Further Exploration of Slide Rules

published 2025-10-11

by Christopher Howard

Before discussing accuracy and precision, these terms require definition. The word accuracy as used here denotes how closely a solution conforms to fact. Precision of a solution is an indication of the sharpness of definition. As an example, consider the value of e, the base of natural logarithms. The value 2.718282 is more precise than 2.718, but both values are accurate.

Analog computers generally yield results having three, or at most, four significant figures. However, for many engineering purposes, three significant figures will be adequate, since the original data will be no better. Unfortunately, many people seem to think that a solution which contains ten significant figures is highly accurate, even though some of the input data have only two or three significant figures.

— Electronic Analog Computer Primer, Stice and Swanson, 1965, pg. 4

Probably the chief advantage in analog computation is that the operator retains a "feel" for his problem. The twisting of a potentiometer represents, in a very real sense, the variation of a controller setting or the changing of a coefficient in the process which is under study. Thus, the analog computer set-up becomes a working model, or simulation, of the real physical problem, and the operator finds himself thinking of one block of computer components as a control valve and another block as a heat exchanger. Changes in settings of computer components thus become meaningful in terms of the real process, and the results of these changes can be interpreted immediately in the same terms. The operator can "think as he goes," and if interesting side avenues open up, these can be immediately explored.

— ibid, pg. 3

I continue to experience delays in getting my THAT analog computer. To make a long story short, I finally figured out how to submit a duty dispute request to UPS, which is the process for getting tariff-related problems corrected, but I was told that they are so backed up, that the process would take at least three months. I opted instead to have the package returned to sender. I'm hoping to get Anabrid to re-send the unit, maybe with the copper cables removed.

Meanwhile, I continue to explore slide rules. Through donations from various friends, I now have a collection of four different straight-edge slide rules, as well a few specialized slide-rule like computers made out of cardboard or thin plastic. The one currently within arms reach is a miniature Deci-Lon 5 slide rule from Keuffel & Esser Co, which has 26 scales, if we include the C and D scales which are repeated on both sides.

For the last few days, I have been using slide rules for all problems involving multiplication, division, or trigonometry. I have also started working through a classic text on the subject, Post Versalog Slide Rule Instructions, by Frederick Post Company, 1963.

On thing that has stuck out at me is the variety of ways available to multiply or divide numbers on a slide rule. Different methods exist using the C and D scales, the CI and D scales, as well as the folded scales, CF and CIF. Each method has different subtleties and different advantages and disadvantages.

I am finding that, broadly speaking, all my slide rule math problems can be categorized into those that do not require the assistance of pen and paper, and those that do. The former includes the most basic conversions, such as converting inches to centimeters; as well as calculating angles based on right-triangle measurements. The latter includes all problems that involve more than one multiplication or division, or that involve any one operation where the decimal places are not at the same location. The pen and paper is required to keep track of the exponents properly.

I find, therefore, that I am having to use pen and paper for some problems in which I might otherwise — using a digital calculator — be able to get by with just doing some rapid fire calculations. This could fairly be cited as a disadvantage of the slide rule. However, I am finding with the slide rule plus pen and paper, it is harder to make mistakes, and when I do make them, they are easier to locate. One can quickly review if the exponents were properly added and subtracted. With the operations on the significand numbers it is easy to see — from a rough approximation — if the result is reasonable or not. E.g., if I calculate that 2.34 x 5.4 = 1.26 x 10¹, I can see that an answer near 2 x 6 = 12 is plausible.

Another mistake I occasionally make is multiplying when I should be dividing, or the other way around. But this is also easier to recognize with the factors laid out on paper. And of course the same mistake can also be made with a digital calculator.

I feel like I am doing more thinking and understanding when I work with a slide rule, as opposed to hitting the multiply key on Emacs Calc, or calling the calc-arctan function.

One fun activity a few days ago: out in the yard I used my miniature slide rule to calculate the elevation of the sun, based on measurements of shadows. It happened to be at about 13 degrees above the horizon, at the time. This is a little rough, of course, if your shadow-casting object is not exactly plumb, but it was good enough for my purposes.

Copyright

CC BY-SA 4.0 Deed