Convergency and Conversion Angle — Page 233, Lesson 220

Let's start with the core idea that drives this whole chapter. Meridians are great semi-circles that join the two poles. That's the definition we build everything on. Because they're great semi-circles meeting at the poles, they must converge as they run towards the nearer pole, and diverge as they run away from the nearer pole. Let me walk you through what that actually looks like. Picture two meridians, call them 'x' and 'y', starting together at the North Pole. As they run away from the North Pole, they diverge — they spread apart. They keep spreading until they cross the Equator, and right there at the Equator, they are parallel to each other. Then, as they continue into the Southern Hemisphere, they begin to converge again, finally meeting at the South Pole. So the full picture is: diverge from the pole, become parallel at the Equator, then converge to the opposite pole. Now, let's put some numbers on this. Take two meridians that are 60 degrees of longitude apart. At the Equator, they are parallel — the angle between them is zero. At the Pole, however, they converge at an angle exactly equal to their difference in longitude — in this case, 60 degrees. Why is that? Because there are 360 degrees of longitude — 180 degrees East and 180 degrees West — and a full revolution looking vertically down on the pole is also 360 degrees. So the angle at the pole is simply the difference in longitude. That's the maximum convergence you can get. And here's the key logical step: at some intermediate latitude, there will be an intermediate amount of convergence. The angle of inclination between the two meridians will be more than zero — that's the value at the Equator — but less than 60 degrees — that's the value at the Pole. So convergence is not a constant; it's a function of latitude. Zero at the Equator, maximum at the pole, and somewhere in between at intermediate latitudes. That relationship — between the difference in longitude and the latitude — is exactly what we're going to build on to define convergency and conversion angle. So hold onto this picture: meridians converge towards the nearer pole, diverge away from it, are parallel at the Equator, and the angle at the pole equals the difference in longitude. That's the foundation.