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Well,
   After reading some of the replies I kept telling myself there is no way
that I would have made such a mistake in my programming as simply forgetting
a set of grouping parentheses- it had to be much worse, much more
complicated than that... that whole parentheses bit was just a mistype on
the email as it was late and I was tired.  I would never make such a silly
mistake as if I were  a child back in pre-algebra, standing by my teacher's
desk as he explained yet again why it is so important for me to get my
parentheses straight.
   However- upon inspection just now after along day of work, I notice that
INDEED, I had forgotten a set of parentheses and must attribute that to
programming my calculator also after long days of work and being tired.  And
upon correction, my problematic LHA values were no longer problematic.
Huzzahs to you all for the help.
   But I am still wondering why the equation worked just fine for all the
other values and only started giving me error messages after LHA>345
degrees.  All my Zn calculations were fine until then.  That will give me
something to do for the next couple of nights.  I've also tracked down the
alternative azimuth equations in Bowditch for even more fulfilling evening
pursuits.
   Further, while we are on the subject: What exactly is meant by Step 3 on
pg 279 of the N.A.?  Is it simply that if the value calculated for X is
greater than 1, then X is assigned the value +1, and hence when A is
calculated (cos-1 X) it is simply 0 degrees True, and 180 degrees True if
the value of X is less than -1 (hence = -1)? And what is defensive coding?
Am I correct to assume simply putting in the If clause in my programming to
insure that if X>+1, then set it equal to +1 &c.?
   Thank you all for your help, once again.  I do hope I am improving.  And
for what it is worth, for the complete example set of values for the Altair
sight I included in my original e-mail:
LHA= 354.0575
Dec=8.885
Lat=38.563
Hc=59.84507789
Zn=168.2510887
Hs=59 59.8 (59.99666667)
DIP=-5.9' (-.0983333333)
IE=-0.84' (-.014)
Ha=59 53.06 (59.88433333)
Ref=-0.6 (-.01)
Ho=59 52.46 (59.87433333)
Int=1.755' Towards (.0292554389)

I have been recently shooting sights down to an intercept of .02'- quite
thrilling.  Although I am shooting from the dry.
                                  Todd Shanklin
                                  Salt Point State Park
                                  N38 33.78  W123 20.35

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