Let me walk you through what you're looking at — Page 444, Lesson 417

This is a page from the General Navigation manual that looks like a data table, but it's actually one of the most important tools you'll use in flight planning. Let me walk you through what you're looking at. What you have here is a convergency table — a grid that gives you the convergency value between two meridians for a given latitude. Convergency is the angle at which two meridians meet at the pole. At the equator, meridians are parallel, so convergency is zero. At the pole, all meridians converge to a point, so convergency equals the change of longitude. The table lets you read that value off for any latitude without doing the math. Look at the structure. The left-hand column is labelled with latitudes — N 50, N 20, N 10, S 10, S 30, S 52, S 60 — and the top row is labelled with longitudes, 4, 37, 42, 48, 54, 18, 59, and so on. The body of the table is filled with numbers like 18 33, 18 37, 18 42, 18 47. Those are the convergency values in degrees and minutes. So at N 50, between longitude 4 and longitude 37, the convergency is 18 degrees 33 minutes. Now, here's the key thing about how this table works. The top row gives you the change of longitude — the difference between your two meridians. The left column gives you the latitude. You find your latitude row, you find your change of longitude column, and where they intersect is your convergency. So if you're at N 50 and your change of longitude is 18 degrees, you read across the N 50 row and find the value under the 18 column — that's your convergency. Let me show you how the numbers behave. Look at the N 50 row. As the change of longitude increases from 18 to 19 to 20, the convergency values climb — 18 33, 18 37, 18 42, 18 47, 18 51, 18 56, 19 01, 19 06, 19 10, 19 15, 19 19, 19 24, 19 29, 19 33, 19 37, 19 41, 19 45. So more change of longitude means more convergency. That makes sense — the further apart your meridians are, the bigger the angle between them at the pole. Now look at what happens as latitude changes. Compare the N 50 row with the S 60 row. At S 60, for the same change of longitude, the convergency values are smaller — 17 36, 17 27, 17 18, 17 09, 17 01, 16 52, 16 43, 16 35, 16 27, 16 19, 16 11, 16 03, 15 56, 15 49, 15 42, 15 36. So at higher latitude, convergency is less for the same change of longitude. That's the opposite of what you might expect, but it's correct — the table is giving you convergency values that already account for the latitude effect. Here's the critical thing to understand about this table. The convergency value you read off is not the change of longitude. It's the convergency — the angle between the meridians at the pole. And the relationship is: convergency equals change of longitude times the sine of the latitude. That's the formula this table is built on. So at the equator, where sine of latitude is zero, convergency is zero. At the pole, where sine of latitude is one, convergency equals change of longitude. The table gives you the intermediate values. Now, why does this matter for navigation? Convergency is what causes great circle tracks to curve on a Mercator chart. When you fly a great circle, your track crosses meridians at changing angles, and the difference between your initial and final track angles is exactly the convergency. So when you're planning a great circle route, you use this table to find the convergency between your departure and destination meridians, and that tells you how much your track angle changes along the route. Let me read you a few specific values so you can see the pattern. At N 20, between longitude 18 and longitude 19, the convergency is 18 14. At N 10, between longitude 18 and longitude 19, it's 18 04. At the equator, N 0, between longitude 18 and longitude 19, it's 18 00. And at S 10, between longitude 18 and longitude 19, it's 17 59. So you can see the convergency decreasing as you move away from the pole toward the equator. One more thing to notice. The table has a column for change of longitude values that go up in steps — 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and so on. And the convergency values are given in degrees and minutes, like 18 33 meaning 18 degrees 33 minutes. So when you read a value, you're getting the full precision — degrees and minutes, not just whole degrees. That's the convergency table. It's a quick reference that saves you from doing the sine calculation every time. You find your latitude, you find your change of longitude, and you read off the convergency directly. That convergency value is what you'll use when you're working out great circle tracks and track angle changes on your navigation charts.