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Just a couple of short notes about the simple pen and paper method of comparing a number of sights of the
same body over a few minutes with a line approximating the apparent rise or 
fall of the body, caused by the
rotation of the earth:

This rise or fall is not a straight line, but an arc. This is why the straight 
'line of best fit' should not be extended
beyond 5 minutes.

The statistical approach, presumably that of simple linear regression, works 
from the opposite direction. A
sample of observations is taken and a process employed that best fits a line 
to them. What I am proposing is
taking the given line of slope (a function of latitude and azimuth of body 
observed) and best fitting the obs to it.
Quite a difference.

If this process has flaws in extreme situations (and I have wondered, idly, 
what might happen at the prime
vertical) then I am indebted for that information, but it doesn't change 
things for all the other occasions.

Properly speaking it is not a system of averaging at all. It is a system of 
choosing, purely by visual comparison,
a line of best fit. I guess this is why it quite acceptable, indeed necessary, 
to ignore extreme values. To put it
most simply, the given line is the fact, the observed values have to 'best 
fit' it. Not the other way around.

   

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