NavList:

Greg,

You wrote:
"Please help me understand the 'instrument time line'. What is the angular resolution of a cross-staff or back-staff? I always thought it was about +/- a degree"

I would say a bit better than that is reasonable. Half a degree is probably normal while +/-10' is possible with a good instrument and a skilled observer. Do you have a cross-staff in your collection of reproduction instruments, Greg?

And you asked the key question:
"and if that's true why would you care about 1 arc minute?"

Previously I characterized these tables as "advice for future navigators". You're quite correct that they had no real practical value before the first double-reflecting instruments were widely available, starting around 1740. So that early dip table is far ahead of its time. This is a common story in the history of navigation. You can find advice from well-meaning shorebound mathematicians that greatly exceeds the observational limits of the era. Even today we have to worry about this. But, you know how it goes... you make a lovely table of dip values calculated from some very clever mathematics... how can you resist publishing it?!

-FER

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