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    Re: Back In Hobby: Some Questions, Please
    From: Alexandre Eremenko
    Date: 2007 Apr 27, 10:59 -0400

    
    Ken,
    The data you posted show the same very strange phenomenon
    that I see in Cook's observations at Point Venus:
    some large unexplainable errors in altitudes. I mean
    the altitudes are substantially less accurate than the
    lunar distances. What could be the reason of this?
    
    Indeed, let's look at the Lunar first.
    The errors in longitude in the 6 Lunars you gave are:
    -51', +5', -33', -29', -62', -90'.
    Which implies the errors in the Lunar DISTANCES, except one,
    are less than 1'.
    Which seems pretty reasonable.
    
    But the errors in LATITUDE are enormous by comparison:
    48', 6', 0', -1', 5', 5', 11', -2', -9', 0, -2', +4',
    This is not what I would expect from artificial
    horizon observations, even with a poor sextant.
    Even if we discard the 2 outliers (possibly some blunders)
    the average absolute error is 3.4' which is too large.
    
    Is it possible that some poor quality wood octant was used
    for the altitudes, and a metal sextant for the lunars?
    
    Alex
    
    On Thu, 26 Apr 2007, Ken Muldrew wrote:
    
    >
    >
    > 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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