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    Re: Ex-Meridian Exercise
    From: George Huxtable
    Date: 2011 Jan 7, 20:11 -0000

    I've taken a look at a modern(ish) edition of Norie's Nautical Tables, that 
    of 1970.
    
    This offers two tables for obtaining the ex-meridian correction. Table I 
    (page 122 to 133) provides a quantity A, which is the variation of altitude 
    (in arc-seconds) of any heavenly body in one minute [of time] from meridian 
    passage.
    
    It's given as A = 1.9635" x cos lat cos dec / sin (lat - dec)
    
    because sin (lat - dec) = cos alt, this becomes
    
    A = 1.9635" x cos lat cos dec / sec alt, in which the trig quantities 
    exactly correspond with those on the slide rule.
    
    But then, because the variation of altitude with time near meridian 
    passageis roughly parabolic, the quantity A, in Norie's, needs to be 
    multiplied by the square of the time difference in minutes, for which 
    another table (table II, pages 134 to 137) is provided.
    
    The slide rule in question works, not in minutes of time, but in degrees of 
    hour-angle, which change by 1 degree in 4 minutes. So, because of the 
    quadratic dependence, the change in alt over 1 degree of hour angle would 
    be 16 x the change over 1 min of time, so the factor 1.9635" should be 
    multiplied by 16, to become 31.416". But the slide-rule is working here in 
    arc-minutes, not arc-seconds, so we divide by 60, to get 0.5236', which 
    corresponds with the slide-rule formula.
    
    There's an additional table III in Norie's, a further correction for 
    increasing deviations from the parabola at larger time-differences from 
    meridian passage.
    
    Does this get Ronald any closer to following what his slide rule is doing?
    
    George
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK
    
    ----- Original Message ----- 
    From: "Ronald van Riet" 
    To: 
    Sent: Friday, January 07, 2011 6:08 PM
    Subject: [NavList] Re: Ex-Meridian Exercise
    
    
    this thread reminded me of a description I read a while ago (and which I 
    have now found again) describing the use of the Blundell 504 slide rule for 
    air and sea navigation (Podmore 1974).
    
    One of the chapters is dedicated to dead reckoning and celestial navigation 
    with a section on Ex Meridian (page 69 in my copy).
    It presents the following equation:
    
    Reduction = .5235 . cos Lat cos Dec sec Alt x HA²
    
    This is exactly how the book gives the equation, no parentheses are used.
    
    This equation was deemed important enough to put a special gauge mark on 
    the said slide rule at this value.
    
    I have been looking in my navigation books for this equation but without 
    success.
    
    Is anyone familiar with the equation and how it is derived?
    
    thanks
    
    Ronald
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