Fun: Still life with slide rules and graph paper

[Doug Kerr]

Here we see the classical bowl of (artificial) vegetables, garnished with some artifacts of a family's professional work.



The slide rule to the rear is a Keuffel & Esser Model N4053-3, the Polyphase Mannheim model, made (as near as I can ascertain from its design details and serial number) in 1943.

It belonged to my father, William John Kerr. He was not an engineer by formal training, but was by practical experience. He was involved in the manufacture of (large) custom production machinery, with the same firm from the time of my birth until his retirement (as Vice President of Manufacturing).

This slide rule is made of mahogany with a cellulose acetate ("celluloid") overlay. The cursor runners have disintegrated, but it is in otherwise excellent condition, and operates very smoothly.

It was this slide rule that my father used to instruct me in the operation of a slide rule (perhaps at about age 10).

It has on it a bunch of little hand-scribed index marks my father added. They represent constants he needed for calculations he often made, such as the weight of a large steel roller of certain dimensions, or the weight of a coil of steel sheet, or the gear ratios needed for proper synchronization of the stages of of a cold roll forming mill.

The slide rule in the front is a Keuffel & Esser model N4083-3, the Log-Log Duplex Vector model. It was made in about 1953. It was bought for me by my father on the occasion of my entry that year into Case Institute of Technology (now part of Case Western Reserve University) to take my Bachelor of Science degree in Electrical Engineering.

Like the other K&E rule, it is mahogany with a cellulose acetate overlay.

In engineering schools in those days, the big ideological dichotomy (like PC vs. Mac today) was Keuffel & Esser vs Pickett & Eckel slide rules. The Pickett & Eckel slide rules were made of aluminum (at one time, they had used magnesium) with a white (or sometimes yellow) finish whose nature I do not know. They were thought to be more "modern", would supposedly last forever without warping, not like that dumb mahogany, and so forth. But the drag on the sliding motion could not be finely controlled, and they often made an embarrassing squeak as the slide was moved.

Besides, being metallic, they were "cold". It was, for example, considered bad form to stroke a young lady's breast with one. Of course at Case that was a wholly hypothetical premise for any instrument, since there were no women at all in the undergraduate school (and only a couple in the graduate school at any given time, and one would hardly - well, never mind).

The slide rule is in essentially perfect condition, and operates with a silky smoothness.

The graph paper is a special kind, "reactance paper". It has a system of vertical, horizontal, and diagonal logarithmic axes so that one could readily determine, graphically, the reactance of an inductive or capacitive circuit element at any given frequency (and also make vector reckonings using impedance vectors whose reactive part had been determined on the chart).

I probably got this sheet early in my association with Bell Telephone Laboratories, likely in 1959. The paper was made for them, interestingly enough, by Keuffel & Esser.

For many years after I had any reason to use this, I kept a folder of it in my file cabinet (because it was "so nice"). When we had the big purge of "excess stuff" late in 2007, preparatory to moving to Weatherford from East Dallas, I threw all that out (along with lots of other kinds of graph paper, engineering drawing "format paper", and other pre-CAD artifacts).

But somehow I remembered that a single sheet of it, folded up, had been for many decades in a little brown box of small capacitors in my retained inventory, and I retrieved it to put in this shot.

[Ken Tanaka]

Oh Doug. You need to show some close-ups of those rules. Most visitors here have probably never seen one of those up-close, much less ever had to use one.

I owned two myself. The best was, indeed, a K&E similar (in number of scales) to the lower rule in your image. It was stolen when I was a sophomore undergrad, so I ended up using the Post rule I purchased as a high school senior...much closer in capabilities to the slimmer rule above. I still have that Post rule which, I believe, was made of bamboo. It almost looks good as new!

Fortunately, by the time I got to my senior year and then to graduate studies (architecture) Texas Instruments had introduced a reasonably affordable scientific hand calculator (red LED display...oooh) that replaced my slide rule needs.

Ahhh...how in the world did we ever figure anything in those days? <g>

[Charles L Webster]

Ah memories, ah nostalgia!

I learned how to calculate using a slide rule, but could never afford a nice wood one, much less the fancy circular ones the "real" engineers used.

I was out of college when the first Bowmar calculators appeared on the market (4 functions only). I was more of the "draw it and then measure/calculate it" kind of engineer, so I used lots of various forms of graph paper much more than the slide rule or calculator. That's what's called "back of the envelope engineering" now.

Thanks for the memories, I haven't seen that graph paper in 30 or 40 years, and haven't held a slide rule in almost as long.

<Chas>
PS, it's a nice still life too

[Ken Tanaka]

Originally Posted by Charles L Webster

Ah memories, ah nostalgia!

I was out of college when the first Bowmar calculators appeared on the market (4 functions only). I was more of the "draw it and then measure/calculate it" kind of engineer, so I used lots of various forms of graph paper much more than the slide rule or calculator. That's what's called "back of the envelope engineering" now.

Thanks for the memories, I haven't seen that graph paper in 30 or 40 years, and haven't held a slide rule in almost as long.

<Chas>
PS, it's a nice still life too

Ach! The Bowmar "Brain"! A hundred bucks to add, subtract, multiply, and divide. No percentages. No square roots. They didn't last long but I sure remember having one. I even remember the sound of the keys rattling if you jiggled the unit.

[Daniel Buck]

I like the set :-)

I think the lighting looks a bit flat though, not much definition in any of the shapes, even the creases on the unfolded paper are just barely visible. Is it a flash shot straight up or a ceiling light right overhead?

It may be a bit classic, but I would try an open window to one side, for some natural side lighting :-)

[Doug Kerr]

Hi, Daniel,

Originally Posted by Daniel Buck

I like the set :-)

I think the lighting looks a bit flat though, not much definition in any of the shapes, even the creases on the unfolded paper are just barely visible. Is it a flash shot straight up or a ceiling light right overhead?

In fact, the lighting was flash bounced from the ceiling (the main beam being a little "behind" the camera).

It may be a bit classic, but I would try an open window to one side, for some natural side lighting :-)

Indeed the shot would have benefited from some more careful attention to lighting.

Regarding the creases in the graph paper, I ironed the paper to try and remove them, before I realized that this was not appropriate!

Thanks for your observations.

Best regards,

Doug

[Doug Kerr]

For those not familiar with the slide rule, it is a visual analog computer, based on the principle of logarithms. In its simplest form, it allows one to multiply or divide two numbers. The principle is that the logarithm of the product of two numbers is the sum of the logarithms of the two numbers,

The simplest slide rule has two identical logarithmic scales, one on the body and one on the slide. By positioning the slide, we can visually add the distances that represent the two logarithms, and read the result off one of the scales. The basic scales have a span of "one decade"; that is, distances along them represent the logarithms of a range of numbers thought of as being from 1 to 10.

The principle is shown at work by this figure.

Here we wish to multiply 2 by three. By moving the slide, we align the "index" (the location of the value "1") of the upper scale with the value "2" on the lower scale. We take our answer (6) from the lower scale where the value "3" on the upper scale lies.

As you can see, division can be conducted the same way. In fact, the figure equally well illustrates the division of 6 by 3 to give 2.

The slide rule is a "floating point device", and the user must keep track of where the decimal point is in the result. For example. multiplying 20,000 by 0.03 (the result is 600) would look just the same as the example shown.

Other scales in which the range of logarithms for numbers from 1 to 10 are repeated two or three times over the length of the main scale allow direct computation of squares (and square roots) and cubes (or cube roots). This is based on the principle that the logarithm of the square of a number is twice the logarithm of the number.

Other scales may be on the basis of the logarithm of the logarithm of the number indicated (the so-called "log-log" scales). These allow us to calculate powers or roots of numbers, based on the principle that the logarithm of x to the power y is y times the logarithm of x.

A movable cursor with a hairline allows one to read matching values off scales not directly adjacent to the other scales involved.

Other scales allow trigonometric functions to be introduced into the calculations. Additional scales are often included to provide for many more esoteric functions. The Log-Log Vector slide rule shown in the still life has 20 different scales (plus the C and D scales appear on both sides for convenience.)

I'll try to do some closeups of one of the slide rules later today. For now, here's a link to an existing shot of a (cold, aluminum) slide rule with 8 scales on its front face:

Its slide is in fact set up to multiply 2 by something. The "basic" scales are those traditionally labeled "C" and "D"; the "A" and "B" scales are normally the "two-decade" scales used for square and square root computation (go figure, to make a bad pun).

Best regards,

Doug

[Ken Tanaka]

Hey, that's a nice mini-tutorial, Doug!

Can you imagine what such a precision-manufactured gadget would cost today? That rule you showed above would cost $500-$1,000. Perhaps Leica can start making them. (Or are they already?)

Wouldn't you know that someone has a basic slide-rule tutorial online? And how ironic that that "someone" would be the Hewlett Packard Museum of Hand Calculators, the gadgets that sent these analog wonders to closets and landfills?!

[Jack_Flesher]

Fun picture! When I was a kid, my dad had a K&E like the lower one shown above -- in fact, dad is 92 and still living, and I bet that K&E is still sitting in the middle drawer of his desk and still safely tucked away in its dark green leatherette case -- I'll be sure to check next time I visit! Anyway, being younger and smarter (hah!) I spent my own hard-earned money on the more modern yellow aluminum Pickett. And what a mistake that was, but I didn't figure it out until about after about a month of use.

As Doug said, it was cold in the hand, and while black on yellow was somewhat easier on the eyes under the harsh fluorescent lighting of the day than the black of white of the K&E, the real issue was the slide resistance. That should have been obvious to me, as I knew darn well aluminum sliding against aluminum does not have good properties... As such, daily cleanings and applications of parafin wax as a lubricant were essential. The other issue was the aluminum was relatively soft, and the rule could be bent with gentle hand pressure which seemed to happen with regularity when the slide was left hanging well out of either end. This required a field fix, and unless you got it back to true it rendered fine adjustments (and associated fine calculations) all but impossible.

I was literally ready to toss it in the trash and buy a K&E when HP introduced the HP35. I forget exactly how much it cost, but it was like 4 times the K&E. It took me several months to decide to spring for it, (all the while limping along with the POS Pickett) and by the time I did, the HP45 was introduced --- and shortly thereafter TI introduced the SR50. Now we had a whole new set of "Mac vs PC" brand arguments! (I won't tell you which calculator I bought, because that turned out to be a mistake too -- except for when it came statistical analysis.)

;-),

[Will_Perlis]

Doug, those K&Es bring back memories of my uncle, the one who treated his migraines by solving nasty equations.

I have my two old Picketts in a frame under glass with a little red hammer hanging from the side. The caption is "Break glass in case of computer failure".

Now that I think of it, slide rules are still being sold and used for some purposes.

[Jim Galli]

Thanks Doug!

I have my grandfather's K&E. He was Kelly Johnson's Radar black box guy on the SR71 and all of the preceding spy planes as well. I bought myself one of those cold yellow Pickett's when I was in high school about 1969. (btw it still slides smooth as silk) It lays at the base of my computer and gets used very often to this day. The best photometric data we've ever achieved where I work was calculated with that slide rule. Upstairs here at home I have a little occupied japan slide rule that is always within reach. In fact I used it earlier today to calculate the values of some waterhouse stops for an 1877 Voigtländer Euryscop lens that I will be taking on a photo adventure next week.

A couple of years ago a visiting scientist was in my area at work, and trying to figure something out he asked me if I had a calculator. I handed him the yellow Pickett. He looked at me with a non amused scowl. Later that month in Costco I bought a decent TI calculator and took it to work. I never learned to use it and I suppose the battery is dead by now.

[Doug Kerr]

Hi, Jim.

Great stories, and I'm glad you still know how to run one!

Best regards,

Doug