The shortest distance between two points

We came across this map, on a very unusual projection, while processing a previously uncatalogued set of nineteenth century French sea charts produced by the Dépôt des cartes et plans de la marine. Most are standard nautical charts, but this one – part of a set of three – is extraordinary.  The world appears to have been turned inside out; the chart is centred on the central Atlantic, and the land masses are progressively larger and more distorted the further they are from this point. The other two charts represent the Pacific and Indian Oceans in the same way.

The title makes the chart’s purpose clear: ‘Carte pour la navigation par l’arc de grand circle’. A great circle is, technically, the point at which the surface of a sphere intersects with a plane passing through its centre. In practical terms, a great circle drawn on the surface of the Earth between 2 points will be the shortest distance between those points (the Earth is not, of course, a perfect sphere, but it is close enough for this to be of use).

Navigational charts are traditionally drawn on the Mercator projection. This has the great advantage of showing a line of constant bearing (rhumb line) on the Earth’s surface as a straight line on the map. This is the simplest course to navigate, as mariners have known for many hundreds of years, but it is not the shortest. The shortest route is a great circle, and this requires constant adjustment of direction to stay on course. Sailing ships were limited by the challenges of winds and currents, and early steam ships by the need to refuel, but from the 1870s this principle began to have more practical applications. A straight line drawn on this orthodromic chart is a great circle course between the two points it connects, enabling navigators to plan their great circle journeys relatively easily. These charts were published in 1879. 

Charts of this sort do not appear to have passed into common use, and there could be several reasons for this. For one thing, the difficulties of plotting a great circle course are sufficient to outweigh the advantages for all but the longest ocean crossing journeys. Mariners continued to use rhumb line navigation well into the late twentieth century, by which time GPS systems had come into use. When a great circle course was followed, for sea or air travel, it was calculated in advance, sometimes using a chart of this sort. The course would then be plotted onto a Mercator projection chart where it was easier to follow. 

The usefulness of great circles can be seen most clearly on a modern map of long distance air travel. This is why aeroplane routes from, say, London to San Francisco always appear oddly curved when viewed on a map, with the route going much much north than you would expect. This is a great circle course, and the shortest way to connect two distant cities. A demonstration can be seen on this useful site http://demonstrations.wolfram.com/GreatCirclesOnMercatorsChart/.

The charts were created by Gustave Hilleret, a naval lieutenant and teacher at the École supérieure de guerre navale, who also published books on navigation. The projection is the Gnomonic projection with Equatorial aspect; the charts’ Bodleian shelfmark is B1 a.61/1 [39-41].

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