# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Old style lunar**

**From:**Ken Muldrew

**Date:**2004 Dec 20, 15:59 -0700

On 16 Dec 2004 at 10:01, Ken Muldrew wrote: > On 16 Dec 2004 at 9:38, Alexandre Eremenko wrote: > > > But if Thompson's time is his local > > apparent time (that is the time elapsed from > > his local Sun culmination), > > then his star altitude is close to the > > correct value, and we still have no explanation > > why his Lunar was so much off. > > I think the key problem is that the data he extracts from the almanac for > the moon's RA and declination show an interval of only 3 minutes between > the two lunar distance shots while his watch shows an interval of 9 > minutes. Since his DR has to be the same for both, he must have made a > mistake in determining Greenwich apparent time for one of the shots, losing > 6 minutes somehow. The error in Thompson's lunars from Nov. 26 seem to stem from a single mistake that he made when going into his almanac to work his time sights (or at least all his data can be explained by a single error; without any record of his rough work, this must remain conjecture). Since the sun has already set, Thompson takes the altitudes of two stars (Capella and Lyra (Vega)) to get his local time. He must then get the sun's right ascension from the almanac in order to get the hour angle that separates the sun from these stars. In order to do that, he has to know Greenwich time. Of course the whole purpose of taking lunars is to find out what Greenwich time is, but it is an exercise in successive approximation, rather than getting an exact answer de novo. He knows approximately where he is and his pocket watch gives him a reasonable approximation to local time. By converting his dead reckoning longitude to hours and adding it to his local time, he gets an estimate of Greenwich time for his almanac interpolations. Thompson's journal contains a list of courses for the journey along with his latitude and longitude for each way point. The positions have been updated to accord with his celestial sights, proportionally dividing up the differences between his account and his actual position for each point between measurements. If we just use his courses to update his starting position, then we should have a reasonable idea of how his account looked on Nov. 26. At Rocky Mountain House where his journey started, he has the following positions in November of 1800: Latitude: 1800 9-Apr 52?21'29" Longitude: 1800 17-Apr 115?12'00" 18-Apr 114?57'45" Using these values as starting points, his courses will look like: Co. true Co. dist N S E W 52?21'29" 115? 4'52" SE S24E 10 9.14 4.07 52?13'32" 114?58'24" ESE S46E 14 9.73 10.07 52? 5' 4" 114?42'23" SE S24E 1 0.91 0.41 52? 4'17" 114?41'44" SSW S43W 1.5 1.10 1.02 52? 3'20" 114?43'21" S48E S19E 2 1.89 0.65 52? 1'41" 114?42'18" SEBE S35E 1.5 1.23 0.86 51? 0'37" 114?40'55" ESE S46E 4.5 3.13 3.24 51?57'54" 114?35'46" ESE S46E 5 3.47 3.60 51?54'52" 114?30' 3" ESE S47E 1.5 1.02 1.10 51?53'59" 114?28'18" SEBE S36E 3 2.46 1.72 51?51'51" 114?25'33" S S21W 8 7.47 2.87 51?45'21" 114?30' 6" S S21W 9 8.40 3.23 51?38' 3" 114?35'13" S22E S1E 1.5 1.50 0.03 51?36'45" 114?35'10" SEBS S13E 11 10.72 2.47 51?27'25" 114?31'14" SSE S1E 12 12.00 0.21 51?16'59" 114?30'54" SEBS S13E 13 12.67 2.92 51? 5'59" 114?26'15" S30E S9E 2 1.98 0.31 51? 4' 5" 114?25'45" SEBS S13E 12 11.69 2.70 50?54' 5" 114?21'27" S32E S11E 11 10.80 2.10 50?44'42" 114?18' 6" S32E S11E 17 16.69 3.24 50?30'11" 114?12'56" SEBE S35E 4 3.28 2.29 50?27'20" 114? 9'17" S36E S15E 5 4.83 1.29 50?23' 8" 114? 7'13" SSE S1E 12 12.00 0.21 50?12'42" 114? 6'53" N30W N9W 4 3.95 0.63 50?16' 9" 114? 7'52" N75W N54W 13 7.64 10.52 50?22'47" 114?24'34" N85W N59W 8 4.12 6.86 50?26'22" 114?35'27" His time sight of Capella is given as: 8:32:20 98?58' 0" 8:33:10 99?13' 0" 8:34:00 99?26'45" ----------------- 8:33:10 99?12'35" 7:54 -22'22" ----------------- 8:41:04 98?50'13" So his watch reads 8:33:10 at the time of his altitude measurement (the correction of 7:54 is added later once he calculates the exact local time that corresponds to the measured altitude). His DR longitude of 114?35'27" converts to 7h38m21s. Greenwich time should then be 8:33:10 + 7:38:21 = 16:11:31. The almanac gives the sun's RA as 16h6'14.3" on the 26th (at noon) and 16h12'30.6" on the 27th. Thompson would have added the proportional log of the difference between these two values, the proportional log of Greenwich time (multiplied by 60 so that hours become minutes, etc.) and the proportional log of 24. The inverse proportional log would have given him the time to add to 16h6'14.3" to get the sun's RA at the time of his Capella altitude. If I do that I get a value of 16h10'28" for the sun's RA at that time. Thompson has written down 16h11'13" for the sun's RA in his notebook and he has used this to find his local time. Using the correct value for RA I get a local time that is 45 seconds ahead of Thompson's calculated time. What I think he's done is to mistakenly add 8h33'10" and 10h33'10" to get Greenwich time. I don't know why he would do this; working by candlelight with little extra paper, I guess. But for whatever reason, that sum gives a sun RA of 16h11'13" and puts his local time late by 45 seconds. When taking out the RA and declination of the moon for his calculated altitudes of Aldebaran and Altair, he correctly adds his longitude by account to his local time, but that time is now 45s off, so those values are similarly shifted. If I calculate the GAT from the values of RA and declination for both of his lunars I find that the Aldebaran time is 45 seconds slow and Altair 45 seconds fast. If I recalculate altitudes based on the correct local time, and then re- clear his lunars based on the proper values, and finally use the improved lunar distances from Frank Reed's online almanac, then I get the following values for the two lunars: Altair: 114?14'54" Aldebaran: 114?45'59" The average is 114?30'27" which is a pretty reasonable value considering that his true position is 114?19' for an error of 11' of longitude. Thompson was merely lucky with the combination of his error and the errors in the almanac that gave him the position 114?11'. Bruce Stark has sent me the almanac pages covering the lunars that Thompson took at Rocky Mountain House. Comparing errors in the original almanacs to the correct values should tell us whether the rather large variance in Thompson's longitudes came from poor sights or poor lunar theory. Ken Muldrew.