NavList:

I propose the following explanation:
the angle of inclination of the Index glass
to the arm is determined from the following condition:
that the arm is vertical when you measure the angle of
60 degrees.
Indeed, 60 degrees is the middle of the range of a typical
sextant. As a result of such choice,
the ark is symmetric with respect to a  vertical line
(the line through the pivot and the 60 degree mark).
Otherwise the arc will have no vertical axis of symmetry,
the sextant will look and feel unbalanced.

Alex

P.S. Recently I found experimentally another interesting
restriction on the sextant design.
The angle of inclination of the horizon glass cannot be too
small. Indeed. imagine that this angle were 45 d.
Then the ray from the Sun at 90 d will reflect to the scope
BYPASSING the index glass. Which of course whould be
prevented. I found this trying to do back observations.
At 125 degrees, I see two images of the Sun: one in the normal
way, another, nearby and much brighter,
obtained by a single reflection in the horizon glass.

The angle of inclination of the horizon glass also cannot be too
large, so that the telescope does not interfere
between the index and horizon glass. I believe the design
was optimized at an early stage using all these restrictions
and other restrictions mentioned by George.

The geometric layout essentially did not change since the
very first sextants by Bird.

A


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