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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).

.............
.............

   

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