But let me hasten to mention that I'm not a collector in the usual sense. These are not just pretty knick-knacks to me but instruments meant to be used. So while I've managed to accumulate a fair number this year, it's simply because I'm always searching for the slide rule that will do insane things and yet be a delight in the hands.
My slide rules work for their keep...
Sterling Slide Rule
Here we have the first rule I ever owned. As I've mentioned elsewhere, I bought this at a grocery store in the early 1970s for who knows what reason, other than it was intriguing. Those were in my language major days, so I never really did anything with it. Then, a few years later I was pursuing mathematics, and so again never really did anything with it. It lay idle for over forty years before some whim a year ago caused me to pick it up and consider it with curiosity.
Note: You can click any of these pics to enlarge to full-size.
I don't think anyone would call Sterling a premier slide rule company, but maybe they had a more profound influence than at first meets the eye. For Sterling produced a ton of plastic slide rules at a fraction of the cost a pro engineering model went for. And they sold them in grocery stores!
This really isn't all that bad of a rule, once I lubed it up with some paraffin. For one thing, it uses engraved markings, a hallmark of better units. And it's fairly easy on the eyes.
On the deficit side, the CI scale is not marked in red, and there's no ST scale for sines of small angles, instead going with minutes markings on the low end.
Still, this is the guy which got me interested in slide rules after all those years, so in a way I have some special fondness for it.
UTO 601
I have a love/hate relationship with this slide rule! First off, it's exquisitely printed. The lettering is precise, crisp and oh-so easy on the eyes. And then, it reminds one of just what is possible with nothing more than its Rietz layout.
Indeed, I first got one of these (off of eBay) after seeing all the magic that's possible in the first five installments of Professor Herning's superior video tutorials. I really ought to put a link to those here once again:
It truly is one of the cutest rules ever made (from Denmark, by the way). So what's to hate?
Well, the plastic (PVC I think) is a bearcat to get cooperation from. In particular, when it grips, the action is jerky. You'll find yourself jumping from one side of the desired number to the other and back again, always failing to land right on the requisite spot. Back and forth, like a stutter.
Still, I have found that a good wax-job with paraffin does wonders for the action, both on the slide and the cursor. So, I'm willing to cut this sweetheart a bit of slack.
The UTO 601 shows up all the time on eBay, generally overpriced. Wait long enough and you'll get one like I did for ten smackers, postpaid, which is what I would value it at.
Despite the creaky action, I really do think this is one of the more elegant rules ever made, and at five inches long it packs a lot of power in your shirt pocket!
Aristo 803
Here's a real gem, another rule for the breast pocket. The Aristo is from Germany. What I love about it is that the lettering is so crisp (like the UTO, above), includes the red reverse labeling for the CI scale, but moreover employs a splash of yellow to keep less commonly used scales from confusing the eye.
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| Remember, you can click on any photo to enlarge it. |
The one I got was a bit slippery, but a buff job with paraffin gave it some grip, as counterintuitive as that sounds. Now it's one of the smoother operating units in my collection.
By the way, both the Sterling and UTO mentioned above have the trig scales on the back of the slide. This Aristo, on the other had, puts everything on front. All three are simplex rules, but with the Aristo and its Euro-style layout (as Professor Herning denotes it) you'll never be flipping the slide midstream whenever trigonometry arises.
Picket 1006-ES
You want small? We've got small! This amazing aluminum unit from Pickett (an American manufacturer) is the daintiest slide rule I've ever seen, six inches long and about the width of a quarter. And yet surprisingly the markings are so crisp that even my old eyes can easily read it.
No corners were cut in its construction either. Apart from the cursor panes, everything is metal and sports full alignment setscrews throughout. After a quick dose of Teflon bicycle lubrication, it really does have the silkiest behavior of any rule I own.
Moreover it's a duplex rule with an incredible array of scales for such a little guy: A, B, C, D, CI, DI, CF, DF, CIF, L, S, T and ST. That they managed to pack this all in without taxing the oculars is quite bewildering.
You'll note that I've used it for quite a few of the exercises on this site, simply because it's so full-featured and wanted to see how much I could squeeze out of it.
There are only two drawbacks, and they aren't deal-breakers. First, it's printed with that god-awful yellow background. Pickett called this an "eye saver," claiming physiologists had proven that shade was less stressful. To which I say, hooey. When you start getting cataracts, a white background is a welcome relief.
Then, the CI scale is printed in black, instead of red. (Scales which read right to left are typically printed in a contrasting color to remind the operator of such.) However, Pickett thoughtfully placed a "<" symbol next to the numbers which read in reverse, so the absence of red isn't that big of a deal.
All in all, I think this is a magnificent rule. If I was only granted one mini pocket type, this would be it. It's powerful, easy to read and slides smooth as silk.
Keuffel & Esser 4181-1
Here's the last of the pocket slide rules in my collection, and it really is something. It has all of the scales mentioned above in the Pickett 1006-ES, but also works in the LL1, LL2, LL3, LL01, LL02 and LL03. Thus this unit can easily handle natural logs and exponentials in addition to arbitrary roots and powers.
The construction is elegant throughout with full adjustments for the tension, alignment of the stator halves as well as the duplex hairlines. Additionally, the hard plastic used is quite smooth behaving, so it's easy to find a required number without pushing or pulling unduly. Finally, reverse reading scales are marked in red which is always a benefit.
About the width of a half-dollar, it still will fit a breast pocket easily and put a wealth of fairly complex calculations at your fingertips.
Pickett N-500-ES
This is the second slide rule I ever bought. It's hard to imagine, but it was just last year, four decades after the Sterling. I was lucky to have found the right dealer, The Slide Rule Trading Company. I had explained how I had developed an interest and was searching for a "serious" unit, one that could handle a wealth of computations but was easy on the eyes. They suggested the Pickett N-500-ES which I then bought, and for a very fair price. Yes, it is a honey and would keep a person satisfied for a lifetime.
I really ought to give this company a plug. It's always a delight when someone is more interested in fulfilling a customer's needs as opposed to just "making a sale."
This duplex rule has all the features of the K & E described immediately above, but is now in the 10 inch size. Likewise, all of the remaining slide rules described here are full-sized.
When I first got it I hassled around with getting the action smooth. The manufacturer's recommendation of Vaseline is a totally false trail, unless you enjoy greasy aluminum detritus all over the place. I finally homed in on dry Teflon lube used for bicycle chains and now the rule is not only silky acting but stays clean. While some people turn their noses up at Pickett metal rules, I've found them to be the most responsive of all after an application of Teflon.
Pickett N4-ES
As much fun as it is to master something completely, I've always felt it's more rewarding to start a journey which never ends. That's the way I see this slide rule. Every time I pick it up I discover some new untapped power within it.
It's another aluminum rule, of course from the American company, Pickett, so all of my previous comments about Teflon lube apply here. Still that hideous shade of yellow, but other than that, one insanely powerful unit with several innovations.
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| You'll want to click to see this one enlarged! |
First off, the A and B scales are missing (which are half-length scales used for squares and square roots). Instead, Pickett has provided two double-length scales on the stator (one for odd digit numbers, the other for even digit numbers). What a difference these greatly expanded scales can make in resolution!
Likewise, the K scale is vamoose, being replaced with a triple-length cube/cube-root scale. No more squinting!
And T scale? Well it's now double, giving tangents from 0 to 45 degrees, wrapping around and continuing from 45 to 84.3 degrees (at which point the tangent explodes beyond a value of 10, of course). Not bad, and no more finding the reciprocal of the tangent of the complement for angles beyond 45 degrees: just read off the value and you're done.
As if that weren't enough, the N4-ES also handles hyperbolic sines and tangents, again with wrapped scales for twice the action!
Finally, there's an additional LL4 scale, greatly expanding the high end range of results possible with numbers raised to an arbitrary power.
This really is one fierce slide rule!
Aristo 0903LL Scholar
Here we have the most recent addition to my collection. Rather remarkably, I got it from Germany for $9 postpaid! And it's in beautiful condition.
The Aristo 0903LL is a German made slide rule. It's quite beautifully laid out, with the contrasting white and yellow backgrounds (as mentioned above) to help the eye group related scales.
It's a simplex rule, but the back of the slide features the S (sine) and LL2 and LL3 (base e exponential) scales. And, oh, it also came with a really decent hard-shell case.
Post Versalog 1460
Here we have the only bamboo slide rule in my collection. The American company name is Frederick Post, however apparently they didn't actually make the things, but arranged for Japanese construction, then imported the final product.
Yes, bamboo really is smooth acting, and supposedly is self-lubricating to boot. I also love the heft of the unit. This guy is a delight to use.
The marking are exceptionally clear and crisp, and the colors contrast nicely with the white.
Now as to the scales, you'll find most of the usual culprits. Unlike the Pickett N4-ES described above, the Post Versalog opted to include the LL0 for smaller numbers, in lieu of the LL4 for larger ones.
However, it uses the same idea of leaving off the A and B scales (which are half-length square-root scales and difficult to read) instead going with a double-length scale. That is, rather than A being shorter than D, we now have R1+R2 being longer than D. This really bumps the accuracy.
Faber-Castell 2/82
After the slide rule bug bit last year, I started yearning for a Faber-Castell, made in Germany. The pictures I saw really caught my eye. There was something so clean and immaculate about their designs.
But they are fairly expensive on the open market. However, one night in a moment of weakness, I jumped and ordered this guy.
It's very smooth to the touch, being made of a far more exotic plastic than cheaper rules. A bit of cleaning was all it took to make it slip and slide neatly.
As for the scales, they're pretty standard for a high end device. Two things are different, however. First off, there's a K (cube) scale on both the stator and the slide (the latter is designated K'). I haven't had to time to explore it yet, but this probably will cut down on the slide realignment for chained operations involving cube roots.
There's also a dual T scale for tangents as I described on the Pickett N4-ES in my collection. But, rather neatly, Faber-Castell also labeled these in reverse (in red) permitting direct reading of cotagents.
And mentioned here, for the first time, is the P scale (Pythagorean), which ought to prove useful with some right triangle or vector manipulations, not to mention working more directly with cosines when "solving" triangles.
It's a very complete slide rule and pleasant to the touch.
Faber-Castell 2/83-N
Here we come to the largest and most complex slide rule in my humble collection. Fabricated in Germany, this is the chap which made me drool when I first saw it. My picture here doesn't do it justice. When you pick up the 2/83-N and simply hold it, its great heft grabs you at once. And with 18-zillion scales, you just know that it will compute anything and everything.
This was very clearly designed to be the end-all and be-all of slide rules.
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| Definitely click to enlarge this beast! |
It's pointless me mentioning what scales are here; pick any slide rule in the world and look for its most obscure scale, and you'll find it on this unit. But I suppose I ought to at least mention a few of the things that stand out.
First off is an inverse DI scale on the stator which ought to prove it usefulness one day. (I'm guessing this will minimize movement of the slide in chained operations).
Then there's the T1 and T2 scales for tangents (with reverse running red markings for cotangents) mentioned earlier with the 2/82, above. Likewise, there's a P (Pythagorean) scale.
Now I'm no expert on this yet, but it looks to me like there are not only the usual A and B half-length scales (for squares and square roots), but also double-length W1 and W2 ones for extended accuracy. Once I get caught up on all my projects, I can hardly wait to tuck into these (say on a frigid, snowy February day).
And there is a full complement of LL0, LL1, LL2 and LL3 scales for handling arbitrary roots, powers and logarithms.
This slide rule is my Circe...
KL-1 Russian Pocket "Slide Rule"
Now here we have a most unusual critter which I only obtained a couple weeks ago. This is about the size, shape and demeanor of a pocket watch, but is built upon logarithmic principles, just like a slide rule. But rather than measuring logs against each other on a slide and stator, instead the equivalent of calipers do the measuring.
It's exceedingly clever and also exceedingly precise for being such a small device. Judging from the plentitude of listings on eBay (almost all from former Soviet Union countries), I gather this was a very common calculator there back in Cold War days.
Don't let its innocuous watch-like appearance fool you. This guy will do multiplications, divisions, reciprocals, squares and square roots, sines and tangents. And for the trig functions just mentioned, it knows how handle small angles (below 5.7 degrees) as readily as larger ones. It's an amazing device.
Can anyone doubt that John Napier's invention of logarithms is one of the most fecund ideas ever?
Concise 28N
As long as we've got circles on the mind, let me show you the Concise 28N circular slide rule, made in Japan. Believe it or not, the last time I checked, the company was still going, surely making it the longest running manufacturer of slide rules.
While it might at first blush suggest "a giveaway party favor," it's actually a very well crafted unit. The discs are decently engraved on some sort of non-cheesy plastic, the inner disc sits recessed within the outer and the cursor has a certain pleasing gravity to it. When you hold the 28N and turn it, you know you're using a serious device.
I gather the company conducted its main business by producing these with personalized or customized logos. The one in my collection touts Corn International of CPC International, Inc. Presumably, these were produced as gifts for potential clients.
As for what it can do, well, there are C, D, CI (in red--yeah!), A and K scales, meaning that this little three inch wonder can handle multiplication, division, reciprocals, squares and square roots, and cubes and cube roots!
And because it's circular, there is never any index swapping. So actually, chained multiplications on the unit are extremely efficient.
The Concise 28N is an eminently well made slide rule.
Some Cheapies
You've now seen the glamorous slide rules in my collection. Here are some of the more slatternly units I've stumbled upon. They still have a curious appeal since their manufacturers managed to put a slide rule in the hands of a person whose purse ran shallow. Honor these for their ready availability, not necessarily their quality!
Don't you think it kind of sad when all the perspicacity, innovation, and engineering of what was once an exquisite product is laid waste by some new technology? I mean, if you study the steady progression of slide rules up to 1960 or so, you come away marveling at what fine products were being crafted.
Then with pocket calculators, it all went into the dust bin.
A few companies apparently struggled to stay afloat, changing their business plans to exploit cheaper production. Plastics...
Witness the top two rules, here. Pickett, which once manufactured very fine slide rules (I think) using a durable photo printing process on aluminum, was now reduced to carnival quality trinkets in plastic. All the mathematics was still there, but the elegance had vanished.
At the top is a Pickett Microline 140, which at least featured the inverse scales in red.
Next down is the same model, sans the red printing--even worse...
Both can handle all manner of computations I suppose, but both seem rather tawdry, harsh on the eyes and fail to imbue the operator with any sense of beauty in function. Moreover, the top and bottom rails of the stator in the first one are slightly out of alignment and there's no way to adjust them.
The third one down is an Acu-Math 400. It's not badly printed or aligned by any means, but it just feels like cheap stamped plastic in the hands. I need hardly add that the CI scale is not in red, and that the S scale employs that dreadful degrees/minutes business (hence failing to provide the useful ST scale). There's naught to commend it, other than it sold for a couple bucks.
I don't even want to describe the fourth rule here (a Pedigree by Empire). It is so poorly produced as to bring bile up the throat. Some pedigree, eh?
There. We got that out of the way. Four slide rules I wish I hadn't wasted my time or money on.
Napier's Bones
Okay, these have nothing to do with slide rules, nor do they depend upon logarithms, but they do come to us from the Scottish mathematician John Napier (1550-1617), who in fact did invent logarithms, which led directly to the slide rule. And they obviously relate to the business of easing computation which is I why include them here.
Napier's bones is a collection of rods (actually, narrow parallelepipeds) labeled with digits. By arranging them this way and that, one can carry out multiplication and division with multi-digit numbers using nothing more than addition and subtraction. The basis of these came from the Arab mathematics of three or more centuries earlier, as well as some ideas from the noteworthy Fibonacci.
What Napier did was make the method tactile, i.e., his bones are something you can actually handle, manipulate and rearrange to simplify "difficult" computations visually.
I fabricated my own set of these using wooden blocks from a hobby store and laser printed the digits on white sticky-back mailing label material.
Addiator
Although I adore mathematics, addition of a column of multi-digit numbers has always vexed me. Not only am I careless at the process, I also loathe it.
So, here is just the cutest device ever, the Addiator, to ease my discomfort. As with Napier's Bones, it has nothing to do with slide rules or logarithms, but as it does tackle the problem of reducing messy arithmetic, I want to include it here.
The operation is slick as can be. You'll note in the photo six columns, permitting a six-digit number to be entered by means of the stylus. (Or if you prefer, think of it as a decimal up to 9999.99). Then one may proceed to plug in a series of addends similarly.
If you examine the photo carefully, you'll note the lower area allows the entry of subtrahends as well, so one can mix the computation as required.
The shift bar at the top is used to clear the result, readying you for the next computation.
These were fairly common when I was a lad of 5, but are becoming a little harder to find now.
As for the modus operandi, it seems to me it must be based upon Blaise Pascal's "Pascaline," considered by many to be the very first gear driven calculator.
Anyway, it's a cute device and well worth remembering.
Abacus
Finally, for completeness, here's the abacus my mother gave me years and years ago. It's beautifully made of some exotic wood and outfitted with brass fittings.
One of these days I've got to sit down and really master it!
And that's it for my collection, to date. I'm pretty well set for a lifetime of exploration. However, I will confess there are still one or two other slide rules I've been drooling over, so stop back later and maybe you'll see them here.
Next installment: Basic Multiplication -- Method #1