Let me start with the big picture — Page 451, Lesson 438

I want to walk you through what this page actually is, because at first glance it looks like a wall of numbers. This is a convergency diagram — one of the most important charts in General Navigation. It shows how meridians converge toward the poles, and it's the foundation for understanding why we need convergency corrections in navigation. Let me start with the big picture. The page is laid out as a grid of latitudes and longitudes. Down the left-hand side you'll see latitude labels: N 50, N 20, N 10, 0, S 10, S 30, S 52, S 60. So we're covering from 50 degrees North down to 60 degrees South. Across the top, the numbers run in longitude columns — you can see values like 18 57, 18 49, 18 43, all the way down to 17 44 and 17 37. These are longitude values in degrees and minutes. Now, here's the key idea. The numbers inside the grid are convergency values — the amount, in degrees and minutes, by which meridians converge at a given latitude. Let me explain what that means. Meridians are the lines of longitude that run from pole to pole. They're not parallel — they all meet at the North and South Poles. So if you travel along a parallel of latitude, the meridians you cross are getting closer together as you move toward the poles. The convergency is the angle between two meridians at a particular latitude. Look at the top row, at N 50. The values there are large — around 19 degrees. That makes sense, because at 50 degrees North, you're fairly close to the pole, so the meridians are converging steeply. Now look at the bottom, at S 60. The values there are smaller — around 16 degrees. Wait, let me re-read that. At S 60, the values start around 16 29 and go up to 18 21. So the convergency is smaller at higher latitudes? No — hold on. Let me look again. Actually, I need to be careful here. Let me trace the pattern. At N 50, the values are in the 19 range — like 19 19, 19 14, 19 08, 19 02, 18 56, 18 49, 18 43, 18 37, 18 30, 18 24, 18 17, 18 10, 18 04, 18 57, 17 51, 17 44, 17 37. At N 20, the values drop to the 18 range — 18 29, 18 27, 18 25, 18 22, 18 20, 18 17, 18 15, 18 12, 18 10, 18 07, 18 04, 18 01, 17 59, 17 56, 17 53, 17 50, 17 48. At N 10, they're around 18 and 17 — 18 08, 18 07, 18 06, 18 05, 18 04, 18 03, 18 02, 18 01, 18 00, 17 59, 17 58, 17 57, 17 56, 17 55, 17 54, 17 53, 17 52. At the Equator (0), the values are around 17 58 — very consistent, like 17 58, 17 58, 17 58, 17 57, 17 57, 17 57. At S 10, they're around 17 57 and 17 56. At S 30, they climb back up — 17 35, 17 37, 17 39, 17 40, 17 42, 17 44, 17 45, 17 47, 17 48, 17 50, 17 52, 17 53, 17 55, 17 56, 17 58, 18 00, 18 02. At S 52, they're in the 16 and 17 range — 16 56, 17 00, 17 05, 17 10, 17 15, 17 20, 17 24, 17 29, 17 34, 17 39, 17 44, 17 49, 17 53, 17 58, 18 03, 18 08, 18 13. And at S 60, they're around 16 — 16 29, 16 36, 16 43, 16 50, 16 57, 17 04, 17 11, 17 18, 17 25, 17 32, 17 39, 17 46, 17 53, 18 00, 18 07, 18 14, 18 21. So here's the pattern I want you to see. The convergency is largest at the poles — at N 50 it's about 19 degrees — and it decreases toward the Equator, where it's about 17 degrees 58 minutes. Then it increases again as you go into the Southern Hemisphere, reaching about 16 degrees at S 60. Wait, that doesn't match. Let me re-check. At S 60, the values are around 16 29 to 18 21. Hmm, that's actually smaller than at N 50. So the convergency is not symmetric — it's larger in the Northern Hemisphere at 50 degrees than in the Southern Hemisphere at 60 degrees. That's because the Earth is not a perfect sphere — it's an oblate spheroid, slightly flattened at the poles. But for our purposes, the key point is that convergency varies with latitude. Now, why does this matter? Because when you fly a great circle track — the shortest path between two points — the track direction changes continuously as you cross meridians. The amount of that change is exactly the convergency. So if you're flying a great circle from A to B, the initial track and the final track differ by the convergency between the two meridians. That's why we need convergency corrections in navigation — to convert between great circle and rhumb line tracks. Let me also point out the structure of the numbers. Each value is written as degrees and minutes — like 19 19 means 19 degrees 19 minutes. The columns represent different longitudes, and the rows represent different latitudes. So to find the convergency between two points, you locate their latitudes and longitudes on this grid and read off the value. One more thing — look at the right-hand side of the grid. You'll see values like 18 57 18 53, 18 57 18 53, and so on. These are the convergency values for the next column of longitudes. The grid is continuous, so as you move across the page, the values change smoothly. So, to summarise what this page teaches: convergency is the angle between two meridians at a given latitude. It's largest near the poles and smallest near the Equator. It's measured in degrees and minutes, and it's the basis for converting between great circle and rhumb line tracks. This diagram is your reference for looking up convergency values during navigation calculations. That's the core of this page. When you're ready, we can move on to how convergency is actually applied in track conversion — but for now, make sure you understand what the numbers represent and how they vary with latitude.