Art. IV. Period Navigation, by J. Gottfred.
In which the author describes the general principles of navigation c
1800, so that the beginner may undertake to study the art.
See also "How David Thompson
Navigated" for an in-depth analysis.
[This article originally appeared in "Northwest
Journal Volume III, July, 1995. Some additional comments were added February
For quite some time now I have had a special interest in
re-creating the navigational techniques of Mr. David Thompson. In this article I
will describe the principles and practices used by navigators of his time. I
shall begin with a description of the modern instrument — little changed in two
The Modern Sextant
The modern micrometer drum sextant, available in
various forms, ranging from inexpensive plastic models to high-priced
precision-cast brass models ; all share the same basic construction and
The A-shaped frame is constructed from various
materials. Cast brass has the best thermal stability, and is the choice for
top-of-the-line models ; it is also the only historic material currently
available. Cast aluminum is a popular choice for good quality, reasonably priced
sextants, while plastic is the preserve of inexpensive 'lifeboat' or 'practice'
The rounded lower edge of the frame is called the limb,
and it is cut with one tooth for each degree that the sextant can measure. The
limb is marked with numbers for the degree that each tooth corresponds to. These
numbers are called the arc. On some sextants the arc is a separate plate
attached to the limb.
The index arm is attached to the frame near the top of
the 'A', so that it pivots around that point. The arm is also attached to the
limb by means of a tangent screw attached to the micrometer drum.
By rotating the tangent screw, the index arm can be made to move along the whole
arc of the sextant. To speed up the process when measuring a large angular
distance, a release is provided which lifts the tangent screw off the toothed
limb so the index arm may be swung quickly to a point close to the correct
position. The index arm has a pointer that points to the arc to indicate the
number of whole degrees that the sextant is set to.
The micrometer drum is graduated in minutes of arc, and each
full rotation of the micrometer drum moves the index arm one degree along the
arc. The index arm is marked with a vernier scale so that measurements to
0.2 or 0.1 of a minute can be read.
The index mirror is attached to the pivot point of the
index arm. The index mirror reflects the image of the body you are observing to
the horizon mirror. The horizon mirror reflects the image of the body to
the eye of the observer, while at the same time allowing the observer to see the
horizon through the clear (unsilvered) part of the mirror. The object is to
adjust the index arm (using the micrometer drum) so that the image of the
observed body appears to touch the horizon.
Mounted on the frame between the index mirror and the horizon
mirror are the index shades. Most models have three or four shades in one
or two colors of varying density. These are colored glass filters which are used
to reduce the brightness of the sun or, if the horizon is dim, reduce the
brightness of the moon or a planet relative to the horizon. All modern sextants
contain glass that is designed to shield eyes from the harmful radiation of the
sun. Old sextants may contain smoked glass shades, which are not safe.
Horizon shades are mounted on the frame in front of the
horizon mirror to cut down the glare from the horizon.
An optional telescope is mounted on the frame between
the observer's eye and the horizon mirror. The telescope is not required for
observations, and on a practice sextant you will often find that you get a
better view by removing it. The chief purpose of the telescope is to increase
the light gathering power of the telescope (and so make dim objects seem
brighter), not to magnify the image.
How the Sextant Measures Angles
The sextant measures the angular separation between two
objects by measuring the angle that the index mirror must be at to bring the two
objects into line. To align two objects, the index mirror moves only one-half of
the angular separation of the two objects. This means that although the arc is
one-sixth of a circle (60º) on a sextant, it can actually measure angles up to
The Instruments of Thompson's Time
The first description of a device using two reflecting
mirrors is attributed to Sir Isaac Newton, who, in 1700, sent a description of
such a device to Astronomer-Royal Edmund Halley. This invention, however, did
not become widely known. In 1732, Englishman John Hadley invented a double
mirror device that measured angles up to 90° (Cotter, 81). This device was
called an octant because the limb was one-eighth of a circle (45°). In
1757, a certain Captain Campbell of the Royal Navy suggested the creation of an
instrument with an arc of one-sixth of a circle so that angles of up to 120°
could be measured (Cotter, 81) — and the sextant was born.
Before the invention of the micrometer drum, the arc on
sextants was marked with degrees and thirds of degrees, and a vernier scale on
the index arm was used directly against the arc for determining the minutes. The
arc was so finely marked that a magnifying glass was attached to the index arm
so that the scale could be read. This type of sextant was called a vernier
The standard marine instrument of Thompson's time was a
wooden frame octant, usually made of teak or mahogany. Sextants and quadrants
(one-quarter of a circle, able to measure angles up to 180º) were also
available, in wood or brass.
David Thompson's Instruments
David Thompson describes his equipment :
'My instruments for practical astronomy, were a brass Sextant
of ten inches radius, an achromatic Telescope of high power for observing the
Satellites of Jupiter and other phenomena, one of the same construction for
common use, Parallel glasses and quicksilver horizon for double altitudes ;
Compass, Thermometer, and other requisite instruments, which I was in the
constant practice of using in clear weather for observations on the Sun, Moon,
Planets and Stars...' (Thompson, 89) and,
'My instruments were, a Sextant of ten inches radius, with
Quicksilver and parallel glasses, and excellent Achromatic Telescope ; a lesser
for common use ; drawing instruments, and two Thermometers ; all made by Dollond.'
[For More on Thompson's Instruments, see "The
Life of David Thompson"]
In Thompson's day, latitude was determined by observing the
altitude of a star, planet, or, more commonly, the sun, at the moment of
transit. A body rises in the East, climbs higher and higher in the sky until
it reaches its maximum height above the horizon (the instant of transit),
whereupon it then descends again to the West. Transit observations are also
called meridian altitude or meridian transit observations. The
meridian is the line of longitude that passes though the point directly
overhead (the zenith). When the sun is on the meridian, it is high noon.
To see how this works, let us draw a circle to represent the
earth, then place us at the top. Label this position Z (Zenith). Next, draw a
horizontal line through the center of the earth to represent the horizon, and
then draw the angle that we measured to the height of the body at transit. For
the sun, the standard symbol is a small circle with a dot in the center.
The angle h is the angle between the horizon, and the
sun in the sky. You should also note that the angle h can be assumed to
have been measured from the center of the earth, because the sun is so far away
that we can't measure the difference between taking the measurement on the
surface of the earth or at its center.
If the sun's declination (which is printed in the nautical
almanac) is north 20 degrees, then we know that the sun is north of the equator
by 20 degrees. We can therefore draw the position of the equator, then draw the
position of the north pole (Pn) at right angles to it.
By looking at the diagram you can see that the following is
Or, to express the same equation another way,
L, is the angular distance from the equator, or in other
words, one's latitude.
The Artificial Horizon
The problem that remains is knowing exactly where the
horizontal lies. At sea, the sea horizon is a close approximation. On land, the
terrestrial horizon is useless. The solution to the problem is Thompson's
'quicksilver horizon for double altitudes'. Any liquid will form a level with
the surface of the earth. A measurement of the angle between an object, and its
reflection in the liquid will be twice the angle from the horizontal to
the object. Such a device is called a reflecting artificial horizon, and
the invention of the device is credited to George Adams, in 1738 (Cotter, 92),
for his mercury artificial horizon consisting of a bowl of mercury and a glass
cover to reduce the effect of wind.
Although mercury is the ideal material, due to its high
density and good reflectivity, many other liquids can be used with success. I
use water in a pewter bowl covered with a small pane of glass . Interestingly,
the American Lewis and Clark expedition (1804-1806) also used water.
It should be noted that when using a reflecting artificial
horizon, you are measuring twice the angle from the horizontal to the height of
the body, and therefore an octant is virtually useless. Even with a sextant,
David Thompson would not have been able to observe for latitude during the
height of summer when at latitudes less than about 48°.
[Thompson used another technique called
"latitude by double altitudes" to find his latitude if he missed transit or if
the sun was too high. Details are provided in "How David
Determination of Longitude
Determining longitude is simpler in theory than determining
latitude, but in practice it is much more difficult. The theory is based on the
fact that the earth rotates through 360º in 24 hours, or 15º per hour, or 1° in
four minutes' time. Therefore, If one knows what time it is where one is
standing, and one also knows what time it is in Greenwich (the 0th degree of
longitude), then, by simply taking the time difference and dividing by 15, one
can compute the distance in degrees that one is from Greenwich. For example,
here in Calgary I have measured the time difference to be 7 hours, 36 minutes
behind Greenwich. This corresponds to 114º of longitude west of Greenwich.
Determining the Local Time
To determine the local time, one needs to find the exact time
of local apparent noon. This is the time of solar transit. One way
to determine local apparent noon is to observe the sun's altitude as it
approaches noon. Then, once transit has occurred, find the time in the afternoon
at which the sun again reaches the same altitude that was measured in the
morning. The time of local apparent noon is the difference between the two
times, divided by two. A watch can then be set to show the correct local solar
time. (By applying the equation of time to the observation, the watch can be set
to mean time, as found in the almanacs. The time on your watch right now
is mean zone time, which is an arbitrary invention of the late 19th
[The best way to determine local time is to
make an observation later in the day when the sun is close to the prime
vertical.- a line at right angles to the meridian which passes through the
zenith. This technique requires knowledge of the observer's latitude. Details of
this technique are provided in "How David Thompson
Determining the Time at Greenwich
Determining the time at Greenwich would be straightforward if
one had a good marine chronometer. Such chronometers had been perfected by
William Harrison during the years 1735-1765 (Bowditch, 36). Unfortunately these
devices were large, cumbersome, and suited only to the relatively gentle motions
of a ship at sea. The only watches available for the land navigator were small,
key-wound, pocket-style watches — often without second hands! Such a watch would be
useful for navigation for only short periods of time.
From 1791 to 1796, David Thompson was equipped with a watch
made by Joseph Jolly of London (Nisbet, 37), and costing twelve pounds twelve
shillings (Glover, xxv). He was also the owner of at least two other watches.
Although these were no doubt excellent watches, none would
have been capable of keeping time to the accuracy required to determine
longitude with any certainty for longer than a few days.
To determine the time at Greenwich, Thompson used the
technique of lunar distances. The moon travels thorough 360º in about 23
days, and therefore moves about ½º per hour. If one measures the angular
distance that the moon is from another object on the ecliptic (usually the sun),
applies various corrections, and then refers to a lunar distance table
listing when such a distance would be observed by an observer in Greenwich, it
is possible to determine what time it was in Greenwich at the instant that the
observation was made. As long as one's watch had been set to local time within
the last 12 hours or so, longitude could be determined with an accuracy of about
20 minutes of arc.
I have used this technique myself, and obtained accuracies of
16 minutes of arc. David Thompson's position of Rocky Mountain House is in error
by only 8 minutes of arc.
Correcting for the Refraction of the Atmosphere
As the sun's rays penetrate the atmosphere if the earth, the
light is bent along a curved path by the increasing density of the air. This
bending is called refraction, and is most familiar in the guise of a
straight stick appearing to be bent once it has been partially immersed in
water. Failure to account for this effect would result in an error of around
half a nautical mile (for latitude observations at around 50º North).
For the purposes of computing longitude by lunar distance,
the refraction problem becomes much more serious, as the observations of the
bodies are usually made much closer to the horizon. For bodies within 10º of the
horizon, the refraction correction is about 5 minutes of arc (approximately a
five nautical mile error), increasing rapidly to about 34 minutes at the
In Thompson's time, tables for computing the refraction
correction had been computed by James Bradley (1693-1762). Bradley also provided
a table for computing the correction to be applied to the mean refraction to
account for altitude (atmospheric pressure) and temperature variations (Cotter,
Thompson never provides any insight to what corrections, if
any, he applied to his observations. However, two quotes from his Narrative
are interesting :
'On my journey to the Missourie I had two Thermometers ; On
my return, on a stormy night, one got broke, and the one remaining I had
carefully to keep for my astronomical observations, so that I can only give the
weather in general terms.' (Narrative, 189)
'...the greatest elevation...by the boiling point of water
gave 11,000 feet' (Narrative, 292).
In these two passages, Thompson indicates that he does
measure atmospheric pressure using the boiling point of water, and, that one of
his thermometers was so important for his astronomical use that he dared not
risk breaking it. I think it is likely that he required this thermometer to
compute the local temperature and pressure for applying the appropriate
correction to the mean refraction.
information has since come to light where Thompson states that he ordered 'a
Fahrenheit's Thermometer for correcting the refraction on the celestial Bodies,
which is very erronious [sic] in the Winter occasioned by the great density of
the air,' (Smyth, 6,7)]
The standard method of computing latitude was
by means of double meridian altitude observations of the sun. [Or by means of
"double altitude" observations. See "How David Thompson
Navigated" for details.]
The standard method of computing
longitude was by the method of lunar distances. (A technique involving
observations of the moons of Jupiter was also used for longitude, but this
technique was much less accurate.)
Refraction corrections for mean refraction and local
atmospheric pressure and temperature were known, and were applied.
Using modern methods, I have computed the location of the
center of the courtyard of Rocky Mountain House to be :
N52º 21' 18" Lo 114º 58' 42" West.
David Thompson computed the same spot to be :
N 52º 22' 15" Lo 115º 7' 0" West.
David Thompson's latitude differs by only 0.95 nautical
miles, or 1,700 meters.
Thompson's longitude is 8 minutes 18 seconds of arc farther
For those who are especially interested in the techniques of
those days, please feel free to write to me with your questions. I will also be
giving a workshop on navigation at the Howling Coyote Rendezvous on October 8,
1995 (see Upcoming Events).
Bowditch, Nathaniel, LL. D., American Practical Navigator
An Epitome of Navigation, Volumes I, II. Defense Mapping Agency Hydrographic/Topographic
Center Pub. No. 9. 1984.
Cotter, Charles H. A History of Nautical Astronomy
American Elsevier Publishing Company, Inc. New York. 1968.
Nisbet, Jack. Sources of the River. Sasquatch Books,
Smyth, David. 'David Thompson's Surveying Instruments and
Methods in the Northwest 1790-1812.' Cartographica 18 no. 4 (1981), pp
Thompson, David. David Thompson's Narrative, 1784-1812.
Edited by Richard Glover. The Champlain Society, Toronto. 1962.
Thompson, David. Original manuscript journals, 1792-1802.
Unpublished. Archives of Ontario.