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 27, 2002.]

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 hundred years.

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 features.

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' sextants.

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.

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 120º.

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 sextant.

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 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.' (Thompson, 137).

[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 true :

Or, to express the same equation another way,

L, is the angular distance from the equator, or in other words, one's latitude.

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 Thompson Navigated".]

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.

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 Century.)

[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 Navigated"]

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.

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 horizon.

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, 104-109).

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.

[Additional 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 west.

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, Seattle. 1994.

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.

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