Refurbish an Old Slide Rule

Some guys my age buy the nice car they never had in high school.  I went on eBay and bought the nice slide rule I never had in high school.  It cost far less than the car!  (The photo are from Slide Rule Museum and Bing Images.)

I went on eBay and bought a Dietzgen Polymath #1733 Decimal Trig Log Log slide rule from the mid-1950s for $2.50 (plus $9.50 for shipping).  If you were at the US Naval Academy in Annapolis, MD; this slide rule was standard issue for plebes in 1955.  These can go for between $40 US used and $500 US for one never sold still in the original box with the original manual.  I was the only bidder, probably because one of the cursor glasses is missing and the other is broken.  In the photo you can see the line from the break. Otherwise, this slide rule is in quite good condition.  It shows no discoloration anywhere.  There are a few light surface scratches from normal use.  Neither the wood from which it is made, nor the plastic laminated to it are cracked or broken in any way.  The slider action is smooth.  It does have someone's initials scratched into one end of the slider.  The original leather case is even in quite good condition.  I will show several things in this Instructable, including how to make new cursor glass from Plexiglass and how to inscribe it with a very fine cursor line, also known as a hairline.

The first question you must ask yourself if you buy a vintage slide rule is: Do I intend to show it as a collectible or to use it as a functional mathematical tool? If it is to be a collectible, you should not clean it up in any way or do any non-factory replacements.  People who are serious about collecting slide rules will buy duplicates and take original parts from one to replace damaged or missing parts on the other.  I intend to have fun practicing real world calculations with this slide rule.

Yes, an electronic calculator is faster and gives more accuracy to more numerical places, and a calculator does not require the user to know where the decimal point should be placed.  But, I want to learn to use the scales I never learned to use when I was in school. It is a bit of a nostalgia thing for me.  At one time I wanted to become an electrical engineer, but never did, and that is fine.

The metal parts on this slide rule show a green colored oxidation.  I am using a pencil eraser to remove it.  I know that often reduces the value of an old object.  But, I want the rule to look nice for my use of it.  I am not trying to sell it as an antique.  In the photo you can see two of the three initials on the slider from the original owner.  Using a pencil eraser on the plastic scales would scratch them unnecessarily.

Different people have different names for the parts of a slide rule. I downloaded and consulted an original Dietzgen manual for a similar Polymath slide rule, but their terminology is rather basic. See the yellow boxes in the photo for more "official," but varied nomenclature. Occasionally I am using terminology of my own that makes sense to me. 

Good quality slide rules can be adjusted for accuracy.  You may notice the DF and CF scales each begin with π.  The C and D scales each begin with 1.  There is a a corresponding inscribed mark on each scale.  These should all align to form an absolutely straight line from the bottommost 1 upward continuously through the uppermost π.  If they do not align, accuracy will be compromised.  Loosen each adjustment screw a portion of a turn.  Use a magnifying glass to be very accurate.  Align the 1 on the C and on the D scales.  Press a finger over the C and D scales so the slider cannot move.  While holding that finger in place, nudge the upper body of the rule left or right until the marks for π on the CF and the DF scales align perfectly.  Pinch the upper and lower rule body together against the slider and hold.  How tightly you hold the body members together has an effect on how much pressure will be needed to move the slider in the body.  Tighten the adjusting screws. Check again with a magnifying glass.  When doing certain calculations, numbers are located on scales from the upper body, but the answer is read on a scale from the lower body. Proper alignment between the upper body and the lower body is crucial to accuracy.

If you look very closely, you may be able to see that the marks for 1 on the C and D scales align very well, but the mark for π on the DF scale is a tiny bit to the right of aligning properly with the mark for π on the CF scale.  

I will need to do some work on the cursor.  Working on the cursor involves removing four small screws on each side to remove each hold down or retainer for the glass of the cursor (eight screws in total).  The safe way to do that is to find a shallow top of a cardboard box and work inside it.  If a screw gets away from you, it will be confined inside the box.  You will not be hunting it deep within the fibers of your carpet.  

Keuffel & Esser slide rules are among the most popular for collectors.  The end pieces in the cursor frame are made from a type of plastic that cracks and breaks away over the years.  This problem is known as KERCS, or "Keuffel & Esser Rotting Cursor Syndrome."  One web site offers new parts to make a K & E slide rule like factory new.  The cost is $75 US.  The photo shows the same part on my Dietzgen rule. It is made of a cast metal that lasts very well.  Dietzgen rules like mine are often mistaken for similar Keuffel & Esser rules.  This is another reason why I am pleased with my purchase.

Some call this entire assembly the cursor.  It is also called the indicator or the runner.  The thin line on the glass is (as mentioned above) the hairline.  

The original cracked cursor glass is 30mm x 45mm and 1.8mm thick.  I have some Plexiglass that is only a tiny, tiny bit thicker.  It worked just fine for this project.  I cut it to about 31mm in width, but left the length about 95mm to allow for a saw kerf when cutting the two pieces apart.  It will be easier to make one hairline before cutting the two pieces apart later.  I used sandpaper on a wooden surface to sand the Plexiglass down to its exact width of 30mm.  Here I am checking it for fit on one of the cursor's glass retainers.   Plexiglass may scratch more easily than real glass, but it is easy to obtain, easy to work, and will not break.

I used a carpet blade in a homemade handle and a straightedge to scribe a new hairline into the Plexiglass.  The hairline should be centered between the two edges and precisely parallel to them.  Scribing with a razor sharp edge worked quite well, even though the hairline is not filled with a black pigment.  Make only one cut with moderate, even downward pressure.  A second cut can easily wander and leave two lines.

I had planned on covering the Plexiglass with masking tape and scribing through it.  Then I planned to mask the rest of the whole piece of Plexiglass and spray it with black acrylic paint.  When the paint dried I would pull the masking off and a thin black line would remain.  That worked well in a trial run on a piece of scrap Plexiglass when scribing with the blade of a sharp pocket knife, but that hairline was a bit thicker than I wanted on this slide rule.  As it happens, simply scribing the Plexiglass left a very nice hairline for this slide rule.  I did experiment with darkening the hairline a little by rubbing the scribed side of the glass with paste shoe polish (black).  The trick is to wipe the excess from the glass with a tissue without removing any from the scribe line.  The shoe polish did darken the line a little, although just scribing a line with a carpet knife works quite well.    

 

 

After I had scribed the line, I cut the Plexiglass to pieces 45mm in length.

Round the corners by pulling along the sandpaper while rocking the opposite end of the Plexiglass upward.  Check often against the glass retainer for fit.  

One piece of glass worked out just right.  The hairline aligned vertically across the scales of the slide rule just as it should.  Somehow the hairline on the second glass appeared cocked to one side when installed in the retainer and screwed onto the rest of the cursor.  I used sandpaper to grind away some of the Plexiglass on one side and one end so the glass had some movement in the cursor.  Then I was able to align the glass properly and it stays in place perfectly after the screws on the retainer are tight.  No cement was necessary to keep it in place.  I think the original glasses were made a little undersize so that they could be adjusted.  Ideally, when the hairline is aligned and over the left index on the front side of the rule, the hairline on the back side of the rule is also perfectly aligned over the left index.  There are some calculations that require setting a number on a scale from the back side of the rule and transferring it to the front side of the rule simply by reading the hairline position on the front side of the rule without moving anything.  

In the end both pieces of glass and their hairlines look very good.  This photo is the side of the rule that includes the A, B, (no C), D, and K scales.  The hairline is set over the number 4 on the left half of the A and B scales.  Follow the hairline downward and you can see the hairline is also over 2 on the D scale, which indicates the square root of 4.  (The A and B scales are used in combination with the C and D scales for squares and square roots.  The K scale is for cubes and cube roots.)    

I now have a very nice fully functional slide rule for far less expense than if it had been sold in its present refurbished condition.  I hope this Instructable will be an encouragement for those who want a good slide rule, but cannot afford one in nearly new condition, or who are frightened away from an auction for a basically sound rule with missing or damaged cursor glass.   

You can practice using a virtual Pickett slide rule at this link. Left click your mouse on the slider and drag it to the left or right.  The slider on the virtual slide rule moves with your movements.  You can do the same with the cursor.  Click and drag on the body of the slide rule to position it on your screen. 

If you have never used a slide rule, it works on the principle of logarithms.  Every number has a logarithm.  When the logarithms of two numbers are added, the effect is the same as multiplying the one number by the other.  Converting back to a number (antilogarithm) gives the product.  A slide rule converts logarithms from digits to physical lengths on a scale.  Moving the scales to add physical lengths allows the user to read the product of a multiplication problem on a corresponding scale.  

The C and the D scales are identical to each other and are commonly used for multiplication problems.  I like to think of a lazy "Z" (inverted) to explain the steps in using a slide rule for a basic multiplication problem.  See the graphic above.  On the virtual slide rule move the slider until 1 on the left side of the C scale is aligned with 4 on the D scale.  Follow the lazy "Z" and look for 2 on the C scale. The number 8 appears directly below it on the D scale.  4 x 2 = 8.  (Note: A slide rule can be checked for basic accuracy by multiplying 2 x 2 or by 4, etc.  The answer should be exactly correct.  Somehow, 2 x 2 on the virtual slide rule did not yield 4, but about 3.995 on one computer!  But, it was accurate on other computers.  That may be a browser problem.  Still, this makes a good check for accuracy.) 

Always remember that the 1 at the right end is 10 times larger than the 1 at the left end (terminology: left index and right index).  For a particular calculation, the left index on C could be (purely for example) 1,000 and the right index 10,000; while the left index on the D scale could be (purely for example) 0.1 and the right index would then be 1.0.  In such a case, the problem might be asking you to figure 0.75 of 8,500.  

The process for division is the exact reverse of multiplication.  (Follow the "Z" in the opposite direction.)  Now you have a taste for using a slide rule.  To learn more, download a basic manual and practice.

All slide rules function in the same way and basically have the same scales.  Any manual, even a very basic manual will teach you how to use a slide rule.  If your slide rule has more scales, like a log log rule, you will need a manual that also covers the additional scales on your slide rule.

 Here are some web pages where you can download free manuals in PDF: several makers, including one from Keuffel & Esser, as well as many other makers.  I found two Dietzgen manuals, one says it covers my slide rule, while the other seems to be more fitting to my slide rule.  Both are similar.  Clicking on either of these two links will load the entire manual for each and that takes a while.  They are very large files.  If you wish to see a list of manuals, click on the first or second link.  You can also go to this link and click on "Slider Rule Library, Manuals & Books" in the menu down the left side of the page.  There you will find quite a variety of manuals, including several from Keuffel & Esser.  I would have expected that manuals with as many pages as these would say something about basic cleaning and maintenance, but they devote themselves entirely to using the various scales to solve all manner of mathematical problems.  The Dietzgen manuals have a few pages at the end with a large number of conversion factors.  The Keuffel & Esser manuals have a couple of pages on the history of the slide rule. 

Care and maintenance: Do not use chemicals or procedures on a slide rule that could leach the markings from the scales or be caustic to the materials.  Do not put a slide rule into a hip pocket and risk breaking or bending it by sitting on it.  Wipe it with a soft cloth to clean it.  A mild soapy solution on a cloth would likely do no harm.  Bamboo slide rules tend to be self-lubricating.  Wooden slide rules can be lubricated with a little furniture polish applied to the moving parts.  Although some do not advise using paraffin, I have always found a little of it rubbed onto the moving surfaces works well.  See more on maintenance and care here.  Here and here are some additional pages on the care and restoration of a slide rule.  If you would like to see original instructions on caring for a Keuffel & Esser slide rule or a Dietzgen slide rule, go to this link.  Scroll down the page to about halfway.

The May 10, 2006 edition of Scientific American contained an article on various things related to the slide rule and its contributions to great engineering feats up to the 1970s, including the journey of Apollo 13 in the US space program.  The crew of Apollo 13 even took a 5 inch Pickett log log slide rule on their voyage.  Today that slide rule is on display in the Smithsonian Institute.  

Slide rules are accurate to about 3 significant digits.  Numbers can be read more precisely at the left end of the rule than the right end of the rule because numbers at the right end of the scale are grouped more tightly, making them harder to read.  Three significant numbers for accuracy means calculations done with a slide rule insured that things built by means of them were a bit over-engineered.  But, for example, there is no point calculating to the nearest hundredth of an inch if your construction tool is accurate only to the nearest sixteenth of an inch.  A ten inch slide rule is generally accurate to 1/10 of one percent in its answers.  

Once carrying a slide rule meant instant status as a brainy geek.  All of that disappeared with the electronic calculator, which was actually designed on the slide rule.

With practice, the speed and accuracy associated with a slide rule can greatly close the gap in a race with a calculator.  Some calculations are definitely faster on a slide rule.  For example, if you need to know the product of π multiplied by any number, find that number on the C scale and read the answer directly on the CF scale (if your slide rule has a CF scale).  I remember an evening when an insurance salesman paid us a visit.  I surprised him by finishing several calculations as accurately and more quickly than he was able to do with an electronic calculator.  He was shocked.  He had also never used a slide rule.  

(The photo is from Bing Images.)