NavList:

   

Reply

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.

   

Reply