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George writes: These are "Vernier" sextants (or "nonius" in some European
languages). There are two scales, one on the main arc, the other on a short
auxiliary arc that differs from the main scale, slightly, in the pitch of
its graduations. What you have to look for is where the rulings between the
two scales align. This provides a precise way of interpolating between
divisions on the main scale. Plath in Germany started to supercede these
instruments with micrometers in 1907, but micrometers didn't appear in English sextants until the late 1920's.

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I thought they were vernier sextants, but since I wasn't allowed to touch, I didn't take a closer look.  I also think that his dating of the quintant as from WW2 isn't correct with the lack of micrometer drum.  I suspect that it is a bit older, but I cannot find any other information after a Google search on the maker other then a sextant from about 1910 in the Mystic Seaport collection.

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George writes:
He mentioned "one quintant (175 deg total)", and  "I see that he  lists his
quintant as a "pentant"." These a valid alternative names for the same
thing; an instrument with an arc-length of a fifth of a circle, that can
measure to 144º. However, I have considerable doubts about the "175 deg
total". No reflecting instrument ever reached nearly such a large angle (in
a single range) that I know of. Indeed, because a Vernier instrument always
must have an added range on the main arc, to allow for the necessary overlap
of the Vernier scale (commonly by 20 º), the working range as always
significantly less than the calibrated arc-length. But usually, even before
that point has been reached, the view in the index mirror, because of its
tilt, has shrunk to a narrow letter-box slot, making the instrument
unusable, or nearly so.

Looking at Jeremy's picture of that quintant, the angle of the
thread-housing for the telescope mount looks a bit odd to me. Is it just a
trick of the angling of his picture, perhaps? But it really doesn't look to
me as if the telescope, when assembled into that holder, is going to point
toward the horizon mirror, as it should.

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There are some more pictures of the scopes attached on the website.  It seems to be aimed correctly.  The dealer, after an email, told me that the arc is marked from 0 to 150 degrees, but there is more arc on either side of the  markings, obviously to cover the vernier.  I was just repeating what the guy posted on the website without being able to verify it. 

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George writes:
The ebony octant looks to be in nice condition, as far as one could tell
from the photo, with all of its joints seemingly tight, and its ivory scale
uncracked. I wonder, though, whether the box it's in is original, or a
modern construction.

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Good eye George!  He does indeed state that the box is custom built in more modern times.  I was surprised how old the octant was considering its condition.

Jeremy