Mercator Charts - Properties — Page 297, Lesson 262

I want to walk you through the properties of Mercator charts, starting with the problem that Mercator himself had to solve. Look at Figure 18.1 — you'll see the shapes on a simple cylindrical projection are stretched in a north-south direction. Mercator realised this stretching happened because the simple cylindrical projection failed to meet the second requirement of orthomorphism, or conformality. Let me define that precisely: orthomorphism, also called conformality, means that at any point on a chart, the scale should be the same in all directions, or should change at the same rate in all directions. On the simple cylindrical projection, the north-south scale was changing at a different rate from the east-west scale, and that's what caused the distortion. Mercator worked out exactly how the scales were changing. He determined that the east-west scale was changing such that, at any latitude, the scale was proportional to the secant of the latitude. Secant is simply 1 divided by the cosine of the angle — so secant of latitude equals 1 over cosine of latitude. But the north-south scale was changing such that, at any latitude, the scale was proportional to the tangent of the latitude. Because these two rates were different — secant versus tangent — the shapes got stretched north-south. You can see this in Figure 18.2, where the latitude spacing is a function of tan(lat). So how did Mercator fix it? He solved the problem by adjusting the positions of the parallels of latitude. On the simple cylindrical projection, the parallels had been projected as parallel lines, with the separation between them increasing in proportion to the tangent of the latitude. Mercator adjusted the parallels so that their separation increased only at a rate proportional to the secant of latitude — matching the east-west scale change. In short, he mathematically adjusted the positions of the parallels of latitude to make the chart orthomorphic, or conformal. Because the chart has been mathematically produced — not drawn by projecting light through a globe onto a flat surface — it is a non-perspective chart. There is no single viewpoint or projection point; it's a calculated construction. Mercator solved this problem in 1569. His solution was so simple, elegant, and correct that we still use his projection today, over 400 years later. A modern Mercator chart looks very different from his own because we have subsequently discovered and explored so many more countries. But the basic principles of the graticule — the network of meridians and parallels — have not changed. He got it right. An example of the adjusted Mercator projection is given in Figure 18.3, which you can see on screen now.