Let me start with the core idea — Page 444, Lesson 417

I want to walk you through what's actually on this page, because at first glance it looks like a wall of numbers — but this is one of the most important reference tables you'll use in general navigation. This is a meridional parts table, and it's the tool that lets us convert a difference in latitude into the correct distance along a meridian when we're working with a Mercator chart. Let me start with the core idea. On a Mercator chart, the meridians — the lines of longitude — are drawn as parallel straight lines. That's the whole trick of the projection: it keeps the lines of longitude parallel so that a straight line on the chart is a constant true course, which we call a rhumb line. But there's a price. Because the meridians are pulled parallel when on the globe they converge at the poles, the scale of the chart has to stretch as you move away from the equator. The spacing between parallels of latitude — the horizontal lines — has to increase to keep the shapes correct. So one minute of latitude on the chart is not the same physical length everywhere; it grows as latitude increases. That's where meridional parts come in. A meridional part is the number of nautical miles, measured along the meridian, that corresponds to one minute of latitude on a Mercator chart, expressed relative to the equator. The table gives you, for any latitude, the accumulated value of these parts from the equator up to that latitude. The difference between the meridional parts of two latitudes is called the meridional difference, and that's the number you plug into your calculations to find the true distance or the course when you're working a Mercator problem. Now let me actually read this table with you, because the layout is specific. Look at the left-hand column. You'll see latitudes running from N 50 down through N 20, then N 10, then S 10, S 30, and so on down to S 60. The N and S tell you the hemisphere — north or south of the equator. The numbers running across the top — 0, 5, 10, 16, 22, 27, 33, 38, 43, 49, 54, 59 — those are the minutes of latitude beyond the whole degree. So the table is arranged so that you pick your whole degree of latitude from the left column, then your extra minutes from the top row, and where they intersect is your meridional parts value. Let me give you a concrete example so you see how to read it. Take latitude N 50 degrees 18 minutes. Go down the left column to N 50, then across the top to 18 minutes. The value at that intersection is 33 18. That number, 33 18, is the meridional parts for 50 degrees 18 minutes north. The format is degrees and minutes of meridional parts — so 33 degrees and 18 minutes of meridional parts. That's the accumulated value from the equator up to that latitude. Here's another one. Take N 20 degrees 14 minutes. Down to N 20, across to 14 minutes, and you get 18 14. And notice something important: the meridional parts value at N 20 is much smaller than at N 50. That's exactly the stretching I mentioned — the higher the latitude, the larger the meridional parts, because the chart scale has expanded more. Now let's look at the southern hemisphere rows, because they work the same way but with a twist. Take S 10 degrees 3 minutes. Down to S 10, across to 3 minutes, and you get 18 02. And S 30 degrees 0 minutes gives you 17 56. Notice the values are still positive and they still increase as you go further from the equator — S 60 has larger values than S 30. The S just tells you it's south of the equator; the meridional parts accumulate from the equator in both directions. Let me trace one full row so you see the progression. Look at the S 30 row. At 0 minutes you have 17 56. As the minutes increase — 1, 2, 3, 4, 5 — the values climb: 17 53, 17 49, 17 46, 17 42, 17 39. Each additional minute of latitude adds a little more to the meridional parts. That's the key behaviour: the rate of increase itself grows with latitude, which is why the numbers climb faster at S 60 than at S 10. Let me show you that contrast directly. At S 10, going from 0 to 5 minutes, the values go from about 18 00 up to 17 54 — a change of about 6 minutes of meridional parts over 5 minutes of latitude. Now look at S 60: from 0 to 5 minutes, the values go from 17 36 down to 17 27 — wait, let me re-read that. At S 60, 0 minutes gives 17 36, and 5 minutes gives 17 27. That's a change of 9 minutes of meridional parts over the same 5 minutes of latitude. So the same 5 minutes of latitude produces a bigger change in meridional parts at S 60 than at S 10. That's the Mercator stretching made visible in the numbers. Now, why does this matter for your navigation? When you're solving a Mercator problem — say you know the true course and the difference of longitude, and you want the distance, or you know the positions and want the course — you use the meridional difference. You take the meridional parts for your two latitudes, subtract the smaller from the larger, and that difference is the meridional difference. That value, combined with the difference of longitude, lets you find the course angle using the relationship that the tangent of the course equals the difference of longitude divided by the meridional difference. And once you have the course, you can find the distance using the difference of latitude and the secant of the course. So this table is not just a list of numbers — it's the bridge between the curved geometry of the Earth and the flat geometry of the Mercator chart. Every time you see a value like 18 51 or 17 08 or 16 04 in this table, you're looking at the accumulated meridional parts for a specific latitude, and the difference between any two of them is the meridional difference you'll use in your calculations. One more thing to notice about the layout. The table is split into blocks, and within each block the minutes run across the top and the whole degrees run down the side. So for any latitude, you always have two coordinates to find: the whole degree from the left column and the minutes from the top row. The value at the intersection is your meridional parts, always expressed in degrees and minutes of meridional parts. That's the essence of this page. It's a reference table, so you won't memorise the numbers — you'll learn to read it quickly and accurately, because in an exam or in flight planning, a misread here means a wrong course or a wrong distance. Take a moment to trace a few values yourself: find N 50 degrees 18 minutes again, find S 52 degrees, find N 20 degrees 14 minutes. Get comfortable with the grid, because everything else in Mercator navigation builds on this table.