The Scottish mathematician and lawyer Archibald Smith first published in 1843 his equations for the magnetic deviation of a ship, or in other words, the error in the ship’s compasses from permanent and induced magnetic fields in the iron of the ship itself. This effect had been noticed in mostly wooden ships for centuries, and broad attempts to minimize it were implemented. But the advent of ships with iron hulls and steam engines in the early 1800s created a real crisis. A mathematical formulation of the deviation for all compass courses and locations at sea was needed in order to understand and compensate for it, and Smith became the preeminent expert in this sphere of activity. With Capt. Frederick J. Evans he extended his mathematical treatment to detailed procedures for measuring the magnetic parameters for a ship, and he also invented graphical methods for quickly calculating the magnetic deviation for any ship’s course once these parameters were found, constructions called dynamo-gonio-grams (force-angle diagrams), or **dygograms** for short.

Today, radio navigational systems such as LORAN and GPS, and inertial navigation systems with ring and fiber-optic gyros, gyrocompasses and the like have reduced the use of a ship’s compass to worst-case scenarios. But this triumph of mathematics and physics over the mysteries of magnetic deviation, entered into at a time when magnetic forces were barely understood and set against the backdrop of hundreds of shipwrecks and thousands of lost lives, is an enriching chapter in the history of science. Part I of this essay presents a brief sketch of the problem and the analysis and solutions that were developed to overcome it. Part II sets out with a discussion of Smith’s graphical methods of computing the magnetic deviation and concludes with a list of the references cited in the essay.

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