# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Practical Haversine Use
From: David Pike
Date: 2021 Nov 13, 12:59 -0800

Tibor Miseta you wrote:
You can see an overflow here at the tens's digit, the 1. This digit actually just counts the number of tens we added to our negative numbers, and because we deduct the same amount of tens, this is neutral, we simply do not have to care with it (between limits, see later). The above example could be written like this, to make it clear:

But there is a danger here: the overflow of the ten's counter. If you add many (more than five?, I don't recall exactly) logarithmic numbers, the tens counter may overfolw, and you will end up with a false result! But adding 10 to a logarithm is like multiplying a natural number by 10 000 000 000, that is so huge, that our grandgrand(grand...)father mathematicians thought it does not exists in practical problems (all problems in navigations are like this), so no one have to care about the overflow.
So ignoring the ten's digit (together with the minus ten counter) is safe for navigation problems.

I had to read your last two paragraphs a couple of times before it made sense, but yes, I see what Rantzen was getting at.  E.g. 0.2x0.2x0.2=0.008 in logs is:
9.3010 -10
9.3010 -10
9.3010 -10
added = 27.9030 -30  antilogged = 8.0/10x10x10 = 0.008 but we also know antlog 7.9030 is also 0.008, so we can ignore the first 2
Many thanks DaveP
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