Originally Posted by MarkCK
I guess I am still confused on the minutes. It appears a lot of the ticks on the vernier scale coincide with ticks on the arc.
I agree. Let's consider the image that's at 26°-and-something (attached). I've marked two vernier ticks with red and blue marks. The red-marked tick (6') is clearly too far to the left of the nearest arc tick, and the blue-marked tick (16') is clearly too far to the right of the nearest arc tick. That means that the correct vernier tick must be someplace in between those two, and if your tolerance for "too far to the right/left" is the same in both directions, then the correct tick is probably close to halfway between the red and blue marks (11').
You could just call it 11', but I think that the 12' tick really looks exact, whereas it's harder to judge for the 10' tick. Vernier scales work by relying on the nature of human visual perception, so to some extent you need to rely on a feeling of "clicking" when you see two ticks that line up, and "not quite clicking" when you look at ticks that don't.
I'll just mention the "divergence" issue again. Around 44', the ticks are obviously way, way off (around halfway between the nearest ticks on the arc). As you look to the left, for a while the ticks get closer, but then they get farther away again, and until 16' I think are obviously not close at all. From 6' to 16', on the other, the ticks are all quite close. Because of how the scale is designed, that's always the way it is: you never need to search the entire vernier scale for the right one. The right one will never be right next to a really really wrong one.
The ticks do look like the converge again around 58', but: the 0' tick and 60' tick are always offset from the nearest arc tick by the same amount (again due to the design of the scale). So if the 0' tick is a bit too far to the left, and the ticks converge as you go to the right from 0', then so is the 60' tick.