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Re: Real accuracy of the method of lunar distances
From: Jan Kalivoda
Date: 2004 Jan 1, 20:08 +0100
From: Jan Kalivoda
Date: 2004 Jan 1, 20:08 +0100
Fred, Maybe we bother the list with the too detailed discussion already. But it is easy to erase our postings, if needed, I hope. I take into account the last posting of Trevor in this thread and I agree with its content. I hope that my approach for finding the error limit of lunars was right. Nevertheless, to verify your point of view, one would need to know the standard deviation of the basic sets of six measurements. We can suppose that it was stable throughout all the period of observations, as you say, but we don't have the data for each measurement to ascertain it, we have the data only for the means from each set of six measurements. But you state that it is possible to deduce the standard deviation you need from the variance of the whole series of the means - without giving any details. Therefore, I repeat here all individual errors of Bolte's 34 lunars observations (the means of sets of six individual measurements) in arc-seconds (details about the method used for finding them are given in my starting posting of this thread): Two outliers, taken at rough sea in two subsequent days and further omitted: +120, +127 (both for a star as the distance body, one easterly distance, one westerly one) Remaining 22 items for a star as the distance body: +18,-5,-15,+72,+16,+7,-14,+8,+54,+12,-47,-32,-34,-28,+39,-36,-7,+19,-27,+13,-5,+25 13 westerly distances, 9 easterly distances, the mean +1.5" 10 items for the Sun as the distance body: +12,+32,+51,+25,+46,+10,+51,+35,-18,+19 3 westerly distances, 7 easterly distances, the mean +26.3" It is clear that values for the Sun have the noticeable bias, probably created by the prevailing easterly distances (taken in forenoon - maybe Bolte took part in many passenger parties during afternoons) and therefore revealing a systematic error. But the standard deviation for the Sun is only marginally worse (33.3") than for stars (29.6"). As I have said before, another set of 82 lunars taken by some captain Behrens (each evaluated observation was the mean of five measurements) gave the nearly identical standard deviation (29.7"), according to Bolte (recomputed by me from his "probable error"). But no other data for these observations are given. Jan Kalivoda ----- Original Message ----- From: "Fred Hebard"To: Sent: Thursday, January 01, 2004 4:43 PM Subject: Re: Real accuracy of the method of lunar distances Jan, If you denote the observed mean (mean of lunar distances during one observing session) by Y and the known distance (computed from chronometer time, what was being used to check these lunars) by u, the standard deviation by s and the number of observations used to compute Y by n, then t = (Y - u) / (s / square root of n). ............. .............