mathematics

Reader Kevin Anetsberger is a fan of nomography (basically, the use of printed charts as calculating aids) and he wrote to say that the sorts of “slide charts” I mentioned in my April 5, 2008 entry are far from extinct—and interestingly enough, the world center of manufacturing for slide charts is back in my home town, Chicago. Kevin mentions three companies, and their Web sites are worth a quick look: Perrygraf, Datalizer, IWA, and American Slide Chart.

And although this was posted in the comments on my LiveJournal mirror, it's worth reposting for everyone else: A monograph on nomographs, courtesy Bill Leininger.

I spent a little time looking for instructions on my father's circular slide rule, and by now I'm pretty sure that the device is a Dietzgen/Gilson Midget Circular Slide Rule. I found what may be a manual for it, but it consists of bad TIF scans of the pages, and it is not easy to read—and the rule itself is so worn that making out the scales in some cases is impossible. It was evidently made by Gilson but private labeled and sold by Dietzgen to fill out their product line. The operation is something I would not have guessed: You position the two sliders separately to appropriate scales, and then slide the two as a unit to a third point to read out the answer. The friction clutch is made such that sliding the short pointer moves only the short pointer, but sliding the long pointer moves them both. (I had not noticed this while fooling around with it.) So you set the long pointer first, then the short pointer (which does not disturb the position of the long pointer) and then move the short pointer by moving the long pointer, at which time the long pointer reads out the answer. Whew.

Interestingly, about 120° of the front face is much more worn than the rest of it, suggesting that my father did a lot of calculating within a relatively narrow range of values. What he used it for is only one of a multitude of things I would ask him, if only I had the chance. What he probably would have said (over a grin) is, “I made things not blow up,” which when your stock in trade is bulk methane would be a very good thing.

If circular slide rules interest you, this page presents a number of different models, none of which precisely match the specimen that I have. And if you want to make your own circular slide rule, here's a page with a full how-to. And here's another site that explains how to make both circular and linear slide rules.

I went in for my upper set work yesterday, and spent eight and a half hours in the chair, from 7 AM to 3:30 PM. It took two solid hours for the surgeon to cut my upper horseshoe out of my mouth, consuming (I asked) twelve burrs in the process, three diamond and eight carbide. The cottage cheese I had for supper last night tasted distinctly of machine shop.

But let all that pass; the less you know the better you'll sleep. What I want to talk about this morning is the fact that slide rules are not dead. By no means; I use them regularly, if not every single day. The catch is that they're not general-purpose mathematical slide rules. They're application-specific slide rules that do one thing only—or perhaps two or three related things.

A good example is something I got from Carol's late father: The Triangulator, shown above. It doesn't do trig calculations, but it sets them up for you, depending on which values for a given triangle are known, and which are unknown. Slip the slide back and forth until the holes show you the unknown (a question mark) and the knowns (printed in black) and it will display the formula you need to run to get the unknown.

I've used the Triangulator a time or two, but the one that I've used the most is shown below: Allied Radio's coil winding calculator. The copyright notice says 1960, and I bought it at a hamfest for a dollar years'n'years ago. You can use it to quickly figure a coil for a radio project, assuming you know the inductance required, and if you don't, the flipside of the calculator calculates resonance and both inductive and capacitive reactance. (Slide rules, like records of old, generally had two sides.)

I have a similar reactance calculator from Shure Brothers, but it doesn't have the coil winding feature. Elsewhere in the collection are a couple of English/Metric conversion items, including one I've discussed here before. My favorite actually looks like a slide rule, and isn't made of cardboard:

I scanned all of what came easily to hand this morning, and if you're interested you can bring down the biggish image files. Image 1. Image 2. Image 3. The most mysterious one in my collection belonged to my father. It's circular, and he clearly used it a lot, because the scales on one side are largely worn away.

I've figured out how to do a few things with it, including fraction/decimal conversions and reciprocals, but whether it's got the ability to do general multiplication/division or even square roots is obscure. (The other side is a straightforward circular trig table.) I discern no equivalent of an A nor a D scale, nor how the two hairlines interact. I think it's this item, but lacking a manual I have no way to be sure, and there's no manufacturer's name on it.

So let it not be said that slide rules are extinct. I'm guessing that somewhere is a manufacturer still producing cardboard species as promo items, as I got a world time calculator at a trade show booth as recently as 1996. I like them, as each one doesn't need its own damned wall wart, and they can show relationships as well as values. Toss 'em in a drawer, and when you need one, well, it still works. “Analog” is a real word!