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Re: 4-digit Circular Sliderules
From: Hanno Ix
Date: 2015 Feb 27, 19:42 -0800
Re: My Circular Slide Rules

2. Usage, part 3

We now switch over to describing a detail on SCALE2. Otherwise, this scale's inner hi-res slide rule is identical to the one of SCALE1. The difference is the color pattern  on the lower right quadrant's rim. The purpose of it is again finding the proper color of the spiral on which a particular number is located.  This design however works faster, I think.

Note that the hi-res spirals and this color pattern are off-set to each other: 1000 of the inner scale is at the top, the first 100 of the color pattern lies to the right of the circle. This is done for clarity and speed. Further, this pattern covers 2 decades - I will get to that later. Ignore the second for now.

The pattern represents the colors of the spirals with the addition of just those numeric values - red, 3 digits - located at the border between two adjacent colors. These numbers are also the ones you will read - black, 4 digits - under the black pointer when it is reset to 1000 on the inner scale. So each colored rectangle represents an entire spiral.

Example of using the color pattern on Scale2:
a = 136; b = 247;
find the color of the spiral on which a*b
lies.

Step I: set the black pointer to 100. Again,  the red pointer will move with it, for now at some random angle apart.

Step II: Fix the disk, move the red pointer to factor a, 136. 136 is not indicated, so at least make a guess based on the red numbers. This will establish the angle between both pointers.

Step III. Release the disk and move it until the black pointer hovers over the factor b, 247 or the position that is as close as you think.  While you do that the red pointer will move along. But make sure the angle between both pointers established in Step II will not get disturbed while both pointers move during this Step III.

Step IV: Notice the color under the red pointer. The result will be on the spiral with that color, here magenta. If the pointer falls on a border between 2 colors you will know the result will be close, left or right, to the line that stretches from the beginning of the spirals to the end.

___________________________________________________________________

part 4.

Now to the second decade. This is simply a repetition of the first. It is meant to solve a nasty issue with slide rules that are not circular: results falling "off scale". I have chosen the numbers in the examples purposefully such that it doesn't occur: the result lies within the same decade. So, for instance, 136, 247 and 136*247 fall all into the same decade, namely 100:1000.

But what to do when the result falls outside the decade in which we found the factors? Example: 3 and 4 fall in the same decade but their product, 12, falls in the next one above. Well, I have provided a second decade in the color pattern so that you still can read the color of the spiral on which the result occurs.

If you ever have used a straight slide rule you will know this problem and how it is handled. You will agree, though, this is not a problem with circular slide rules: the inner most spiral is just a seamless numerical continuance of the most outer one and v.v.  because the beginning and the end of a decade are represented by the same angle.

This however causes another problem which all logarithmic slide rules have: they can calculate only with most significant digits without an indication in what decade the numbers fall. Consequently, 3*4 could be read as 0.012, 12000 or 120,0000.

So, it is upon you, the user, to find the correct decade of the result! The way to do that is by using the so called scientific notation of numbers.  I will not go into that because there are a number of excellent websites that describe it in any detail you wish, e.g. the following one:
This completes the present discussion of he theory and practice of doing multiplications with my Circular Slide Rules. If there should be a need to describe division and other operations I will gladly do so. Just let me know.  Also, please let me know if there is an inaccurate, incomplete or mangled section or if you wish to see more examples - I will oblige.

I am still working on building a series of these slide rules and discuss them when finished.

Most of all I hope you will enjoy the slide rules!

H

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