Let me unpack that — Page 422, Lesson 379

Let me walk you through what this table actually is, because it looks like a wall of numbers at first glance, but it's doing something very specific and very useful. This is an arc-to-time conversion table. What that means is it converts an angle, measured in degrees and minutes of arc, into its equivalent in time — hours and minutes. The reason we can do this at all is that the Earth rotates 360 degrees in 24 hours. So 15 degrees of arc equals 1 hour of time, 1 degree equals 4 minutes of time, and 1 minute of arc equals 4 seconds of time. That's the whole principle sitting underneath this table. Now, the stated main use in this Almanac — and this is the key sentence — is the conversion of longitude for application to L.M.T. Let me unpack that. L.M.T. stands for Local Mean Time. The idea is that longitude, which is an arc measured in degrees east or west of the Greenwich meridian, can be converted into a time difference. And that time difference is what you apply to Local Mean Time to get UT — Universal Time — or the other way around. Here's the rule you need to hold onto: you add the longitude time if you are west, and you subtract it if you are east. So if you're west of Greenwich, your Local Mean Time is behind UT, so you add the converted longitude to L.M.T. to get UT. If you're east, your L.M.T. is ahead, so you subtract. And the table's particular practical use, as stated, is in the case of sunrise, sunset, and similar events — because those are published in UT, and you need to convert to your local time, or vice versa, using your longitude. Now let me actually teach you how to read the table, because the layout is the tricky part. Look at the first column of numbers. You'll see entries like 6, then 264, then 17, then 36. Let me decode that pattern for you. The first number, 6, is the degrees of arc. The second number, 264, is the minutes of arc — wait, that can't be right, 264 minutes is over 4 degrees. Let me re-read it. Actually, look more carefully. The pattern is: 6, 264, 17, 36. I think what's happening is the table is giving you, for each degree value, the equivalent time. So 6 degrees of arc converts to 24 minutes of time — because 6 times 4 minutes per degree is 24 minutes. And 264 — hmm, that doesn't fit a simple pattern. Let me look at the structure differently. I see entries like 30, 2, 00. That reads as: 30 degrees of arc equals 2 hours and 00 minutes of time. That works — 30 degrees times 4 minutes per degree is 120 minutes, which is 2 hours exactly. And I see 45, 3, 00 — 45 degrees equals 3 hours, which is correct, because 45 times 4 is 180 minutes, or 3 hours. And 90, 6, 00 — 90 degrees equals 6 hours, correct again. So the table is organized in blocks. Each block starts with a degree value, then gives the time equivalent as hours and minutes. For example, the block for 30 degrees gives 2 hours 00 minutes. The block for 31 gives 2 hours 04 minutes — 31 degrees times 4 is 124 minutes, which is 2 hours 4 minutes. The block for 32 gives 2 hours 08 minutes. And so on, each degree adding 4 minutes. Now, what about the minutes of arc? Look at the entries like 264, 17, 36. I believe the structure there is: 264 minutes of arc — no. Let me re-read. I see 6, 264, 17, 36. I think the first number 6 is degrees, and then 264 — that's too big for minutes. Actually, I think I'm misreading the column layout. Let me look at the repeating pattern: 85, 5, 40, then 145, 9, 40, then 205, 13, 40, then 265, 17, 40, then 325, 21, 40. So we have 85, 5, 40. Then 145, 9, 40. The difference between 85 and 145 is 60. The difference between 5 and 9 is 4. And 40 stays constant. So I think the structure is: the first number is the arc in degrees, the second is the time in hours, and the third is the time in minutes. So 85 degrees equals 5 hours 40 minutes. Check: 85 times 4 is 340 minutes, which is 5 hours 40 minutes. Correct. 145 degrees equals 9 hours 40 minutes. Check: 145 times 4 is 580 minutes, which is 9 hours 40 minutes. Correct. 205 degrees equals 13 hours 40 minutes. 205 times 4 is 820 minutes, which is 13 hours 40 minutes. Correct. So the table reads: arc in degrees, then time in hours, then time in minutes. And it covers the full range — I see it going from small values like 6 degrees up through 359 degrees, which is 23 hours 56 minutes. That makes sense because 359 degrees times 4 minutes per degree is 1436 minutes, which is 23 hours 56 minutes. And 360 degrees would be 24 hours exactly, the full rotation. So the table gives you, for any longitude expressed in degrees, the equivalent time directly. You look up your longitude in the first column, and the table gives you the hours and minutes to apply. Now, one thing I want to be honest about: this excerpt is the raw table data, and the surrounding text is minimal. The key stated facts are: it converts arc to time, its main use is longitude conversion for L.M.T., you add if west and subtract if east to get UT or vice versa, and it's particularly used for sunrise and sunset calculations. The table itself is reproduced by permission of Her Majesty's Stationery Office — that's just a copyright note, not something you need to memorize. So the practical skill here: when you have a longitude, say 85 degrees west, you look up 85 in the table, get 5 hours 40 minutes, and because you're west, you add that to your Local Mean Time to get UT. If you were 85 degrees east, you'd subtract it. That's the whole operation. Does that make sense? The table is essentially a lookup so you don't have to multiply by 4 every time — it's pre-computed for every degree from 0 to 359.