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>> Come on Alex, do I quibble about your 0.0 error averages with 1.0 SD's ;-)
>> Of course you have the excuse that your sextant only reads to 1!0.
>
> I did not quibble:-) I just brought to your attention
> the fact that SD characterizes the precision of an individual
> observation. In my case, when the sextant reads to 1', the theoretical
> limit is .5', and SD=1'  seems OK.
> But I would not be completely satisfied with a series taken with
> SNO and having SD=0.6', because SNO's theoretical limit
> (accuracy of reading the scale) is 0.1'.

OK, I'll take the bait.  First a question.  What is the smallest marked
increment of measurement on your SNO-T?  If I recall it is 1 minute (like
your box compass).  A magnifier is used to aid in visually interpolating the
last significant figure, so +/- 0.1' when recorded.  What is the smallest
marked increment of measurement on the box compass?  1 minute.  How do we
know that you don't have some jury-rigged sub-miniature super-high-power
magnify device with you that lets you read the box compass scale to 0.1'?


To be clear, I am joking. I do get the difference, some scales can only be
read to the closet subdivsion. (Just between you and me, are you
interpolating?)

> In one of your message of yesterday, you again expressed
> your worries about almanac's rounding of Sun
> SD (semidiameter) to 0.1'. Unfortunately I cannot site that message
> literally, because we are on the NavList now, instead
> of the good old Nav-L.
>
> So let me explain why I think that this rounding
> (and the whole procedure of determining IC from Sun)
> seems correct to me.
>
> Sun's SD changes slowly and regularly over the year.
> So it is safe to assume that the almanac's value of
> Sun's SD is within 0.05' of its real value.
> (When you round a number, you introduce an error of 1/2
> of the last preserved digit).
> Thus the maximal rounding error in 4SD is (4 times 0.05)=0.2
> (not 0.4 as you assume!).

The current message was posted on NavList. I quote me, "While on the subject
of matching published 4SD exactly, I find that foolish. SD 15.8" one day,
15.9' the next.  4SD jumps from 63.2' to 63.6' in one day? Really?  No, not
really.  It's at a rounding point, so SD is closer to 15.85'.  And 4SD
closer to 63.4'."

How the heck does a world-class mathematician subtract 63.2 from 63.4, or
63.4 from 63.6 and get 0.4?  New math? 

Here I am not joking.  My typos are probably legend.  I stand by my
assertion that a one-day jump in 4SD should not be 0.4' in reality, and
interpolation is prudent in some situations.

> Now when you do IC test, you ADD two observations, and
> compare the result with the almanac value.
> If the dirreference is greater than 0.4'
> the test results should be rejected.
> (This is what the rule says).

I can live with that (4SD for the SD interpolated at the time).  An example
of my case for interpolation follows:  On July 25 I observe 4SD as 63.1'.
Published SD is 15.8' = 4SD 63.2'.  Off by -0.1' so accepted.  July 26 I get
the exact same observed 4SD, 63.1'.  Now SD is 15.9' = 4SD 63.6.  Off -0.5
so rejected. Using an interpolated SD of 63.4', both days would be off -0.3'
so accepted.

In the case of being 0.5' over published (63.7') on the 25th, that would be
rejected.  The same reading on the 26th would accepted.

To some extent the 4SD figure seems to magnify any individual errors IMHO.
What we have really done is move one limb to the opposite limb and measured
the diameter (after IC), so an average of the on the arc and off the arc
figures (after IC) should equal 2SD in a perfect world.  In this case the
0.4' 4SD test becomes 0.2' for diameter (2SD). Which allows for combined
errors of no more than 0.2', or 0.1' (worst case scenario) per observation
before rejection.  That's pretty near the man/machine limits even at the
upper limit of rejection.  An interpolated SD provides. IMHO, a fighting
chance.

My real concern is that I undershoot 4SD perhaps 95% of the time.  If 4SD or
2SD observations were on both sides of published or interpolated 4SD or 2SD
I could accept that.  Being under the mean most of the time causes me to
look for a systematic error.

Bill




Bill


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