NavList:

From: George Huxtable <george@hux.me.uk>
Subject: [NavList 6728] Re: sextants on aeroplanes
To: NavList@fer3.com
Date: Saturday, December 13, 2008, 8:27 AM

Gary LaPook wrote in [6658]-

"There is a distinction between sextants, octants and quadrants. Because
of the double reflection operating principle of the marine instruments
it is possible to measure an angle of  90º, one quarter of a circle,
with an instrument having a calibrated arc of only one-half that, 45º,
one-eight of a circle, an instrument called an octant.
 If the arc is one-sixth of a circle, a sextant, you can measure angles
up to 120º and if the arc is one-quarter of a circle then you can
measure an angle of half of a circle, 180º, and you then have an
instrument called a quadrant."

========================

In trying to resolve these matters, I fear that Gary has added to the 
confusion. Historically, instruments which could measure up to 90º, were 
known as "quadrants". That applied to instruments without a mirror,
which 
then required an arc of 90º, and, also
 later, to Hadley's 2-mirror 
invention, which did the same job with an arc of only 45º. It was called a 
reflecting quadrant, a Hadley quadrant, or sometimes just a "Hadley".

A bit later, the working range was extended to 120º, which required an arc 
of 60º, and that being a sixth of a circle, it was christened a
"sextant".

(Later still, a few instruments were made with a range extended to 144º, and 
an arc of 72º, known as "quintants")

But all this was logically inconsistent with the use of the word
"quadrant", 
for an intrument measuring to 90º, so those instead became known as 
"octants", because their arc was an eightth of a circle. There is no 
difference at all between a reflecting quadrant and an octant; they are two 
names for the same thing.

So Gary is wrong when he writes-

"Quadrants must be made larger than sextants which are larger than
octants. An octant is sufficient
 to measure any angle from horizontal to
straight up so can be use for normal celestial navigation and this is
how they are used in aircraft. Sextants and quadrants allow a greater
range of measurement which might be useful for lunar distance
measurements, horizontal sextant angles for coast wise navigation and in
the rare case of a body within 30º of the zenith with an obstructed
horizon below it but a clear horizon in the opposite direction in which
case the navigator could turn his back to the star and use the opposing
horizon for the sight. (I don't know if this was ever actually done in
real life.) Since these types of sights are never taken from an aircraft
it is never necessary to have more than an octant on an aircraft. My
tamaya sextant actually measures up to 125º and my SNO-T goes all the
way to 140º but these are both sextants."

The first account I have read of that trick of measuring up from the
 
opposite horizon was on the Malaspina exploration, near Callao, in 1790, 
when the morning Sun was visible to the West, but the horizon beneath it 
couldn't be seen because of the nearby coast (a dip-short situation, 
really). Usually, if you're close to visible land, celestial navigation 
isn't called for: except when, as here, surveying an unknown coast. 
Malaspina was pleased to have, in his kit, an early quintant, perfect for 
such a task.

Gary's SNO-T sextant, measuring up to 140º, is only 4º short of being a
true 
quintant. Quintants were mostly used by hydrographic surveyors, to measure 
wide horizontal angles. Lecky, in his "Wrinkles", was keen to push
quintants 
for navigators, but I've never really understood why. I wonder if, when
Gary 
wrote "Quadrants must be made larger than sextants which are larger than 
octants.", he was thinking of quintants rather than quadrants.

However,
 in writing "if the arc is one-quarter of a circle then you can 
measure an angle of half of a circle, 180º, and you then have an instrument 
called a quadrant", he was describing a device which, as far as I know,
has 
never existed. Not that it's impossible, necessarily. I've been
pondering a 
scheme which might allow a two-mirror reflecting instrument to measure 
angles up to 180º, which would allow wall-to-wall observations from one 
horizon to the opposite one, and so allow dip to be measured. More about 
that later, unless it turns out to be nonsense.

George.

contact George Huxtable, now at george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.