NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: How were tables put together?
From: J Cora
Date: 2006 May 26, 09:55 -0500
From: J Cora
Date: 2006 May 26, 09:55 -0500
To solve the navigational triangle one had to use the product and ratio's of trig functions. Logarithms made the calculations easier by converting it to sums and differences. I dont know when the first tables like
ho211 or any potential predecessors came out but my copy shows a date of 1943.
I think that slide rules came into use early on as
napiers bones were based on the same principle.
Which lead me to wonder why tables were the
popular solution in this century rather than some
kind of logarithmic calculator?
My guess would be just more opportunities for
errors to creep in while trying to manipulate the
logarithms.
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ho211 or any potential predecessors came out but my copy shows a date of 1943.
I think that slide rules came into use early on as
napiers bones were based on the same principle.
Which lead me to wonder why tables were the
popular solution in this century rather than some
kind of logarithmic calculator?
My guess would be just more opportunities for
errors to creep in while trying to manipulate the
logarithms.
On 4/20/06,
jimattac@aol.com <jimattac@aol.com> wrote:
I will try dig up some old articles I have regarding this.In the end, no matter how clever the math is, the task of putting together a few pages of these sorts of tables is a daunting task.Jim
-----Original Message-----
From: coralline algae <corallina@ gmail.com>
To: NavList@fer3.comSent: Thu, 20 Apr 2006 17:54:55 -0700
Subject: [NavList 57] Re: [NavList] How were tables put together?
If you would post the links to any articles about
briggs and napier, I would appreciate it.
The topic of how the first log tables were computed, as well as the early trig tables is of great interest to me. The best explanations for logarithms that I found were
http://mathforum.org/library/drmath/view/51432.html
http://mathforum.org/library/drmath/view/55600.html
Also though I assume it came later was calc the area under 1/x say between 1.0 and 1.1 where geometric interpolation can be used
log(1.1 ) - ( 0.1*1/1.1 + (( 1 - 1/1.1)*0.1)*0.5 )
gives an error of only .0001
On 4/20/06, jimattac@aol.com <jimattac@aol.com> wrote:I have read with interest the account of Napier and then Briggs developing early tables of logarithms. Tedious and laborious to say the least.It seems in time there was a plethora of more sophisticated mathematical tables being generated such as navigation tables.How were these put together. Pencil and paper and combining existing tables? Did they farm the work out to groups of people? Did they start to use expansion series to develop them?Thinking about putting together a set of sight reduction tables without a calculator let alone without a computer really hurts my brain!Jim
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