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    Re: Back In Hobby: Some Questions, Please
    From: Ken Muldrew
    Date: 2007 Apr 26, 11:57 -0600

    On 26 Apr 2007 at 10:21, Alexandre E Eremenko wrote:
    
    > > Peter Fidler in 1791, using a "brass sextant of five or six inches radius
    > > made by Ramsden"
    > 
    > That is of a "toy size" by the standards of that time...
    
    Not surprising. This sextant was loaned to him by Philip Turnor and since 
    there was every likelihood that all of Fidler's belongings would be 
    confiscated by the Indians, he probably wasn't inclined to give him a 
    valuable sextant for the trip.
    
    > > reports the following two latitudes (among many celestial
    > > observations, but I'm pretty sure that I know where he was when he made
    > > these two).
    > >
    > > 51�50'47" (actual latitude 51�02'55")
    > > 52�21'37" (actual latitude 52�15'35")
    > >
    I should have been more careful with these positions. Both of these are 
    river crossings so I know where he was at the time within about a mile, 
    but I mixed up his outgoing journey with his return. Here are the real 
    numbers for his outgoing journey along with my best guess at his actual 
    position using his DR and topographical notes.
    
    Nov. 10, 1791
    Double meridian alt of sun's LL 37�06'30"
    Index error                         9'20"
    Temp 37�F, Lat 53�36'52"
    [best guess at actual latitude 53�37'] 
    
    Nov. 14
    alt LL 36�14'00"
    ind err    9'20"
    Temp 30�F, Lat 52�59'37"
    [53�01']
    
    Nov. 18
    alt LL 35�24'30"
    ind err    8'00"
    Temp 24�C, Lat 52�26'54"
    [52�22']
    
    Nov. 19
    alt LL 35�07'30"
    ind err    8'10"
    Temp 25�C, Lat 52�21'37"
    [52�16'43"]
    
    Four lunars: 112�45'W, 113�40.75'W, 113�3'W, 113�7.25'W
    longitude 113�09'04"W
    [113�36']
    
    Nov. 28
    alt LL 32�13'00"
    ind err    8'10"
    Temp 19�F, Lat 52�02'57"
    [51�52']
    
    Dec. 8
    alt LL 31�39'15"
    ind err    8'10"
    Temp 37�F, Lat 51�00'37"
    [51�02']
    
    Two lunars: 113�25'W, 113�14.25'W
    longitude 113�19'35"W
    [113�28']
    
    Dec. 11
    alt LL 31�29'30"
    ind err    8'10"
    Temp 29�F, Lat 50�50'41"
    [50�51'10"]
    
    Dec. 16
    alt LL 31�29'45"
    ind err    8'10"
    Temp 32�F, Lat 50�34'38"
    [50�37']
    
    Dec. 22
    alt LL 31�44'15"
    ind err    8'10"
    Temp 26�F, Lat 50�23'48"
    50�20']
    
    Two lunars: 112�58.25', 112�30.25'
    Longitude 112�44'15"
    [114�W]
    
    The assumed latitudes for Nov. 19 and Dec. 11 should be correct, giving 
    errors in Fidler's observations of 5' (appalling) and 29" (poor).
    The errors in his lunars (51', 31', 6', 2', 3', 14', 62', 90' (none of 
    which are corrected for errors in the almanac)) show that he was getting 
    large errors quite often, but a 5' error in latitude has to be from a 
    sloppy observation.
    
    > > David Thompson used a 10 inch radius brass sextant made by Dollond. His
    > > latitudes at Rocky Mountain House from 1800 and 1801 were:
    > >
    > > 52�21'29"
    > > 52�21'27"
    > > 52�21'35"
    > > 52�21'32"
    > >
    > > The actual latitude is 52�21'20" but it should be remembered that Rocky
    > > Mountain House is at an altitude of 3200' and Thompson did not account
    > > for that in his calculation.
    > 
    > Cook's companions did worse with their lalitude.
    > If you average these you get 1".3 accuracy!!
    > While the max error of the individual numbers is about 0.3'
    > and I suppose this is as good as you can expect in general,
    > with any sextant. These latitude data are probably not individual
    > shots but the averages themselves, am I right? And the art horizon was
    > used, correct?
    
    The artificial horizon was used, but each of these readings is a single 
    meridian altitude observation (no averaging). Here are the actual readings 
    from his journal:
    
    Apr 9, 1800: sun's LL
    90�35'00"
      -22'37"
    90�12'23" lat 52�21'29"
    
    Feb. 20, 1801
    53�37'00"
      -21'19"
    53�05'41" lat 52�21'27"
    
    Feb. 21, 1801
    54�10'00"
      -21'19"
    53�48'41" lat 52�21'35"
    
    Mar 5, 1801
    63�09'15"
      -20'30"
    62�48'45" lat 52�21'32"
    
    If we correct these for refraction due to altitude, we get quite 
    remarkable numbers:
    
    52�21'22"
    52�21'13"
    52�21'21"
    52�21'20"
    
    I'm going to check some of Fidler's later journals to see if he used a 
    different sextant and whether his accuracy improved. It is thought that 
    Fidler's observations served as the basis for Arrowsmith's mapping of 
    Western Canada in the early 1800's although there is evidence that someone 
    was also passing David Thompson's data to Arrowsmith as well. I suppose 
    when you're filling in a empty continent, errors of 5' in latitude aren't 
    a big deal.
    
    Ken Muldrew.
    
    
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