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Greg, George H. wrote:
"Greg hasn't (yet) told us at what angle his plastic plate should be held. It 
doesn't matter (much) for his present small angles, but it will become more 
important as angles increase. Should it be held vertical, at right angles to 
the observer's sight-line to the horizon?"

This is a good point. I have assumed that you're holding the plate 
perpendicular to the tape measure. Is there some way to guarantee that? In a 
traditional cross-staff, the design ensured that the cross-piece was very 
close to perpendicular to the staff.

And he wrote:
"So, the dimension that needs to be measured, if the tan formula is going to 
work, is between the cross-piece (or plastic plate) and the centre of the 
eyeball. Not a practical proposition, obviously, but what is the best that 
can be done? There's a notch in the edge of the skull-bone, just close to the 
side of the eye, which isn't far from a plane drawn through the centre of the 
eyeball. Just the spot where the user of a cross-staff would press the end of 
the staff. There was much argument, then, about whether different individuals 
should shave off a suitable amount from the staff, appropriate to their own 
eye-socket dimensions."

This is what I was getting at about not knowing the exact length of the 
baseline. But rather than try to figure it out theoretically, we today, with 
our experience with sextants, can treat this as a calibration question 
comparable to checking index error, or maybe arc error, in a sextant. You 
measure a series of known angles, possibly with the plate clamped onto a 
fixed mounting, and then find whatever additional length added to the 
observed baseline yields minimal error in the observations. You can then hold 
the end of the tape (or the end of the staff in a cross-staff) wherever you 
find comfortable, as long as it's repeatable, and then add in that "index 
correction" distance to every observed baseline.

And George wrote:
"in this aspect, the cross-staff wins, hands-down, on convenience, being 
direct-reading. You read the angle straight off, marked on one of a number of 
scales, each dependent on the chice made from a range of transoms of varying 
lengths."

Once it's calibrated, the angle conversions could be printed up in a small 
table, one for each of the three horizontal lines. The slide rule would save 
you an interpolation step if the printed table isn't fine enough.

Crossing the threads and tangling them up a little, why didn't those 
Polynesian navigators a thousand years ago ever invent the cross-staff? Is it 
possible that the "dead reckoning" cues in the tropical Pacific, things like 
bio-luminescence, are so much better there than in the Atlantic that 
Polynesian navigators simply never had any practical reason to go beyond the 
tools of dead reckoning (and possibly basic zenith stars)?

-FER



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