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  The American Surveyor     

The Mapping of Western North America Print E-mail
Written by Geoff Miller   
Tuesday, 09 July 2013

Editor's note: The author of this article has also contributed two other articles to our Online-Only area. One of them, Long Term Almanac, or, what to do when you can't use your total station and GPS has received more hits (21K+) than any other article in this area. The author also has a new book, Conestoga Highways, which has a surveyor as the protagonist, available from Amazon Kindle.

I. The Beginning
The canoe glided silently through the still waters of the great lake. As the birch bark craft neared the shoreline, one of the occupants leapt out and pulled it onto the rocky beach. He held it steady while his colleague debarked carrying a box of sensitive instruments.

The two men had been travelling for the past year, paddling and portaging through 1600 miles of wilderness. They were English, and each had initially been sent to North America to a small settlement known as York factory on the southwestern shore of Hudson’s Bay. It was now mid-July 1791, and the place they had labored so long to attain was on the northwestern shore of Lake Athabasca, at the mouth of the Slave River. A huge inland sea, the lake straddles what is now the far northern segment of the border between Saskatchewan and Alberta.

Thirteen years earlier, while British colonies along the eastern seaboard of North America were embroiled in a desperate war for independence, another explorer, Peter Pond, had been the first person of European descent to set foot in the cold, rugged Athabasca wilderness. Pond was Canadian, and at the time he represented a loosely conjoined group of fur traders based in Montreal. By 1780, that group coalesced to become the powerful ‘North West Trading Company’. The Nor’westers were a dynamic, adventuresome lot who pushed far into the wilds of western Canada in aggressive attempts to capture market share in the lucrative fur trade.

The two men now standing on the shore of Lake Athabasca worked for Pond’s competition; an established and venerated enterprise named the Hudson’s Bay Company (HBC). HBC was based in London and had enjoyed nearly monopolistic control of the Canadian fur trade for more than a century. As the upstart Nor’westers became a serious economic threat, the HBC soon realized that it must either expand into new fur-rich territory, or remain content with more meager returns from the nearly trapped-out regions along the lower Saskatchewan and Churchill Rivers. The financial stakes were high. HBC’s London committee recognized the important need for accurate maps of the vast, and thus far, poorly charted Canadian northwest. With this in mind they hired Philip Turnor, a talented astronomer/surveyor, to serve them in the newly created post of company surveyor:

    “…for settling the Latitudes, Longitudes, Courses, and Distances of the different Settlements Inland…”

Turnor reported to the HBC’s principal inland outpost, Cumberland House, in the fall of 1778. Located approximately 250 miles south of Reindeer Lake along the Saskatchewan River in far eastern Saskatchewan province, Cumberland House served as the hub from which many of the important HBC surveys would later originate. For nine years Turnor performed admirably his duties as surveyor. He made careful, detailed observations in the vicinity of Hudson’s Bay and explored a considerable distance inland along the north branch of the Saskatchewan River. He then returned to England to advise the committee and to prepare detailed maps of the routes he had explored. That work set the stage for his far more significant second trip to the new world.

Returning to Hudson’s Bay in 1790, Turnor’s orders were to push deeper into the wilderness, to the lucrative terrain around Lake Athabasca and the Great Slave Lake. He was also charged with finding and training an assistant.

“Take up the sextant, Peter,” said the older man. “Check that the mirrors are perpendicular to the arc and record the index error carefully. The main purpose of this voyage is to fix the longitude of this site. Our lunar distances must be right. There’s no room for error.”

“Aye, Mr. Turnor,” responded Peter Fidler. The young apprentice opened the sextant case and began the exacting process of aligning the instrument.

Fidler knew he was extremely fortunate to be travelling with the renowned Philip Turnor. Barely a year earlier he had been nothing more than a clerk, working to chronicle daily affairs and to catalog trade goods and furs at remote outposts. Another capable young man named David Thompson had trained under Turnor for six months, but a badly broken leg that stubbornly refused to heal had sidelined Thompson for Turnor’s planned survey to Lake Athabasca. In desperate need of a replacement, Turnor enlisted Fidler’s help; giving him a crash course in surveying astronomy in the summer of 1790.
   
Following his Athabasca survey, Turnor would return to England for good. However, the two men whom he trained, Fidler and Thompson, would carry the HBC surveying torch in impressive fashion. Over the next several decades, each would travel approximately 50,000 miles in the course of his duties, on foot, on horseback, by canoe, and by dogsled, through difficult and dangerous terrain; all the while keeping written accounts of his progress. Between landmarks where celestial observations were made to fix latitude and longitude, they recorded compass bearings and estimated distances, in order to fill in the courses of rivers, trails, shorelines, etc.

The maps prepared by Turnor, Thompson, and Fidler covered almost the entirety of western Canada. Thompson, in particular, prepared a large map of all the regions he had charted (as well as those explored by Turnor and Fidler). He had personally generated almost seventy bound volumes of field notes which provided the foundation for his huge work. Taking two years to prepare, from 1812 to 1814, it measures 7 x 11 feet, and covers the latitude range 45N to 60N and the longitude interval 84W to 124W. The great map now resides in the archives of Ontario. Appreciation for the magnitude of Thompson’s accomplishment is easily gained when one realizes that this map covers more than 1.7 million square miles, an area considerably larger than the entire Louisiana Purchase!

Longitude Determination
Although Thompson, and to a lesser extent, Fidler, have become well known as the men who mapped Canada, it was Philip Turnor who brought the crucial technology across the Atlantic that enabled them to determine longitude. Until the 1760s, surveyors and navigators were plagued by a frustrating inability to determine, with any degree of accuracy and precision, east/west position. It had long been known that the Earth’s rotational period was remarkably constant (at fifteen degrees per hour) and that this could be put to direct use to find one’s longitude. Conceptually, it was remarkably simple. All one had to know was the local hour angle of a celestial body, and, at the same instant, the time at a reference location of known longitude (e.g. Greenwich). For example, at local noon the Sun’s local hour angle is zero. If at that same instant the time in Greenwich is 19:30 hours, then the site is (19.5 – 12) x 15 = 112.5ş west of Greenwich. Simple enough…if one has access to Greenwich time.

In 1761 an English clock maker named John Harrison completed work on a marine chronometer that could keep time reliably for months on end. The story of Harrison’s accomplishment, and his attempt to garner Britain’s famous longitude prize, has been extensively chronicled. However, chronometers such as Harrison’s were hardly used at all for many decades. The Royal Navy didn’t put chronometers in her warships until the 1840s, a full 80 years after the longitude prize was awarded. Until well into the nineteenth century, clocks suitable for navigational use were expensive, laboriously hand made, and extremely difficult to obtain.

In parallel with the development of marine chronometers ran the refinement of two other workable methods for Greenwich time determination. One was the Jovian moon method conceived and largely developed by Galileo. The other, known as the method of lunar distance, was based on measurement of the celestial location of the Earth’s moon.

Which Moon(s) to Use?
Accurate determination of the orbital elements of the four largest moons of Jupiter permits reasonably precise calculation of times when the moons begin, or end, either a transit of, or an eclipse by, the parent planet. These times were tabulated in the nautical almanac. Thus, anyone viewing such an event could set his watch to Greenwich time. The method was simple, and was used extensively on many large mapping surveys in both Europe and the United States. Despite its utility, however, the method suffered from a number of significant drawbacks. Firstly, a telescope is required, a necessity that precluded its use at sea. In addition, the optical requirements for resolving these occultations required that the telescopes be lengthy and rather heavy, and that their mounts be sturdy. Such equipment wasn’t very portable. Finally, Jupiter is only visible at night, for only part of the year, and eclipses and transits of its moons are rather infrequent.

By contrast, the lunar distance method didn’t require heavy, bulky equipment. The moon was also accessible the vast majority of the time; only for a few days before and after a new moon would interference from its proximity to the Sun cause problems. However, the method certainly had its drawbacks. It wasn’t until 1767 that sufficiently accurate and precise tables appeared in the nautical almanac to permit its use. Data acquisition required a trained eye and a steady hand, and the computations to work up a result were lengthy and daunting. Nonetheless, lunar distance was the key method brought by Turnor to determine longitudes throughout western Canada.

II. Longitude by the Light of the Moon
The lunar distance method was the most exploited technique for the determination of Greenwich time, and hence, longitude, both on land and at sea until about 1850. Capitan James Cook used it to map much of the Pacific. George Vancouver used it from 1792 until 1795 to map the northwest coast of North America, and David Thompson, Peter Fidler, and Philip Turnor, among others, used it to map western Canada. Lewis and Clark employed it on their famous overland cross-continental voyage, and many members of the U.S. Army’s corps of topographical engineers use it on military mapping surveys. One of the engineers, William Emory, while travelling with Stephen Kearny’s army during the Mexican war, sat in the Santa Fe plaza and used lunar distance to fix the longitude of our state capitol. He later made extensive use of the method in the official survey of the U.S.–Mexican border.

The method is simple in concept. All celestial bodies move from east to west, a consequence of the Earth’s rotation about its axis. The Moon is no exception; however, its westward motion is slower than that of other objects because of its monthly trek around the Earth. As a result of its prograde orbit, the Moon rises in the east approximately 50 minutes later every day. It is this slow eastward movement, relative to other celestial objects, that forms the basis for the method. One measures the angle between the Moon and another body, the ‘lunar distance’, and compares the observed value to pre-computed quantities tabulated in the almanac. The Sun was the reference object most often employed, but lunar distances to selected navigational stars were also given in the almanac; values being listed for every three hours of Greenwich time. Astoundingly, time determination by lunar distance had been considered since the early 16th century, but two major roadblocks prevented its practical application for more than two and a half centuries.

The invention of the octant in the early 1730s (and soon thereafter, the introduction of its more precise sibling the sextant) solved one important problem faced by blue water navigators; how to make a precise lunar distance measurement (to within one arc minute) from the moving deck of a ship. In fact, these elegantly simple double-reflection instruments; sextants, octants, quintants, reflecting circles, etc., did more than just provide one of the missing links along the path to effective longitude determination. They also allowed for much improved altitude measurements to be made, which considerably improved latitude determination. The mariner’s sextant truly revolutionized the practice of celestial navigation, but a full solution to the longitude problem remained out of reach until a second major obstacle was overcome.

The ability to compute the Moon’s celestial coordinates to the accuracy and precision needed for lunar distance work remained an important navigational goal. For decades after Newton’s universal law of gravitation laid the theoretical foundation that described gravitational interaction, the world’s greatest mathematical minds attempted to devise formulae with which one could calculate the exact location of the Moon at some future date and time.

The problem was daunting. The gravitational interactions among the Earth, its moon, and the Sun, the so-called ‘three body problem,’ evaded a rigorous solution. In addition, the asphericity of the Earth required that, from the perspective of the Moon, it could not be treated as a point gravitational source. As if that weren’t enough, significant gravitational perturbations from the other planets, in particular Jupiter and Venus, added to the complexity of the system.

Enter Lehonard Euler. Euler’s genius was well recognized by the middle of the 18th century, and he was asked to work on the lunar issue because of its importance. Even though the great Swiss mathematician could not derive an analytical solution to the problem, he was, nonetheless, able to formulate an approximate method that promised adequate precision. Euler’s work was necessary but still insufficient to finalize the lunar distance method. Precise astronomical measurements were still needed in order to evaluate various orbital constants.

The young, talented German astronomer Tobias Mayer finally put all of the pieces of the problem together. After years of painstaking observations of the Moon’s position, Mayer used his data and Euler’s methods to produce, in 1755, the first set of lunar tables suitable for navigation. The French mathematician Nicolas-Louis de Lacaille had already outlined the way to transform a lunar distance measurement into a longitude value, so by the mid 1750s, the lunar distance method was in workable form.

The seven years war between England and France created great risk to sailors on the high seas and delayed further testing of longitude methods. After the war ended, the publication of two key documents brought lunar distance into practical use. In 1763 the astronomer Nevil Maskelyne published an easy to follow account of how to apply the method in his ‘British Mariner’s Guide.’ Two years later Maskelyne was appointed Astronomer Royal, and he used his newly acquired position to request permission from the board of longitude to begin publication of a ‘Nautical Almanac.’ The first edition of the almanac was for the year 1767. The era of accurate longitude determination had thus begun.

Note: To see a 123Kb Word doc of Part 3, which includes an explanation of Lunar Distances complete with illustrations, click HERE

 
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