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Ken,

> errors. He used a Dolland brass sextant of 10" radius with a vernier
> divided to 15". His DR position can be back calculated using the almanac
> data below but I haven't done it for this case.
>
> >From Thompson's notebook:
>
> Feb 17, 1801 - Aldebaran
> Sun RA  22?01'17"
> Moon RA  29?01'50"
> Dec  15?05'03"N
> SD  15'10"
> HP  56'10"
> Sun TA  51?56'10"
> Sun AA  51?56'10"
> Moon TA  33?56'48"
> Moon AA  33?11'26"
> D  35?53'06"
> Temperature -6?F
> Longitude 114?39'00"W
>
> Witchell's method corrections:
> Corect'n 1      -12"
> Corect'n 2   -51'42"
> Corect'n 3       12"
>
> time of sight   moon FL to aldebaran
> hr| min| sec| deg | min| sec
> 7 | 35 | 25 |  37 | 03 | 00
> ....36 | 25 |.......02 | 30
> ....37 | 22 |.......01 | 25
> ....38 | 16 |.......01 | 15
> ....39 | 11 |..........| 45
> ....40 | 12 |..........| 15
> 7 | 37 | 48 |  37 | 01 | 35  | avg
> ...-19 |-44 |....| -21 |-19  | watch & index errors
> 7 | 18 | 4  | 36 |  40 | 16
>
> time of sight   procyon
> hr| min| sec| deg | min| sec
> 7 | 45 | 01 |  75 | 08 | 15
> ....46 | 06 |.......20 | 15
> ....47 | 03 |.......31 | 15
> 7 | 46 | 04 |  75 | 19 | 55  | avg
> ...-19 |-44 |....| -21 |-19  | watch & index errors
> 7 | 26 | 20 | 74 |  58 | 36
>
> The watch error is calculated from the time sight and then put back into
> the tabular results (so he calculates the local apparent time when the
> altitude of Procyon is 7?26'20", compares that to the watch time that he
> wrote down and then gets a correction). That correction is then put back
> into the lunar data to get the proper time for his lunar shot.
>
> d  36?24'55" at 7h18m04s LAT
>
> 1801 Almanac lunar distance (GAT)
> 12:00  37?22'31"....15:00  35?51'25"
> JPL lunar distance
> 12:00  37?23'19"....15:00  35?52'16"
> D 35?53'06"
> GAT from 1801 almanac: 14h56m40s
> GAT from JPL data: 14h58m21s
> LAT   7h18m04s
> Longitude from almanac: 114?39'06"W
> Longitude from JPL data: 115?04'17"W
>
> If we clear the distance using a calculator, then we get:
> D  35?53'16"
> resulting in:
> GAT from 1801 almanac: 14h56m18s
> GAT from JPL data: 14h57m59s
> LAT   7h18m04s
> Longitude from almanac: 114?33'44"W
> Longitude from JPL data: 114?58'54"W
>
> True longitude (modern survey): 114?58'50"
>
> So if Thompson had an almanac based on a better theory of the moon as well
> as a calculator to clear his lunar more precisely, his longitude would
> only have been off by 4"  ;-)
>
> But seriously, when we looked at a bunch of Thompson's lunars last year
> (the posts are in the archives) we found that his standard deviation was
> 20' (in longitude) using the old almanacs and would have been 14' if he
> had the JPL data, so not bad but not great. But we do have to consider
> that he got this sextant in 1792 and there was much rough travel in the
> interim (perhaps 30,000 miles by canoe, horseback, dogsled, and foot).
> There are instances in his journals where his canoe is overturned in
> whitewater and the sextant has to be fished out downstream. Sometimes he
> has to rely on other fur traders to carry his sextant (a practice so
> abhorent that he notes it in his journals). He had no opportunity to have
> the instrument serviced so one has to be impressed with the performance he
> coaxed from the instrument.
>
> Note: I haven't corrected the data for temperature or pressure (his
> altitude above sea level was about 3250 ft.).
>
> Ken Muldrew.
>

   

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