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    Re: Multiplication by addition of logs
    From: Alexandre Eremenko
    Date: 2019 Sep 4, 11:53 +0000

    You added 3 numbers with characteristic -1. This gives -3.
    You added mantissas and obtained characteristic 1.
    Now (-3)+1=1-3=-2.
    This is how characteristic -2 is obtained.
    
    Alex.
    
    ________________________________________
    From: NavList@fer3.com [NavList@fer3.com] on behalf of Ashley Betts [NoReply_AshleyBetts@fer3.com]
    Sent: Wednesday, September 4, 2019 1:16 AM
    To: eremenko---.edu
    Subject: [NavList] Multiplication by addition of logs
    
    Hi All,
    
         I'm finding it a bit difficult to find a source of information on how to 
    correctly process logs for multiplication. I'm using the haversine method to 
    reduce an artificial horizon sighting I took in my backyard. My goal it to 
    only use Nories tables for the reduction. I followed the approach documented 
    at the start of the tables (and as mentioned on here) but the aspect I'm 
    struggling with is how the characteristic of the log is adjusted during the 
    additions for the multiplication aspect of the formula 
    (hav(LHA)*cos(Lat)*cos(Dec)). I have looked at a few example reductions on 
    this site but I can not see how the characteristic of the log is adjusted in 
    these examples. I ended up solving using an excel spreadsheet to see the 
    actual values which then lead me to understand what characteric I needed for 
    the resulting log, in this example. I however want to understand how I derive 
    this value without the assistance of spreadsheet or other source going 
    forward.
    
    The example that I used involved:
    
    LHA = 322deg
    
    Lat = 35S
    
    Dec = 8deg 49.3min
    
    The values I got from the table were:
    
    log.hav(LHA) = -1.02528
    
    log.cos(Lat) = -1.91336
    
    log.cos(Dec) = -1.99483
    
    If I add the mantissa's the result is 1.93347
    
    The resulting log I need is -2.93347. I can see no association between the 
    original characteristics (all -1) or the carry over (1) and the resulting -2 
    that is needed.
    
    Can someone point me in the right direction here with either an explanation of 
    how to go about it or a source that explains this?
    
    Regards,
    
    Ashley
    
    
    
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