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Alex, you wrote:
> I have to say that several years ago
> I decided not to
> participate in any discussion of statistics on
> this list.

However, your statement:
>  The tables in Bennett do not have sufficient
>  accuracy ... because they are
>  rounded to 1'.
>  ... and the errors will accumulate).
seems inconsistent with this decision.

And that "will accumulate" seems inconsistent with:
>  They will do both things: cancel but still
>  accumulate.

Bill Noyce, you wrote:
> I only bothered to look at the first two lines of data presented ...

If 100 was a small sample then 12 is even smaller!  What does this
0.61 indicate? That values that are either rounded up or down will, on
average, have a rounding 'error' of 0.5?

I'm not sure that this much is in contention.  The claim leading to
the experiment was that the roundings could add up to an error of 3
minutes of arc (0.5x6).  Which seemed to be what Alex was saying, too:
"the errors will accumulate".  While in theory this 3' error is
possible, I set out to show that in practice it is so unlikely as to
present a negligible risk.

I think the results speak for themselves: 86% within 1', 14% within 2'.

As for the "well-established fact", if this indicates [0.5 x sqrt6 =
1.22], then we may not need to argue about that, either - this may not
be inconsistent with the results of the experiment.

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