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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@navlist.net [NavList@navlist.net] on behalf of Ashley Betts [NoReply_AshleyBetts@navlist.net]
Sent: Wednesday, September 4, 2019 1:16 AM
To: eremenko@math.purdue.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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