Let me walk you through what this chapter is built from — Page 422, Lesson 381

This is the start of Chapter 26, "Time (3)" — and it's really the chapter that ties the Sun's motion to the practical navigation problems you'll solve on paper. Let me walk you through what this chapter is built from. The chapter opens with a contents list, and I want you to see the skeleton of it, because it tells you exactly what skills you're about to build. First there's "Sunrise and Sunset" on page 421 — that's the theory of when the Sun actually appears and disappears at a given place. Then "Sunrise and Sunset Tables – Methodology" on page 422 — that's the practical procedure, the step-by-step way you use published tables to compute those times. Then "Twilight" on page 424 — that's the period of partial darkness before sunrise and after sunset, and it has its own definitions and rules. After that come two sets of practice questions, pages 430 and 431, with answers on 433, and finally an "Air Almanac Extract" on page 436 — that's the actual reference data you'll be reading from. So the whole chapter is a progression: understand the geometry of sunrise and sunset, learn the table method, then handle twilight, then drill it with questions using a real almanac extract. Now, the key idea I want you to hold onto before we even open the tables. Sunrise and sunset are not just "when the Sun is up." They're defined by the position of the Sun's upper limb — the top edge of the solar disc — relative to the visual horizon. At sunrise, the top edge of the Sun first appears above the horizon. At sunset, the top edge has just passed below the visual horizon. That's the precise definition you'll be working with, and it matters because the Sun's disc has a real angular diameter, and the atmosphere refracts light, so the geometric centre of the Sun is actually below the horizon at the moment we call sunrise or sunset. The tables and the almanac are built around that definition. And that leads straight into twilight. Twilight is the interval when the Sun is below the horizon but the sky is still partially lit. The chapter will define its phases — and the key distinction you'll need is between the different types of twilight, which are set by how far the Sun's centre has sunk below the horizon. That's the core of page 424. Let me also point you to the figures on page 432, because they show this beautifully. shows the situation at sunset at a position A, where the top edge of the Sun has just passed below the visual horizon — that's the exact moment of sunset as defined. And is the same scene labelled as Figure 26.4, "Twilight 1" — it's the same geometry, but now you're looking at the onset of twilight. Then on page 433 there's a figure marked "Case (ii)" — that's a second scenario, a different geometric case you'll need to distinguish when you're working the problems. So here's how I want you to think about this chapter as a whole. You're learning to answer one practical question: given a date and a position on the Earth, at what time does the Sun rise, at what time does it set, and how long is twilight? The answer comes from the Air Almanac extract and the table methodology. The definitions of sunrise, sunset, and twilight are the foundation — get those precise, and the table work becomes mechanical. Let's start with the sunrise and sunset theory on page 421, and I'll build the geometry with you from the ground up.