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    Re: Fw: Chichester's Calculations ( comparisons of sight reduction methods)
    From: Gary LaPook
    Date: 2008 Dec 15, 17:33 -0800

    For some reason your posting left off the first two steps in the  H.O. 
    211 solution.
     First you enter the table with LHA and take out "A" (44567.)
    Next you enter the table with declination and take out "B" (2729)  (and 
    "A" ( 46387) which is used later.)
    Then you add "A" and "B" (44567 + 2729 = 47296) and enter the table with 
    this total in the "A" column and take out the corresponding "B" value 
    This is where you posting begins, subtracting this "B" value (2610) from 
    the previously obtained "A" (46387) value taken out which corresponded 
    to declination.
    I have attached the solution and an excerpt from H.O 211 with all the 
    pages needed for the solution. Only four pages were needed for this 
    example because several of the values were found on the same pages but 
    the general solution calls for seven table entries and can use up to 
    seven different pages. The solution also requires five additions or 
    I learned celestial from Mixter, fourth edition, and this book included 
    a complete reprint of H.O. 211 so this is the first sight reduction 
    method that I learned. I soon bought a set of H.O. 214 and never looked 
    back, H.O. 211 is my least favorite method of sight reduction. Of the 
    _tabular_ methods I much prefer Dreisonstok at this point. (But I am 
    real partial to my Bygrave slide rule.) When my eyes were younger I 
    preferred the Weems Line Of Position Book but I have greater difficulty 
    now using the Rust diagram. Apparently others complained about this 
    because Weems includes a mathematical solution for azimuth in addition 
    to the Rust diagram in the 1944 edition of his book. He made some other 
    changes at the same time. He changed the arrangement of table A so now 
    each page is entered by latitude not by LHA which adds convenience for 
    working a number of sights from the same assumed latitude similar to the 
    convenience of H.O. 249, H.O. 218  and of H.O. 214 compared to the 
    _inconvenience_ of H.O. 229 (I still don't know why they changed the 
    arrangement and ruined a good thing!) He also changed the size of the 
    book from a handy 10 by 6 inches to a much larger 14 by 8 1/2 inches, 
    not so handy but it does make the printing larger.
    So comparing the various standard methods of paper based sight reduction 
    the Haversine- Cosine method takes the most work. The Sine -cosine 
    method is a little bit less work but there is the problem with logs of 
    negative values of cosine for LHA. Although this method can work with 
    some cases, since it cannot be used in all cases it just makes a 
    navigator's life more difficult to learn both of these methods. (It is 
    probably the best method to use with a calculator, however.)
    All the short tabular methods are more convenient than the previous 
    two.Of the short methods H.O. 211 takes the most work (although it does 
    allow working from the D.R. but this normally doesn't make any 
    difference in practical navigation) followed by H.O 208 and the shortest 
    solution is the Weems Line Of Position Book.
    The inspection tables, H.O 214, H.O. 218, and H.O. 249 have the same 
    arrangement of tables and are equally convenient. H.O. 249 volume 1 is 
    especially good when working a round of star sights as you don't need to 
    compute individual LHAs so for this use it is better than the other 
    tables. H.O 214 includes the necessary factors to allow working from a 
    D.R. but you can also calculate these factors for H.O. 218 and H.O 249 
    if you need to do this, such as for practice sights from a known 
    location. These tables are only slightly faster than the Weems book. All 
    the inspection tables take up more space on the shelf than the short tables.
    H.O 229 is not as convenient as the other inspection tables and requires 
    more interpolations. However these  tables might provide slightly 
    greater accuracy for high altitude sights but this probably makes no 
    difference for practical navigation.
    waldendand@YAHOO.COM wrote:
    > Here's an HO 211 solution:
    > Hearty thanks to (and check out his other great programs!):
    >     REM HO-211 SIGHT REDUCTION v3.9
    >      REM 22 OCTOBER 2004
    >      REM Copyright (C) 2004 by Stanley Adams, All Rights Reserved
    >      REM sadams16@yahoo.com
    >      REM www.geocities.com/sadams16
    >  Give K the same name as Dec.
    >  K~L: Add K and Lat, if contrary name.
    >    Subtract smaller from larger, if same name.
    >  If t > 90° then take K from bottom of table (90°-180°).
    >  Take Z from bottom of table (90°-180°) except when K is same name as Lat
    >    and greater than Lat, then take Z from top of table (0°-90°).
    >  If Lat = N and t = E then Zn = Z
    >  If Lat = N and t = W then Zn = 360°-Z
    >  If Lat = S and t = E then Zn = 180°-Z
    >  If Lat = S and t = W then Zn = 180°+Z
    >    Lat > 0° is N,  t > 0° is W
    >    Lat < 0° is S,  t < 0° is E
    >  K and T angles within 8° of 90° cause inaccurate Hc, interpolate B(R)
    >  If A(Z) is negative when Z is near 90°, then interpolate B(Hc), or use zero
    >  Hc is below horizon if K~Lat > 90°
    > LAT=   43°00.0'N,  DEC=   20°06.0'N
    > LHA=  339°00.0'W,  T  =   21°00.0'E
    >  A(Dec)= 46387.0
    > -B(R)  =  2610.0  Interpolation OFF
    >        -----------
    >  A(K)  = 43777.0      ?    K  =  21°24.5'N
    >                          +-Lat=  43°00.0'N
    >                               -------------
    >  B(K~L)=  3160.0      ?    K~L=  21°35.5'
    > +B(R)  =  2610.0
    >        -----------
    >  A(Hc) =  5770.0      ?    Hc =+ 61°07.0'
    >  A(t)  =     1.1
    > +B(Dec)=  2729.0
    >        -----------
    >  A(R)  = 47296.0
    > -B(Hc) = 31603.0  Interpolation OFF
    >        -----------
    >  A(Z)  = 15693.0      ?    Z = N 135.8° E,  Zn = 135.8° T
    >  Verify: Hc =  61°06.7',  Z = 135.8°,  Zn = 135.8°
    > >
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