# NavList:

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

**Re: Longhand Sight Reduction**

**From:**Hanno Ix

**Date:**2014 Jun 15, 21:57 -0700

Greg, you wrote:

*The graphical logs are about 6 pages vs. 15 of numerical logs. Lets call it a 3 to 1 space savings by using the graphical format. The same could be done for trig right ?*

and my answer was, I don't know.

I worked somewhat on it since and found that the total length is indeed simply proportional to the number of steps of angles on your sin() ruler. That sounds perhaps obvious but it isn't. It would not be the case for tan(). Now let's estimate the lenghth of your sin() ruler:

For CelNav, the finest resolution of a table is 2 arcmin I think. So let's assume the same for this ruler. That would make it 90* 30, or 2700, bars on your ruler. From my 20 inch slide rule I know that 5 mm per decade is hard to read, 10mm per decade is nicely readable. This latter choice would render the total sin() ruler 2700 mm or 1,063 " long.

The Graphic Table I posted a copy of the other day has 20 lines per page, and a length of a line is ~ 5" . That makes 100" per page. In this scenario your sin() ruler would cover ~ 11 pages. However, there are choices you can make one being 25 lines per page. For this version you would need only 8 to 9 pages for your sin() ruler. Not bad.

Frankly, however, a simple sin() table with 2 arcmin per step is much shorter: 2 pages only. I have one. If you compare now both implementations of a sin() reference you see immediately why this is so. There is lots of white space on a page of the sin() rule whereas virtually the entire real estate of a table is covered by numbers. So the information per square inch is much higher on the table.

This is in contradiction of your observation. Are we sure we are comparing apples with apples?

Hanno