NavList:

Örjan Sandström, you wrote:
"for me when sun rises in mid winter it is roughly 20° east or west of my south (65°N), that means it is never even close to ever being east or west of me."

The trick is clearly not useful in autumn and winter. But try it in spring or summer. Find the time of sunrise on, for example, May 1 in latitude 25°S. That's 90° south of you. On that same day, determine when the Sun reaches the prime vertical in your latitude. They nearly match. It's not a perfect match because of the way sunrise is determined. To see a perfect match, look up the time when the Sun's unrefracted center has an altitude of 0° at latitude 25°S on May 1.

I would note that this is a "neat" trick, but it has very limited practical value. It's no problem calculating these things in the modern world. And historically, if you wanted the time when the Sun was on the prime vertical (for a time sight with significantly uncertain latitude, for example), you could also calculate directly without much effort. Using a sunrise value 90° away in latitude would only be useful in that rare circumstance where you just happen to have sunrise tables for global latitudes but you have no other mathematical tables. 

One last thought: would you ever want to know the true azimuth of the Sun when it's below the horizon. I can think of one use. If you use a polarizer to look at the sky near the zenith after sunset, it will determine the direction of the Sun even if the western part of the sky is obscured by clouds and even if the Sun is below the horizon. So being able to determine the time when the Sun is on the prime vertical below the horizon, as it would be in fall and winter, could have some small practical value.

Frank Reed