On a clear day on a small body of water a sailor can aim for a point visible on an opposite shore. But when a destination is not visible, as on the open sea, the mariner must try to proceed along a constant, predetermined, directional course. A constant course is a practical necessity since it is much more difficult to navigate a curved course.

Determining a constant course is more complicated than it might seem at first because our system of "compass" directions, N, S, E, W, etc., is defined by the coordinate system of meridians and parallels fitted to a sphere. (The needle of a magnetic compass usually varies somewhat from the true direction.) As pointed out in Chapter 1, meridians are lines that converge to each pole and define the directions N or S. A second set of lines, called parallels, is perpendicular to the meridians at every intersection. They form a set of circles that define the directions E or W. This spherical coordinate system is not spaced at equal distances as is a rectangular system on a flat surface, and therein lies the problem.

The Navigator's Rhumb
The constant course the mariner must follow is a fixed direction. In practice it is determined by drawing a straight line from starting point to destination on a nautical chart, a map showing coastlines and navigational hazards. If the course were due E, W, N. or S there would be no problem because those directions are indeed constant. But, because the meridians lie at an angle to one another, any oblique, constant course, such as NE, which by definition must cross each successive meridian at the same bearing, becomes a complex curve. It is called a rhumb line (from "rhumb": any of the 32 points of the compass) or loxodrome. A rhumb spirals poleward (Figure 10-1).

Up to the beginning of the 16th century the fact that an oblique compass course is a curve was not a matter of concern. On the early "portolan" charts of the Mediterranean a base of parallels and meridians was not needed since frequent passages and relatively short distances within the enclosed area led to accurate relative locations. Courses were not long enough to cause problems. As an aid to navigation these early charts were crisscrossed by numerous sets of straight lines radiating from compass roses (Figure 10-2). These "rhumb lines enabled the navigator to determine the correct compass course easily. Apparently the system worked well in the confined Mediterranean area.

Plane Charts
Early in the 16th century mariners began regularly plying the much more extensive oceans. A chart of these larger regions had to be based on some systematic transformation (a map projection) of the spherical surface of the earth to a flat sheet as a base on which to draw the chart. The map projection employed was one in which the meridians were drawn as straight, equidistant, parallel lines; perpendicular to these, the parallels were also drawn as equidistant, parallel lines. Drawing the converging meridians as parallel lines, in effect, makes the sea surface flat. The charts made on such a base were called Plain charts (later, Plane charts), and navigating by them was called Plain (Plane) sailing.

On the charts the parallels and meridians formed a grid of equal rectangles. On the earth the parallels are everywhere about the same distance apart, but the meridians are progressively closer together as they draw closer to the pole. Ideally, the E-W width of the rectangles was based on the spacing of the meridians at the latitude of the center of the chart area. Thus, the higher the latitude the narrower the rectangles would be. Such projections are all called Equirectangular no matter what parallel is chosen to be central.

The tradition of covering the charts with crisscrossing, radiating straight lines and the practice of "sailing by the rhumb" were continued. This created difficulties since on these charts a straight line oblique to the meridian is not a rhumb. A greatly exaggerated example will illustrate the problem. Suppose a navigator were heading for Bristol, England, from the Carolina colony in the New World. He would draw a straight line on his chart between the two, as in Figure 10-3, which would show his course to be about N 62°30° E. If the mariner maintained that course he would actually miss England entirely, going far to the north. If the navigator's chart were based on another Equirectangular projection, the indicated course would be different, and wrong. In the 16th century sailing on the open ocean was adventurous, to say the least. The couplet of the 19th-century poet Arthur Hugh Clough captures its essence:

Where lies the land to which the ship would go?
Far, far away is all her seamen know.

Mercator's Solution
The fact that a rhumb is a complex curve on the earth globe was recognized by cosmographers early in the 16th century, but the problem of how to construct a chart that would show rhumbs as straight lines was not solved until 1569. In that year the Flemish cartographer, Gerardus Mercator, published a large world map on a projection he had devised for the purpose of navigation. Instead of spacing the parallels equally, Mercator expanded the distances between them progressively poleward to match the rate at which the spacing of the meridians had been expanded by making them parallel. On a chart made on a Mercator projection any rhumb plots as a straight line with the correct compass angle. Figure 10-4 shows a Mercator map of the same area as Figure 10-3 and the correct compass course, about N 72° E.

Although the projection solved the problem of sailing by the rhumb, it was not adopted immediately. Determining distance on a Mercator chart was more cumbersome than on a Plane chart, and the latter remained in use well into the 17th century. Since then, however, nearly all navigational charts have been made on the Mercator projection.

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