The core idea is simple: the Earth rotates 360 degrees in 24 hours — Page 422, Lesson 378

All right, let's get into the heart of this. This is the conversion of arc to time, and it's one of the most practical skills you'll use in navigation. The core idea is simple: the Earth rotates 360 degrees in 24 hours. That means in one hour, it rotates 15 degrees of longitude. And in four minutes, it rotates exactly 1 degree. That's the fundamental relationship we're working with. Now, what I'm showing you here is a conversion table. It's a quick-reference tool that lets you convert an amount of longitude, measured in degrees and minutes of arc, directly into time. You'll see the columns are labelled "hour" and "min" — that's hours and minutes of time. Let me walk you through how to read it. Look at the first column. It starts at 0 degrees and goes up. At 0 degrees, the time is 0 hours, 0 minutes. At 1 degree, the time is 0 hours, 4 minutes. At 2 degrees, it's 0 hours, 8 minutes. At 3 degrees, 0 hours, 12 minutes. You see the pattern — every degree of arc adds 4 minutes of time. Now, here's the key detail. Look at the row for 15 degrees. The time is 1 hour, 0 minutes. That's the 15 degrees per hour relationship I mentioned. And you'll see it again at 30 degrees — that's 2 hours, 0 minutes. At 45 degrees, 3 hours, 0 minutes. At 60 degrees, 4 hours, 0 minutes. And so on, all the way up to 360 degrees, which is 24 hours, 0 minutes — a full rotation. But here's where it gets really useful. The table doesn't just handle whole degrees. It also handles minutes of arc. Look at the row for 1 degree and 1 minute — that's written as 1 degree, 1 minute of arc. The time is 0 hours, 4 minutes, 4 seconds. So the 4 minutes for the degree, plus 4 seconds for the minute of arc. Because 1 minute of arc equals 4 seconds of time. Let me show you another one. Look at 1 degree, 15 minutes of arc. The time is 0 hours, 5 minutes, 0 seconds. That's 4 minutes for the degree, plus 1 minute for the 15 minutes of arc — because 15 minutes of arc is a quarter of a degree, and a quarter of 4 minutes is 1 minute. So 4 plus 1 equals 5 minutes. Now, you'll notice the table is organised in blocks. Each block covers a range of degrees. The first block goes from 0 to 15 degrees. The second block goes from 15 to 30 degrees — you'll see it starts at 15 degrees, 0 minutes, which is 1 hour, 0 minutes, and goes up to 30 degrees, which is 2 hours, 0 minutes. Each block adds 15 degrees, which is 1 hour. So if you need to convert, say, 75 degrees of longitude to time, you'd look at the block starting at 75 degrees. You'll see 75 degrees, 0 minutes of arc equals 5 hours, 0 minutes. And 75 degrees, 15 minutes of arc equals 5 hours, 1 minute, 0 seconds. The table goes all the way up to 360 degrees, which is 24 hours. And you'll notice the pattern repeats — 360 degrees is a full circle, and 24 hours is a full day. Now, why does this matter? Because in navigation, you're constantly converting between longitude and time. When you're calculating the time of sunrise or sunset, when you're working out your position from the sun, when you're dealing with time zones — you need to know how much time corresponds to a given difference in longitude. And this table gives you that conversion instantly, without having to do the arithmetic every time. The key numbers to remember are these: 15 degrees of arc equals 1 hour of time. 1 degree of arc equals 4 minutes of time. And 1 minute of arc equals 4 seconds of time. Everything else in the table is built from those three relationships. So when you're using this table, you read the degrees of longitude in the left column, and the minutes of arc in the next column, and then you read across to find the corresponding time in hours and minutes. It's a direct lookup — no calculation needed. That's the conversion of arc to time. It's a tool you'll use again and again, so it's worth getting comfortable with how the table is laid out and how the numbers relate to each other.