Guess Who Was President of the Slide Rule Club?

My junior high school (in central New Jersey) had a slide rule club, and I was a member.  As I recall, the other members tolerated me mainly because I knew how to use the log-log scales, which mystified just about everyone else.  I certainly wasn't elected to any exalted position in the club!  But this fellow was: Michael Bloomberg.  Yes, that Michael Bloomberg...

Engaging the Mathematical Mind...

I've posted before about the way in which doing math by slide rule forces one to estimate the answer before “reading” it from the slide rule.  You can't get an answer from the slide rule without actually understanding the math in the problem you're trying to solve.  Calculators eliminate that requirement, to my regret – and, I think, to the detriment of our young folks learning how to apply math to the real world.

Here's a calculator that changes that, in an interesting way: it won't give you the answer until you've supplied an acceptable estimate.  That is exactly how it works with a slide rule.  As I read the description of the QAMA calculators, it occurred to me that there's an even simpler way to make a calculator that “behaves” like a slide rule: simply disable the decimal point display!  Such a calculator, if you were to (say) divide 1 by 7, might display 142857143 – and it would be up to you to figure out where the decimal point belonged.  When I divide 1 by 7 on the slide rule at my desk, I read off the answer as 143 – the same answer as the decimal-less calculator, but to less precision.  In both cases, I'd have to estimate the answer in my head to figure out that the decimal place was before the first “1” (the correct answer is 0.143, to three decimal places).

I don't suppose I'd actually be able to talk people into disabling the decimal display :-)

In the News...

Here's something I don't get to write very often: slide rules in the news!

I have several of the Gilson slide rules in my collection, including a couple in pristine condition...

Mysteries of the Ancients...

The Lost Art of Nomography...

Nomography is a word you don't hear much any more, though when I was a kid nomographs were quite common in the electrical engineering world (and in other engineering and science specialties as well).  They're closely related to slide rules, which long-time readers will know are a special interest of mine.  Here's an interesting paper on the Lost Art of Nomography (PDF)...

Slide Rules...

Amazing!  I'm not the only one who thinks it would be a good idea for today's kids to learn about slide rules...

Surprise!

On the way home from work last night, I picked up a package at the Post Office.  It was from a friend (Franz M.) in Munich, Germany, and it was full of slide rules.  I haven't purchased any slide rules for many months, so for the first time in a long while I had the pleasure of opening up a box with some beautiful old instruments in it.

My favorite of the bunch is a circular “Columbus Calculator”. Mostly it is conventional in design, except that it's made of engraved metal (that is, the scales are engraved).  I'm pretty sure that the engraving is photolithographic, and it's very nicely done.  The face is plated (with brass, I think) and the plating has worn, exposing parts of the underlying metal – yet the scales are still perfectly readable and usable.  I've never seen another like it, nor can I find any reference to it online...

Slide Rule Humor...

Via a fellow slide rule collector who wishes to remain unnamed:

TEACHER ARRESTED IN NEW YORK

A public school teacher was arrested today at John F. Kennedy International Airport as he attempted to board a flight while in possession of a ruler, a protractor, a compass, a slide-rule, and a calculator.

At a morning press conference, the Attorney General said he believes the man is a member of the notorious 'Al-Gebra' movement. He did not identify the man, who has been charged by the FBI with carrying weapons of math instruction.

'Al-Gebra is a problem for us', the Attorney General said. 'They derive solutions by means and extremes, and sometimes go off on tangents in search of absolute values. They use secret code names like 'X' and 'Y' and refer to themselves as 'unknowns', but we have determined that they belong to a common denominator of the axis of medieval with coordinates in every country.'

As the Greek philanderer Isosceles used to say, 'There are 3 sides to every triangle'.

When asked to comment on the arrest, President Obama said, 'If God had wanted us to have better weapons of math instruction, he would have given us more fingers and toes..'

White House aides told reporters they could not recall a more intelligent or profound statement by the President.

It is believed that the Nobel Prize for Physics will follow.

Before and After

This evening I sat down to start restoring a fine old Dring & Fage slide rule, and I finally remembered to do something I've been meaning to do for a long time: show a “before” and “after” photo.

This particular slide rule dates back to the mid-1800s. It's an unusual style, with two slides on each side of the body. The condition of this example is superb, with almost no damage or even signs of wear. The only notable problems are (1) it is filthy, as you might expect from something 150 years old, and (2) the parts fit too tightly to move smoothly.

In the photo above, the top piece is a segment of an uncleaned slide and the bottom piece is a segment of a cleaned slide. This rule has four slides plus a rather large body – it took me 45 minutes to clean the first slide, so the whole rule will probably take about 5 hours to clean.

The cleaning process is simple, but tedious: I soak an old washrag, fold it into quarters on my worktable, sprinkle some Bon Ami onto a corner of the washrag, and then carefully scrub one little piece of my work at a time. The trick is to scrub hard enough to get off all the soiling, but not hard enough to do any damage to the finish – the only way I know how to do this is trial-and-error, starting with very little pressure and working my way up.

Once I've thoroughly scrubbed the entire workpiece, I inspect it carefully for any firmly adhered stuff. These chunks I carefully work off with dental picks. This particular piece had a few specks of something that looked like wax, plus a few paint droplets. Most of the pieces this old that I restore have far more adhered junk.

The last cleaning step is to rinse the workpiece, which is more of a challenge than it sounds. Slide rules like this have very finely engraved lines on them, and if they're made from certain woods (such as mahogany) open pores. These engravings and pores accumulate soap, feldspar powder from the Bon Ami, and fine particles of whatever the slide rule was exposed to in its life. All of this stuff must be rinsed out, and usually the force of the tap water is not enough – I also have to scrub out all the pores with a very fine, stiff-bristled brush. That last bit can be quite tedious!

Once I've cleaned the entire slide rule, and all the parts are thoroughly dried, I'll apply several coats of Johnson's Paste Wax. That will protect any bare wood that's been exposed, and it will fill in small pores and scratches. I let the wax dry for a few hours and then polish it up with a shoe-polishing rag. In the photo above, the bottom slide has been cleaned but not waxed; it will be a little darker and much shinier once it's been waxed.

One interesting thing I've learned about these old wooden slide rules is that they are impervious to water. When I first started restoring these instruments, I was afraid to get them even slightly wet – I figured that would raise the grain and ruin the finish. After a few accidental soakings caused no harm, I started getting bolder about the use of water – and now I don't hesitate to put a 200 year old instrument directly in the tap water. The only slide rule I've ever damaged with water was an unfinished wooden rule made by Lawrence (an American manufacturer of crude, low-end slide rules), and even that one was easily fixed with a little fine sandpaper. The combination of water and Bon Ami cleans the old wooden instruments better than anything else I've ever found…

Fowler's Universal Calculator

This is a fine example of a watch-style circular slide rule, albeit a very large one – it is 87mm (about 3½ inches) in diameter. Click on the photo at right for a large version, or visit my slide rule collection for all the details.

Using one of these slide rules is a bit more work than an ordinary linear slide rule (turning the knobs is slightly tedious), but they pack a lot of accuracy into a very small package. With its three-segment D scale, this one can multiply and divide with the same accuracy as a linear slide rule that is 49 cm (over 19 inches) long – not back for something that fits conveniently into your pocket!

The Fowler watch-style slide rules (they made many models) seem somehow quintessentially English to me: heavy, sturdy, practical, and yet quite sophisticated. I know of no American-made slide rule even remotely like this one, though several American manufacturers made circular slide rules. There were several English manufacturers of fine watch-style circular slide rules, at least one French manufacturer, and even the Soviets made a cheap imitation. But the English models have a unique style that, for whatever reason, was never duplicated outside of England…

Keuffel & Esser 1744

This slide rule (click to enlarge the photo at right) was made around 1897 and sold by Keuffel & Esser. It may have been actually manufactured by Dennert & Pape (in Germany); they made the earlier versions of this model and I'm not sure when Keuffel & Esser actually took over the manufacturing themselves. I've posted this up on my collection web site, including high resolution scans and lots of details.

This one posed an interesting restoration challenge that I had not run into previously – sometime in its history, someone spilled a liquid onto one side of it, and then let the liquid evaporate without cleaning it up. This left a layer of gunk on the slide rule that looked a lot like rust, and was quite difficult to remove – no solvent I have would dent it; I had to soak and abrade it (using Bon Ami). Some staining still remains; I could see under a microscope that the colorant has migrated into the plastic.

In addition, this slide rule had 110 years worth of the grey “gunk” that seems to accumulate on anything that humans touch. I probably really don't want to know what's in it! Usually this gunk cleans off easily with soap or alcohol, but on this slide rule some of the gunk had hardened into something resembling granite. To clean the slide's tongues and grooves I had to resort to carefully picking off the rocky gunk with a dental pick – hard work for these old eyes...

Fun Project

It's a rare and special treat when I can combine my hobby with my professional skills and experience. Over the past few weeks I've been spending some of my spare time doing exactly that – creating a web site to display slide rule information. The information is a compendium of all the models of slide rules ever made by Hemmi, who was the world's largest slide rule manufacturer. The data on this site was collected by Paul Ross, with help from several other slide rule collectors. It is now the “gold standard” reference for everything Hemmi.

The original web site was created (by Paul Ross) using Microsoft Excel. This was a tool familiar to Paul, and therefore very easy for him to use. But the resulting web site only works well with Internet Exploder (Microsoft pays little attention to compatibility), is very slow to download (because the HTML file is huge), and is a purely static page (you can't interact with the web page in any way). Paul is a slide rule god, not a geek. I'm a geek. I volunteered to help, and Paul eagerly accepted.

Last night I posted the first beta test version of the new site, and sent a message to slide rule collectors to have them start banging on it. I got my first bug report this morning, and I'm sure I'll get more. The new site “understands” the Hemmi slide rule data – you can do things like sort the slide rules in various ways, and limit the slide rules that you're looking at. From a technical perspective, one of the most challenging things was figuring out how to display the large amount of data in a way that was both compact and easy to read. This depends on the way the web browsers lay out tables, which is a very tricky thing. To help with this problem, I made many of the user interface details changeable on the fly – something not often seen on web sites.

Bottom line: it was lots of fun!

Soviet Slide Rule

This circular slide rule is markedly different in almost every respect from the usual slide rules manufactured in the Soviet Union. Instead of being "just good enough", and generally lacking in any non-functional attributes, this thing is overbuilt, rugged, and pays great attention to both function and beauty.

It weighs over a pound, is almost 9" in diameter, and can multiply, divide, take sines and tangents, and inverse sines and tangents -- all accurate to 3 or 4 decimal places. Almost certainly it is a military slide rule, probably associated with artillery (calculating the elevation of the gun to aim it is a fairly involved exercise in mathematics).

You can read more about it here.

Ivory Sector Rule

The beautiful old instrument at right is a very fine example of a "sector rule". These sector rules were computational tools, the equivalent of a calculator in their time -- the 1700s and 1800s. This particular sector is made from ivory and brass by the English instrument makers Nairne and Blunt; it dates from about 1790.

You can read more about this instrument at my collection web site.

Slide Rule Collection

If you're wondering where my slide rule collection went to, here it is.

Adventurous Visitors

Just a few weeks ago I was searching for information on an unusual French slide rule (the “Supremathic"). I posted a question a Yahoo Group (ISRG), and a French slide rule collector named Marc Thomas responded with some very useful information. He and I exchanged several emails, and a couple of weeks ago he mentioned that he and his wife (Dominique) would be visiting the U.S. to see their daughter. It turns out that their daughter lives in Riverside, California, which is just 100 miles or so north of us. So Marc wondered if perhaps he could visit while he was over here.

Although meeting another collector (and showing off my collection!) sounded like an interesting experience, my first thoughts were to discourage him. Most Americans who try to find our home have trouble (we’re way, way out in the boondocks!), so what were the chances of a Frenchman, in unfamiliar territory, locating us? I wrote back to tell him I’d love to meet up, but that he should be concerned about the distance and remoteness. I figured that would be the end of that…

But yesterday morning, I got another email from Marc — he and his wife were in Riverside, and he wondered if it would be possible to visit with us that very afternoon! So I wrote up some very detailed directions for him, and sent them off by email. The plan was for him to arrive sometime after 4 PM, and he’d call if he couldn’t make it.

Well, 4 PM rolled around, and no call from Marc. And 15 minutes later, a little red car came rolling up our driveway, and out popped Marc and Dominique. They made it!

For the next couple of hours, we had a most enjoyable meeting with these folks. It turns out that Marc is a professor of mathematics, and Dominique a professor of history. Dominique and Debbie immediately got into a conversation about cats, and dogs — and Dominique was fascinated by our birds, especially the hummingbirds. Marc and I went through a couple dozen of my slide rules, and it was great fun to show him several that he had read about, seen photos of, but had never actually seen in person. Debbie got to show off her collection of ribbons from dog competitions, and it was a lot of fun to watch Dominique going through them — she particularly liked the multi-colored “title” ribbons.

Marc and Dominique wanted to drive back to Riverside in the daylight, so they had to leave quite early. We could hardly blame them for wanting to drive while it was light, but we would have greatly enjoyed a longer visit. It was quite an adventure for them to drive all the way down here, and they got to see some parts of California rarely seen by most Americans, let alone people from another country. And it was quite an adventure for us as well — meeting this very interesting couple with a vastly different life experience than ours, but still having many points of common interest. Marc is the first slide rule collector who has ever actually seen my collection — while I have parts of it on the web, and I correspond with dozens of collectors, not a single one has ever made it out here before!

Slide Rules

If you found this blog because you were looking for Tom Dilatush, the slide rule collector, you’ve found some scribblings by the right guy — but you’re in the wrong place.

Mike Konshak (the proprietor of the indispensable International Slide Rule Museum) offered to host my slide rule collection on his web site. That was such an attractive offer that I could hardly resist, and my collection is now slowly making it’s way onto the web at this new location. As I write this, I’m approaching 100 slide rules scanned, photographed, and documented.

So go take a look!

Slide Rule Lessons

Two of my readers (independently, so far as I know) actually asked me to publish lessons on how to use a slide rule. I published one last week, and this morning I was working on a second lesson. Then it occurred to me that someone else might have done this already, so I Googled a bit and found that my friend Mike Konshak, of the International Slide Rule Museum, already had an excellent slide rule course up on the web!

I don’t see much point in duplicating what he’s done, and I don’t see much opportunity to do it better. So at the risk of alienating a significant fraction of my readers, I hereby declare my slide rule lessons have been adjourned. Go look at Mike’s course!

Slide Rule Collection

Thanks to a very generous fellow — Mike Konshak, of the International Slide Rule Museum — I now have access to a “real” server to host the web site for my slide rule collection. If you’d like to see the beginnings of it, you can find it here. Right at the moment there are only a dozen or so items on line, but I’ll be posting more on a regular basis, hopefully a few each evening I can spare some time.

I’d love to hear what you think of it — leave comments here, or drop me a line…

Slide Rule Lesson #1

This post, dear readers, is being inflicted upon you at the request of one of my, er, less conventional readers. He actually asked me to explain a bit about how slide rules work, and how you use them.

So I’ll start with the basics. The “scale” you see in the photo (click on it to enlarge it) goes by many different names, depending on exactly where you find it. On the slide rule that I scanned to make this picture, it’s called a “C” scale; that name is just a convention and doesn’t actually mean anything. Virtually all slide rules made after about 1900 used “C” to mean this line. One early device that used this line was called “Napier’s bones"; they were engraved on ivory sticks (the “bones"), and invented by the famous mathemetician Napier. Later they were found engraved on sticks of wood invented by a fellow namd Gunter; these were called “Gunter’s rules” and were in use for hundreds of years.

Whatever instrument you find this line on, you read it from left to right, with the values ranging from 1 to 10 (even though the right-hand side just says “1"; this is another common, though not universal, convention). You’ll note that ticks are not evenly spaced, as they would be on a ruler that was measuring a distance. Instead, the position of the number is proportional to the logarithm (base 10) of that number. The center of the scale isn’t 5, as you would expect on an ordinary ruler — it’s about 3.2. And the logarithm of 3.2 is about .5, which is why it’s halfway across the scale.

Confused yet? Let’s try an example, just to show you how a Gunter’s rule was used. Suppose you wanted to multiply 2.2 times 3.3. You would start by taking a pair of dividers (like a compass, but with two points instead of a point and a pencil or pen). The first step is to lay the divider along the rule from 1 to 2.2 (see the red “divider” on the left side of the photo). Now for step two: take the divider without changing its setting and put the left-hand point onto 3.3 (see the red “divider” on the right side of the photo). The answer — 7.26 — is read a the right-hand point.

What magic allowed this to happen? Well, it’s the magic of logarithms. You can multiply any two numbers together by adding their logarithms and then taking the antilogarithm of the result. You could do this with the giant tables of logarithms found in old reference books, but that’s quite tedious and only makes sense if you need your answer to a quite high precision. But if you only need two or three decimal places of accuracy, the Gunter’s rule could give you the answer quite conveniently. With a little practice, you can multiply two numbers on a Gunter’s rule in just a few seconds, and very reliably. It’s a machine that automates the computing and addition of logarithms, and taking the antilogarithm to get the answer you want.

The same general principle can be used to divide. Using the same photo, we can show how to divide 7.26 by 2.2. The first step is exactly the same as above, setting the dividers for 2.2. The second step is to set the right-hand point of the divider on 7.26 — and then the answer, 3.3, is under the left-hand point.

Modern slide rules perform multiplication and division using exactly the same principles, but use a number of ingenious mechanical aids to make it faster and more accurate than a Gunter’s rule. More about these improvements in a separate post…