If it's for sighting sunups and sundowns, I can see how the slit would
be necessary.
Normally, the moments of sunrise and sunset are when the tip is visible
on the horizon. Mathematically, you want the moment that the center is
on the horizon. Due to refraction, when the tip is visible, the sun is
actually 0.75 degrees below astronomical sunup or sundown. The ancients
would have realized the problem when summers were 2 to 4 days longer
than winters. A one-day error could throw the Jewish calendar off by a
month.
The slit would let you see the sun when it was optically at the correct
distance above the horizon. When tiny head movements caused it to wink
on both sides of the core, you would be at the correct azimuth.
Ninety percent of American men have an interpupillary distance between
55 and 70mm. If the user had an IP of 62mm and the core of the mystery
item is 86mm, he would stand 250cm (about 9 feet) away to have the core
just block the sun. At that distance, the slit would be 0.2 degree
high. The center of the slit should be 22mm above the observer's eye level.
Sunlight would be visible in the slit about 4 minutes. When the
observer first saw a glint of light, it would be his 2-minute warning.
Just above eye level and 86cm in front of the observer should be a rod
to suspend a plumb bob on a loop. At that distance a degree would be
29mm. The reason for the 86cm distance in front of the observer is that
at that distance, when the string lines up, it will appear tangent to
one side of the ball and then the other as the observer closes one eye
and then the other.
The slit ball design could be thousands of years old, but steel eye
screw makes me think this item was made after published equinox dates
were available anywhere on earth, regardless of the local civil calendar.
In WWII, the British and the Germans had sun-sighting devices to
calibrate compasses on aircraft on the runway. The ancient Vikings set
their compasses that way. The wooden ball looks more precise than would
be needed to calibrate a compass. I wonder if it was for map making.
In Washington's time, surveys were likely to be very poor because
compass readings aren't reliable. Yet accurate maps were drawn long
before Washington. With a slit ball, an explorer wouldn't even have to
know the time or date to determine north within a fraction of a degree.
Then he could get precise bearings with a transit.
It would take four markers, like the bone spacers. The first would go
below the ball. The second would mark the spot from which sundown was
sighted. The third would mark the spot from which sunrise was sighted.
The transit would then be placed over the first marker. It would
bisect the angle between the other two markers in order to place the
fourth marker due north.
If the map maker wedged the spacers in the slit and wrapped the ball
tightly, the ball and spacers should travel well.
I just don't know where to find a picture of a map maker using a split ball!