First, the big idea — Page 449, Lesson 430

Let’s look at what’s actually on this page, because it’s not a paragraph of text — it’s a table of numbers, and it’s one of the most important tables in General Navigation. What you’re seeing is a meridional parts table, and I want to walk you through exactly what it is, how it’s laid out, and how you’ll read it, because you’ll use this for Mercator chart work — specifically for plotting and for solving problems involving true courses and distances on a Mercator projection. First, the big idea. On a Mercator chart, the meridians — the lines of longitude — are drawn as parallel straight lines, and the parallels of latitude are also straight lines, spaced further apart as you move away from the equator. That stretching is deliberate, and it means a minute of latitude on the chart is not a constant length — it changes with latitude. So if you want to measure a distance or work out a course accurately, you can’t just use ordinary latitude minutes. You need a special quantity called meridional parts. Let me define that precisely. Meridional parts are the number of nautical miles of longitude that correspond to one minute of latitude at a given latitude, measured along the meridian on a Mercator chart. In other words, they tell you how many units of longitude spacing you need to represent a given change in latitude, so that the chart stays conformal — meaning angles and shapes are preserved locally. Now, the table itself. Look at the structure. The page is divided into latitude bands, and each band is labelled with a latitude value like N 60, N 50, N 20, N 10, S 10, S 30, S 52, S 60. So the table covers both northern and southern latitudes, from the equator up to 60 degrees. The numbers in the body of the table are the meridional parts values — each one is a number of meridional parts, and they increase as you go to higher latitudes, because the longitude spacing stretches more. Let me show you how to read a specific entry. Take the row labelled N 60. The first value in that row is 21 13. That means at latitude 60° North, the meridional parts value is 21.13 — or more precisely, 21 degrees and 13 minutes of meridional parts. The format is degrees and minutes, just like a coordinate. So 21 13 means 21° 13′ of meridional parts. The next entry is 21 27, then 21 25, and so on — each one is a slightly different value because the table is giving you meridional parts for each minute of latitude within that band. Here’s the key thing about the layout: the table is arranged so that each column corresponds to a specific minute of latitude, and the values increase as you move across the row. For example, in the N 60 row, you see 21 13, 21 27, 21 25, 21 23, 21 20, 21 16, 21 11, 21 06, 21 01, 20 55, 20 48, 20 41, 20 34, 20 27, 20 19, 20 11, 20 03 — and then it drops to 19 55. That drop tells you the row is moving to the next minute of latitude, and the values are decreasing because you’re moving toward the equator — at lower latitudes, the meridional parts are smaller. Now, why does this matter for you as a pilot? Because on a Mercator chart, a minute of longitude is constant — it’s the same length everywhere — but a minute of latitude is not. So if you want to measure a distance along a meridian, you can’t just use the latitude scale directly. Instead, you use the meridional parts difference — the difference between the meridional parts at your starting latitude and your ending latitude. That difference, in meridional parts, is what you use to compute the true course and the distance for a Mercator sailing problem. Let me give you the practical formula, because this is the heart of it. For a course between two points, you compute: - Difference in longitude — the change in longitude between the two points, in minutes. - Meridional parts difference — the difference between the meridional parts at the two latitudes. Then the true course is given by the arctangent of the ratio: difference in longitude divided by meridional parts difference. That gives you the course angle relative to the meridian. And the distance is found by taking the difference in latitude in minutes and dividing by the cosine of the course — because on a Mercator chart, the distance along the rhumb line is the latitude difference divided by the cosine of the course angle. So when you look at this table, you’re not just reading numbers — you’re reading the tools you need to solve those problems. Every entry is a meridional parts value for a specific latitude, and you’ll look up the values for your two latitudes, subtract them to get the meridional parts difference, and plug that into the course formula. Let me also point out the latitude labels again, because they’re easy to misread. You see N 60, N 50, N 20, N 10 — those are northern latitudes. Then you see S 10, S 30, S 52, S 60 — those are southern latitudes. The table is symmetric in the sense that the meridional parts values are the same for a given absolute latitude, whether north or south — because the stretching on a Mercator chart depends only on the absolute value of latitude, not on the hemisphere. So the value at N 60 is the same as the value at S 60. One more thing to notice: the values are not perfectly monotonic — you’ll see small irregularities like 21 27 followed by 21 25, then 21 23. That’s because the table is giving you values for each minute of latitude, and the meridional parts function is smooth but the printed values are rounded to the nearest minute. So don’t be alarmed by the tiny variations — they’re just rounding. Now, let me tie this back to the Mercator projection itself, because that’s the reason this table exists. On a Mercator chart, the meridians are parallel straight lines, and the parallels of latitude are also straight lines, but they’re spaced further apart as you go to higher latitudes. That spacing is exactly what the meridional parts table encodes. The meridional parts for a latitude tell you how many units of longitude spacing correspond to that latitude, so that the chart remains conformal — meaning a rhumb line — a line of constant true course — plots as a straight line on the chart. That’s the whole point: on a Mercator chart, a constant course is a straight line, and the meridional parts table lets you work with that straight line mathematically. So when you’re in the exam or in the aircraft, and you have a Mercator chart and you need to find the true course between two points, you’ll do this: 1. Note the latitudes of the two points. 2. Look up the meridional parts for each latitude in this table. 3. Subtract to get the meridional parts difference. 4. Note the difference in longitude between the two points. 5. Compute the true course as the arctangent of (difference in longitude ÷ meridional parts difference). 6. Then compute the distance as (difference in latitude in minutes ÷ cosine of the course). That’s the complete workflow, and this table is the reference you’ll use every time. Let me also make sure you understand the units clearly. The meridional parts values are in minutes of longitude — technically, they’re the number of nautical miles of longitude that correspond to one minute of latitude at that latitude. So a value of 21 13 at N 60 means that at 60° North, one minute of latitude corresponds to 21 minutes and 13 seconds of longitude — or, equivalently, 21.13 nautical miles of longitude spacing. That’s why the values increase with latitude: at the equator, one minute of latitude corresponds to exactly one minute of longitude — so the value would be 1 00 — but at 60° North, it’s stretched to about 21 minutes of longitude. So the table is essentially a lookup table for the Mercator stretching factor at each latitude. And that’s the key insight: the meridional parts value at a latitude is the cumulative stretching from the equator up to that latitude, measured in minutes of longitude. Now, let me walk you through one concrete read of the table so you’re comfortable with the format. Look at the N 50 row. The first value is 20 13, then 20 12, 20 11, 20 10, 20 08, 20 06, 20 03, 20 00, 19 57, 19 53, 19 49, 19 45, 19 40, 19 35, 19 30, 19 25, 19 19. So at 50° North, the meridional parts start around 20° 13′ and decrease as you move to lower latitudes within that band. The pattern is the same as in the N 60 row — values decrease as you approach the equator. And notice the S 60 row at the bottom: 15 01, 15 04, 15 07, 15 10, 15 15, 15 20, 15 25, 15 30, 15 36, 15 42, 15 49, 15 55, 16 02, 16 09, 16 15, 16 22, 16 29. Here the values are increasing — because you’re moving away from the equator toward the south pole, so the stretching increases. That’s the same behaviour as the N 60 row, just in the southern hemisphere. So the rule is simple: the further from the equator, the larger the meridional parts value. And the table gives you the exact value for every minute of latitude from the equator up to 60 degrees, in both hemispheres. Let me also clarify the format one more time, because it’s easy to misread. Each entry like 21 13 is two numbers separated by a space — the first is degrees, the second is minutes. So 21 13 is 21 degrees and 13 minutes of meridional parts. When you do the subtraction for the meridional parts difference, you’ll be subtracting these degree-minute values, and you’ll need to handle the borrowing correctly — just like subtracting times. For example, if you have 21 13 and 20 03, the difference is 1 degree and 10 minutes — or 70 minutes of meridional parts. Now, one practical tip for the exam: when you’re solving a Mercator sailing problem, you’ll often be given the latitudes and longitudes of two points, and you’ll need to look up the meridional parts for each latitude