NavList:

Stan wrote, on July 27-





"In Bowditch Table 23 (28), Correction of Amplitude as Observed on the 


Visible Horizon, the correction values do not always increase monotonically 


from left to right (increasing declination) for a given latitude.  (For 


example, look the lines for latitudes of 25, 30, 32, 36, and 44 degrees.) 


How can this be explained?





FYI, those lines are from "recent" editions of Bowditch.  The table in the 


1938 edition does not have the same correction values.  I do not have it in 


front of me right now, but, as I recall, even though the values are 


different, they do increase monotonically."





====================





I think those small discrepancies can be simply explained. Mine is the 


2-volume edition of Bowditch, in which the relevant table is Table 28, in 


volume 2, which dates from1981.





The table lists the small difference between amplitude observed when a 


body's centre is on the true celestial horizon (that is, exactly 90º from 


the observer's zenith), which is itself tabulated in Table 27, and the 


amplitude you would get if the body was on the apparent horizon, affected 


by refraction and dip, at a true altitude of -42'. The table shows that 


difference for various latitudes and declinations. For example with a 


latitude  of 32º, then for various declinations at 2º intervals from 0º to 


24º, the tabulated difference in degrees is as follows-


0.4, 0.4, 0.4, 0.4, 0.5, 0.4, 0.4, 0.4, 0.4, 0.4, 0.5, 0.5, 0.5


Is this the non-monotonic behaviour that worries Stan?





At low values of latitude, the real correction changes hardly at all with 


declination, but it's the difference between two quantities which do change 


significantly with declination. And presumably, those two quantities have 


each been calculated only to the nearest 0.1º. Indeed, one of the 


quantities appears to have been taken directly from fig 27, where it's 


given to the nearest 0.1º. So each term in the subtraction has a "random" 


fluctuation of +/- 0.05º. It's no surprise, then, to see the result 


wobbling about, itself rounded to the nearest 0.1º, just as Stan observed. 


It's entirely the result of the accumulation of rounding errors.





Remember, those basic tables were produced years ago. Done today, each term 


would be calculated by computer to umpteen decimal places, and then the 


rounding-off would occur only as a final step after the subtraction. That 


would produce the monotonic behaviour that Sten expects.





George.





contact George Huxtable, at  george@hux.me.uk


or at +44 1865 820222 (from UK, 01865 820222)


or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


----- Original Message ----- 


From: <slk1000@aol.com>


To: <NavList@fer3.com>


Cc: <slk1000@aol.com>


Sent: Tuesday, July 27, 2010 5:50 PM


Subject: [NavList] Re: HO 249 Vol 1, epoch 2010, Typo

















 Dave,





I agree, but how the heck did you ever notice this?  Working on old 


problems?





Here's another one for you:  In Bowditch Table 23 (28), Correction of 


Amplitude as Observed on the Visible Horizon, the correction values do not 


always increase monotonically from left to right (increasing declination) 


for a given latitude.  (For example, look the lines for latitudes of 25, 


30, 32, 36, and 44 degrees.)  How can this be explained?





FYI, those lines are from "recent" editions of Bowditch.  The table in the 


1938 edition does not have the same correction values.  I do not have it in 


front of me right now, but, as I recall, even though the values are 


different, they do increase monotonically.





Stan


























-----Original Message-----


From: Dave Walden <waldendand@yahoo.com>


To: NavList@fer3.com


Sent: Tue, Jul 27, 2010 8:10 am


Subject: [NavList] HO 249 Vol 1, epoch 2010, Typo








Seems to be a little typo in Table 4, GHA Aries FOR THE YEARS 2006-2014, at 


the back of Vol 1.  Part a. for May 1, 2010 reads 219-49.  Perhaps it 


should be 218-49?


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