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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
David Thompson's Navigational Technique
From: Ken Muldrew
Date: 2004 May 28, 11:35 -0600
From: Ken Muldrew
Date: 2004 May 28, 11:35 -0600
As promised to Bruce Stark earlier in the week, here is an account of how David Thompson used celestial navigation to figure out where he was (Thompson in particular, although the same methods were used by Peter Fidler and Philip Turnor). This article is intended as a supplement to the lengthy and informative discussion of David Thompson's navigational technique written by Jeff Gottfred and published in the Northwest Journal (Gottfred, Jeff. How David Thompson Navigated. Northwest Journal Vol. 9. ISSN 1206-4203. Available at: http://www.northwestjournal.ca/dtnav.html). Although Gottfred covers almost the entire subject in this excellent article, there are a few minor points that can be clarified for completeness. Many will be uninterested in such minutiae, but for others, the way these navigators of old approached the subjects of time and computation are so foreign to our modern way of thinking, that only a careful recreation of their methods can capture their mindset (and their accomplishment). Some sample data from a few days at the beginning of Thompson's Journey to the Kootanaes of 1800 will be used to demonstrate the most common elements of Thompson's technique. Thompson is on foot here so his courses are easy to transcribe and compute (when he travels by canoe he can fill an entire page with the courses of a day's travel). Also, I happen to have photographs taken from the microfilmed copy of this journal, so there is no need to rely on someone else's transcription. Images of the journal entries used here can be found temporarily at http://www.ucalgary.ca/~kmuldrew/dt.html. There is also a copy of his great map there, but it is hastily patched together from separate images, so it isn't a great copy, but it's good enough to see how he reduced the immense number of observations that he took on his journeys into a practical document. He used Cook's survey of the Pacific coast for this map, but otherwise it was almost all from his own data. How David Thompson came to learn navigation is a story that is well known, but very briefly, David Thompson was taught practical astronomy by Philip Turnor, astronomer for the Hudson's Bay Company. Turnor had been a student at Christ's Hospital Mathematical School, of which William Wales was the master. Wales recommended Turnor for the position which he began in 1778. During his tenure with the HBC Turnor instructed David Thompson, Peter Fidler, and Malcholm Ross in practical astronomy. Ross drowned before he could accomplish much, but Thompson and Fidler both had outstanding careers as explorers. Turnor returned to London in 1792 or 3 and worked for Maskelyne as a computer for the Nautical Almanac. He died unexpectedly and Maskelyne was forced to pay off his debts in order to retrieve the books and materials that he needed to perform his calculations. Thompson, educated by Turnor in 1789, defected to the Northwest Company in 1797 and remained with them until his retirement. After surveying much of what is now Western Canada, he constructed his great map of the North West. He later surveyed the boundary between the United States and Canada as far as the Lake of the Woods. The Journey to the Kootanaes of 1800 began at Rocky Mountain House, the Northwest Company fort along the North Saskatchewan River where the town of the same name sits today. Thompson had over-wintered there and had about 10-15 lunars and several meridian altitudes of the sun at that location, so he was very confident of its position at 51?21'30" N and 114?52' W. Below are his journal entries for the period of October 5th (the start of the journey) to October 12th (where he takes his first lunar). The transcription is my own (from photographs I took of the microfilmed copy of Thompson's journal borrowed from the Archives of Ontario), but I consulted Belyea's edition (Thompson, David. Columbia Journals. Barbara Belyea, ed. McGill-Queen's : Montreal, 1994.) for help with some of the illegible words (though many minor differences remain). The table of courses appears at the end of the Journey to the Kootenaes trip. I have only transcribed the portion from October 5 to 12. No changes to spelling or punctuation have been made (I would normally change "fs" to "ss" for legibility but here it is left as written). It's also wise to keep in mind that Thompson's journals are "fair copies". These are not the original notes written in the field, but rather the condensed version that is copied out later. Thompson, like Turnor, keeps a very spare, professional record of the events that occur. Very little emotion is allowed onto the page, sometimes he even neglects to mention the birth of one of his children. Fidler is more emotive, and much more graphical, committing geographical information from natives into roughly sketched maps in his journals. Fidler is also an order of magnitude easier to read. [in the following, * stands for a circle with a dot (the sun), ) stands for the moon, and letters that follow ^ are superscripted] Thompson's Journal - Journey to the Kootanaes. Rocky Mountain. October 1800 October 5th. Sunday. A fine cloudy Day. At 8 Am the Men crossed the River, La Gafs?, Beauchamp, Morrin, Pierre Daniel, Boulais & myself, with the He Dog, a Cree, and the Old Bear, a Pekenow Indian, our Guide. We had an afsortment of Goods, amounting to about 300 Skins, each of us a light Horse, belonging to himself, and 3 Horses of the Company's to carry the Baggage. We met several Blood Indians going in to trade. Our Co to the crossing Place of the Clear Water River may be about SEbE 2 ? M. After crossing that Stream we went on about SE 1 ? M to the parting of the Roads where finding we had forgot to take a Kettle with us, I sent La Gafs? back again to the House for one. mean Time we went on to the Bridge, which is a few Sticks laid acrofs a Brook. Our Co during this Time thro' mostly thick Woods of Pine and Aspins may have been SEbS 1 ? M to a small Brook with very little water and which we crofsed. It goes into the Clear Water River then SbW 10 1/2M to the Brook Bridge, here we put up to wait La Gafs?, who came in the Evening with 2 Kettles - fine weather. October 6th Monday In the Morn Cloudy, with a small shower of Rain - afterwards fine - At 6 Am set off. lost ? Hour in crofsing the Bridge, which we found very bad - we went on thro' a willow Plain about SE 4M, then we entered the woods, then Co SE 4M South 3M very bad swampy Ground thick Woods of Pines. Co SbE 2M small Plains, saw a Herd of Cows - end of Co stopped an Hour at 10 Am to refresh our Horses and take Breakfast at 11 Am we set off and went SE ? M to a bold Brook. Co along it mostly SEbE 1M when we crofsed it. Then Co SE 6M to a Plain in which we went abt S 3M, at end of a Rill of Water. crofsed it. Co SbE 4M when we came to 5 Tents of Pekenow Indians, with whom we staid to smoke about ? H. we then went on SbE 1 1/4M and crofsed a Rivulet, which a small Distance below us falls into the Red Deers River. Co SSW 2M to the Red Deers River, which we also crofsed, we then went on up along the River, mostly on the Gravel Banks, which formerly in high Water, were part of the Bed of the River. SWbS 2M SW 2M in these Cos several crofsed & recrofsed the small Channels of the River, as they came in our Way and at end of Co recrofsed the River altogether, and went on thro' a tolerable fine Plain SW 2M to a bold Brook, which falls into the last mentioned River, here we had a grand view of the Rocky Mountains forming a concave segment of a Circle, and lying from one Point to another about SbE & NbW all it's snowy cliffs to the Southward were bright with the Beams of the Sun, while the most northern were darkened by a Tempest, & those Cliffs in the Concave were alternately brightened by the Sun & Obscured by the Storm which spent its Force only on the Summits. All the above Cos by the Sun. we then crossed a Plain, abounding with small Willows. Co SbSW 6M by the Compafs, to the Foot of a high woody Hill extending along the Mountain, where we found 5 Tents of Pekenow Indians - Into one of them belonging to our Guide we went & put up at 5 Pm. It is surprising what a quantity of Ground in some Places it was not less than 500 Yds broad, by different Channels, with gravel Banks between them, while at present it is contracted into a Stream of from 40 to 50 Yds and its Depth upon a Medium about 2 ft at abt 3 1/2M pr Hour, with here and there a few small insignificant Channels occupying rarely more than 200 Yds and in general much lefs. Let us ask The Cause of this. is it that the heavy Rains and melting of the Snows have carried away such Quantities of the Particles of the Mountain as greatly to have diminished its' height, and therefore does not attract the Clouds & Vapours so strongly as formerly; or that the Earth and Ocean in these Climes do not yield the Vapours so freely as of Old; or if they do, are they driven by some unknown Cause to break and difsolve before they reach the Mountains. whatever Opinion we may form, the Fact is certain, that at present and for several Years past the Mountains do not send forth above two Thirds of the Water they did formerly for we see upon the Banks of all the Rivers large Trees that have been carried down by the Stream, and left either a great way from their present Boundaries, or a great Height upon the Banks far above the greatest known Level of the present Times - These Trees are not only to be found singly, but in vast Numbers, piled so intricately together that it is next to impofsible to disentangle them. October 7th Tuesday In the Night an exceeding heavy Fall of Rain, which in the Morning changed to Snow, and continues all Day. in the Even the weather moderated. The Snow is now about 1 foot deep. October 8th Wednesday A Cloudy Day, with at times small light Snow. Went a hunting with a Pekenow Indian. Killed a Jumping Deer, very fat, & my Companion killed another, which we brought with us to the Tents, where we arrived in the Evening - In this Excursion we crofsed the Red Deers River which here, is mostly confined to one Channel of about 40 yards & very strong current, with Banks of Rock. found the Country very bad, full of Large Swamps and high Knowls covered with thick Woods, that were in many Places burnt. Animals of all Kinds were numerous: but the Weather was too Calm for Hunting. October 9.th Thursday. A very fine Day. We wait a Pekenow Indian who is to come with us by his Promise as our Guide. In the Afternoon he came, but I soon found by his Conversation, that his Company like the rest of his Nation now present was intended only for the Spot, for the sake of Smoking and what else they can get - They are so jealous of the Kootanaes coming in to Trade, that they do all they can to persuade me to return, afsuring me that it is impofsible for me to find them, and that in endeavouring to search them out, our Horses will fall by Fatigue and Hunger, and perhaps also ourselves. At Noon Obsd Merid Altde of *LL 63?-30'1/2 error 22'-30" Lat^de 51?-47'-21" N Dec^n 6?-23'-59" S October 10.th Friday A cloudy stormy Day, with high Drift & Snow 'till 10 Am when it cleared & became tolerable fine. Went a Hunting with our Guide & a young Man killed a Bull of which we brought 2 Horse Loads to the Tents - Every where thick Woods of Pines with Spots of Aspin, and much, very much deep swampy Ground - The Indians difsuade us all they can from going any further, but our Guide tells me, They purposely misrepresent the Country for their own private Views. October 11th Saturday A very fine Day, but the Snow thawed very little. At 10 Am we set off & went about SbW 3M SSW 1M SbW 2M end of Co pafsed a small Brook, which falls close by us into the Red Deers River, which Last may be about SSE 1M from us. put up at end of Co - but I went a hunting with La Gafs? and our Guide on the Heights of the River - where I killed a Bull, with Horns of a remarkable Length, measuring 35 inches along the Curve - we brought most of the Meat to the Tents where we arrived in the Evening. -Cloudy-. October 12th Sunday. Latde by Acct. 51?-42' N # *AR - 13-10'-28" Dec - 7-29 S )AR -131-44-36 Dec - 23-4 ? N SD - 15..10 HP - 55..39 *TA - 17-52-39 AA - 17-55-26 )TA - 58-20-12 AA - 57-51-11 D --- 71-13-54 +2'+19" -2'-1" +2" Longde 114?..45' W October 11.th Distance of * & ) NL # 20-47'-32" -- 71?..5'..15" 48..12 -- 5 ~~ 48..56 -- 4..30 49..36 -- 4..15 50..18 -- 4..15 50..56 -- 4 ~~ 51..32 -- 3..45 52.. 4 -- 3..30 ------------------------ 20..49..53 -- 71..4..19 -2..53 -22..15 ------------------------ 20..47..~~ 70..42..4 Double Altitudes # *UL 20..57'..8" -- 38?..27'..15" 57..52 -- 37..~~ 58..32 -- 46..45 ------------------------ 20..57..51 -- 38..37..~~ -2..57 -22..15 ------------------------ 20..54..54 -- 38..14..45 # *LL 21..~~'..~~" -- 38?..3'..45" ~~ ..35 -- 11..45 1..12 -- 20..45 ------------------------ 21.. 0..36 -- 38- 12.. 5 -2..49 -22..15 ------------------------ 20..57..47 -- 37..49..50 Courses Co by * Dist M N S E W Latitude longitude 52?21'30" 114?52' Rocky Mountain House SEbE 2.5 1.39 2.07 52?20'27" 114?48'14" Crofsed the Clear Water River SbE 1.5 1.06 1.06 52?19'38" 114?46'18" Parting of the Roads SEbS 1.5 1.24 0.84 52?18'42" 114?44'46" Woods to a Brook. Crofsed it. SbW 10.5 10.3 2.05 52?10'50" 114?48'7" The Bridge and Brook. SE 4 2.83 2.83 52?8'41" 114?42'58" A Plain, full of willows, &c. SE 4 2.83 2.83 52?6'32" 114?37'50" Thick woody Pine & Swamps. S 3 3 52?4'15" 114?37'50" " -- very Swampy. SbE 2 1.96 0.39 52?2'46" 114?37'7" Small willow Plains SE 0.5 0.36 0.36 52?0'29" 114?36'28" A bold Brook which we crofsed SEbE 1 0.56 0.83 52?0'3" 114?32'57" At end of this Co SE 6 4.24 4.24 51?58'50" 114?27'18" Thick woods. S 3 3 51?56'33" 114?27'18" Plain - narrow. End of Co Rill with water SbE 4 3.92 0.78 51?53'32" 114?25'53" Thick woods to 5 tents of Pekenow Indians SbE 1.25 1.22 0.25 51?52'35" 114?25'26" Crofsed a strong Rivulet SSW 2 1.85 0.77 51?57'8" 114?26'41" Horse Plain - end of Co entrance the Red Deers River SWbS 2 1.66 1.11 51?49'51" 114?28'29" Upon the Gravel Banks of ? ? " SW 2 1.41 1.41 51?48'46" 114?30'46" " -- end of Co crofsed the Red Deers River SW 2 1.41 1.41 51?47'41" 114?33'3" a fine small Plain. End of Co crofsed a Rivulet SbSW 6 0.42 5.99 51?47'21" 114?42'48" a Spring with willows - to the ? - at the bridge ? ? Obsd for Lat^de SbW 3 2.94 0.59 51?44'40" 114?43'45" ? & Plain with a small Brook, near the Red Deers River SSW 1 0.92 0.38 51?43'50" 114?44'22" " " " SbW 2 1.96 0.39 51?42'3" 114?45' crofsed a small Brook, which falls in ? ? River at SSE 1M Obsd for Long^de The latitudes and longitudes given for the above courses have already been corrected for the latitude measurement on the 9th and the longitude measurement on the 12th. If we update the latitude and longitude strictly from the courses (using a latitude of 52? to calculate longitude-it would be far too much work to look up the cosine of each latitude with an end result that might differ by about 2 or 3 seconds of longitude, well below the expected error), we get the following table: Co by * Dist M N S E W Latitude longitude 52?21'30" 114?52' SEbE 2.5 1.39 2.07 52?20'17" 114?48'38" SbE 1.5 1.06 1.06 52?19'22" 114?46'54" SEbS 1.5 1.24 0.84 52?18'17" 114?45'32" SbW 10.5 10.3 2.05 52?9'20" 114?48'51" SE 4 2.83 2.83 52?6'52" 114?44'15" SE 4 2.83 2.83 52?4'24" 114?39'39" S 3 3 52?1'48" 114?39'39" SbE 2 1.96 0.39 52?0'6" 114?39' SE 0.5 0.36 0.36 51?59'47" 114?38'24" SEbE 1 0.56 0.83 51?59'18" 114?37'3" SE 6 4.24 4.24 51?55'36" 114?30'9" S 3 3 51?53' 114?30'8" SbE 4 3.92 0.78 51?49'35" 114?28'51" SbE 1.25 1.22 0.25 51?48'32" 114?28'26" SSW 2 1.85 0.77 51?46'55" 114?29'41" SWbS 2 1.66 1.11 51?45'28" 114?31'29" SW 2 1.41 1.41 51?44'15" 114?33'46" SW 2 1.41 1.41 51?43'1" 114?36'3" SbSW 6 0.42 5.99 51?42'39" 114?45'46" SbW 3 2.94 0.59 51?40'6" 114?46'43" SSW 1 0.92 0.38 51?39'18" 114?47'20" SbW 2 1.96 0.39 51?37'36" 114?47'58" Presumably this is what Thompson has in his field notes. When he comes to calculate his longitude from his lunar on the 12th he has already updated his latitude from the measurement on the 9th, so by account he figures his position as 51?42' N 114?48' W on the 12th. To get a lunar distance Thompson takes eight sights between the near limbs of the moon and the sun and records the measured distance and the time by his watch. He then measures the altitudes of the sun's upper and lower limbs (he uses the term "double altitudes" because he is using a mercury artificial horizon, he is not finding his latitude by sighting two time-separated altitudes (the classic double altitude technique)). From the upper limb altitude he finds his watch is 2' 57" fast and from the lower limb altitude he finds his watch is 2' 49" fast. He averages these to get a watch error of 2' 53" fast. Then he averages the time and distance measurements from his lunar and subtracts the watch error from the average time and the index error from the average distance. The time for his lunar, 20h 47min is now used to get information from the nautical almanac. Right ascension and declination for both the sun and moon are reduced from the Greenwich time that results from adding the longitude by account (converted to h:m:s) to the local time (as well as the equation of time if the nautical almanac used mean time in 1800, although perhaps they still used sun time then). The true altitudes of both the sun and the moon are then calculated (the following method comes from Patterson's notebook that Lewis & Clark carried): 1. Find the hour angle of the body for the estimated Greenwich time and take the log secant. Add that to the log tangent of the declination and, removing 10 from the index, this is the tangent of an angle A. 2. When the latitude and the declination are of different names, or the hour angle is greater than 90, add the latitude to the angle A, otherwise subtract, to get an angle B. 3. The sum of the log cosine of B, the log cosecant of A and the log sine of the declination, rejecting 20 in the index, is the sine of the true altitude. When I do this for the values given by Thompson I get an altitude of 17?52'54" for the sun and an altitude of 58?20'8" for the moon. I can't account for the slight differences between Thompson's values and my own (I used Raper's Nautical Tables, Thompson would have used either Moore's or Maskelyne's). The apparent altitudes are calculated by reversing the typical operations of accounting for refraction and parallax. He then reduces the true distance between the sun and the moon to the assumed Greenwich time. I don't have an 1800 almanac so I can't check that directly, but if I calculate the true distance given the right ascensions and declinations given above, I get a true distance of 71?13'55". This seems an odd thing to do but I have checked several of Thompson's lunars and the D value that he writes down is always the true distance from the almanac for the assumed time. The typical procedure (as far as I understand it) would be to clear the observed lunar distance and then use the almanac to find the Greenwich time that corresponds to that distance. Thompson, however, always uses his assumed time (the local time adjusted by his longitude by account to find Greenwich time) to get a D value that corresponds to his assumed position. He clears his observed distance using Witchell's method. Moore (New Practical Navigator, 1796) describes the method thusly: {begin quote} First add the sun or star's and moon's apparent altitudes together, and take half the sum; then subtract the less from the greater, and take half the difference; then add together: The cotan of half the sum, The tan of half the difference, and The cotan of half the apparent distance, Their sum, rejecting 20 in the index, will be the log tan of an angle A. Second, when the sun or star's altitude is greater than the moon's, take the difference between A and half the apparent distance, but if less, take their sum, then add together: The cotan of this sum or difference, The cotan of the sun or star's apparent altitude, and The proportional log of the correction of the sun or star's altitude; Their sum, rejecting 20 in the index, will be the proportional log of the 1st correction. Third, if the sum of A and half the apparent distance was taken in the last article, take now their difference; but if their difference, take now their sum. Then add together: The cotan of their sum or difference, The cotan of the moon's apparent altitude, and The proportional log of the correction of the moon's apparent altitude. Their sum, rejecting 20 in the index, will be the proportional log of the 2nd correction. Fourth, when A is less than half the apparent distance, the 1st correction must be added to, and the 2nd correction subtracted from the apparent distance; but when A is greater, their sum must be added to the apparent distance, when the sun or star's altitude is less than the moon's; but when the moon's altitude is less, their sum must be subtracted to give the corrected distance. Fifth, in table X [Moore's table numbering], look for this last corrected distance in the top column, and the correction of the moon's altitude in the left-hand side column; take out the number of seconds that stand under the former and opposite to the latter. Look again in the same table for the corrected distance in the top column, and the principal effect of the moon's parallax in the left hand side column, and take out the number of seconds that stand under the former and opposite the latter. The difference between these 2 numbers must be added to the corrected distance if less than 90?, but subtracted from it if more than 90?; the sum or difference will be the true distance. {end quote} If we use Thompson's data to do this we find a first correction of 2'19" and a second correction of -2'-1". The table gives us a third correction of 2". I have done this for several of Thompson's lunars and the corrections always agree with those he writes under his almanac data, whereas all the other approximate methods that I have tried give different corrections. Thompson's cleared distance is his observed distance minus the index error plus the semidiameters of the moon and sun with the three corrections added. The cleared distance is 71?13'30". Thompson then subtracts the cleared distance (71?13'30") from the true distance that he obtained from the almanac (71?13'54") to get a difference of 24" (D by account being greater than the cleared, measured distance). 24" in distance corresponds to 12" in time which converts to 3 minutes of longitude. He then subtracts 3' from his longitude by account (subtract because his D by account was greater) to get a corrected longitude of 114?45'. He never bothers with a corrected Greenwich time because he deals only in local time. Greenwich time is merely for taking values out of the almanac. Having corrected his longitude he can now go back over the endpoints of all his courses and correct them proportionally so that when he goes to map out the landmarks on his journey, he will have accurate data. The practice of using distance to correct longitude confused me for some time since Thompson never writes down his d or "D" values (where "D" here refers to the cleared, observed distance, not the D that Thompson actually records). I could take his average sight and correct it for semidiameter and then apply the 3 corrections from clearing the distance, but that value never agreed with his recorded D value (although at times it was only out by a couple of seconds, other times it was out by many minutes). It's clear now though that Thompson is correcting his longitude based on a difference between assumed and measured distance, not based on a difference in time. Our current perspective on time is so different from that used by navigators of old that it can obscure our understanding a straightforward procedure. There are probably a lot of errors, omissions, or unintentional obfuscations in the above. I would welcome any corrections or comments where I haven't been clear. Ken Muldrew.