomson’s brother, Lord Kelvin, recognized that instrument’s value as a general-purpose mathematical device.

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###### J. Amsler-Laffon's Mechanical Integrator

Complicated devices like this were often used in ship design. Measuring the surface area of a cross-section drawing of the hull gives the engineer information about the ship's capacity and center of gravity, which determines seaworthiness.

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###### J. Amsler-Laffon's Mechanical Integrator design drawing

Complicated devices like this were used often in ship design. Measuring the surface area of a cross-section drawing of the hull gives the engineer information about the ship’s capacity and center of gravity, which determines seaworthiness.

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###### What is a Planimeter?

Planimeters are instruments for measuring the area of any two-dimensional shape on a plane (hence the name: plane + meter). They generally work by tracing the shape’s perimeter with a pointer, which moves a measuring device.

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###### Planimeter

Planimeters became commercially available in the second half of the 1800s. The most popular of several styles was the polar planimeter, in which the linkage moves relative to a fixed point. Modern planimeters often use digital electronics.

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