# Slide Rule

1. Jul 20, 2008

### robertm

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So I am thinking of making the leap here (these are pretty expensive for my budget). I have never used one before, however, I usually like to write out equations and make little sketches for my personal visualizations. I was thinking a more visual mathematical interface such as the slide rule might actually be beneficial for me.

I will be entering my freshman year in a few short months (), and will be doubling up on mathematics courses relevant to a physics degree.

So what do you think grey beards? Would it be worth my time/effort? Any suggestions on model's would be greatly appreciated as well!

Last edited by a moderator: May 3, 2017
2. Jul 20, 2008

### Integral

Staff Emeritus
I would say, no.

While there are some advantages to a slide rule, eternal batteries and automatic significant digit tracking. The time required to become proficient would be better spend on math (at your stage). Further note that in either math or physics and numerical result is not real goal. In both math and physics the real value of the problem lies in the process leading to the result.

3. Jul 20, 2008

### robertm

Hmmm, good point. I am definitely not going towards an engineering track where the individual numbers would matter significantly more...

I know I do not need one. Maybe I should just right my current interests off as a bit of nostalgia. I am a sucker for gadgets.

4. Jul 20, 2008

### BobG

I would say yes, but I collect slide rules.

Slide Rule Universe is a great site to research slide rules, but they are expensive. A new, in-the-box slide rule is a great collector's item, but if you use it, the value drops immediately. They also charge a fairly high price for used slide rules.

E-bay is the better option. Rod Lovett has been tracking slide rule prices on eBay for several years. You can get a feel for what a reasonable price is for different slide rules by checking his site. http://sliderules.lovett.com/srsearch.html

For example, Slide Rule Universe charges over $200 for a Post Versalog in near mint condition. On e-Bay, you should pay less than$100, and only over \$50 for very good condition with the original leather case. The only difference is you'll probably have to do at least a little cleaning and restoration work (you can find info on how to clean and restore slide rules at Slide Rule Universe).

The basics of using a slide rule is very easy. A Reitz or Mannheim style is pretty easy to learn (with Mannheims being more common in the US), plus it's good to learn the basics before getting the more exotic scales. You'll have a A and D scale on the slide rule body and a B and C scale on one side of the scale. You pull the slide out and turn it over to get trig functions and base 10 log scale. Believe it or not, this is all you need provided you're good with logarithms and are comfortable working with complex numbers.

The more fun slide rules are the duplex rules that start adding special functions, such as a natural logarithm scale that's usually broken up into around 8 segments (for instance, the Post Versalog advertises 8 log log scales, but it's really one long scale broken up into 8 segments to give you a good range. They start including reversed CI scales and scales that run from pi to pi instead of .1 to 1, and so on. The idea being to provide enough flexibility that you can set your problem up to minimize slide rule movements and minimize the number of times you have to read a value from your slide rule (you only have 3 significant digits, so you lose a little accuracy every time you transpose a value from your slide rule onto paper). While the basics are very easy to learn, learning to set the problem up to get the quickest and most accurate answer is tougher. The extra scales do give some extra capabilities, but not many. For example, you can solve quadratic equations on a Post Versalog very quickly using kind of a visual iterative method, but you could also do the same thing just a little slower using a Mannheim or Reitz and the quadratic equation.

You could also solve equations like $$e^x = x^4$$ for x, and probably better than a person could using a graphing calculator. Using and understanding your calculator takes as much time and effort as using a slide rule, but most don't realize that. Very few calculator owners could solve something like $$e^x = x^4$$ correctly, in spite of the fact that it's so easy it's pathetic. I knew one person who never realized just about all of the constants he'd ever used in college were stored in his calculator until his very last semester before graduating. Learning to use a slide rule well is easier than learning how to use your calculator well.

Generally speaking, a good graphing calculator is a little better than a slide rule, but a good duplex slide rule with 20+ scales is in the same ballpark. A Post Versalog is immensely more capable than your standard scientific calculators like the TI-35.

Of course, the extra scales have their own hazard. You start to use the log log scales so much, you get stuck if you have to deal with a number larger than the highest value on your log log scales. You almost forget you could do any size number using your base 10 logarithmic scale and the fact that the natural log of a number is just 2.30 times the base 10 log (which is why it's good to use the basic Mannheim or Reitz style first instead of jumping right into the fancy duplex rules).

5. Jul 20, 2008

### Cyrus

http://www.pilotshop.hu/shop5/images/jeppesen/st-csg.jpg [Broken]

oooohh...........ahhhhhhhhh..........

Last edited by a moderator: May 3, 2017
6. Jul 20, 2008

### LowlyPion

I agree. Best not to bother with a slide rule. Calculators are easier and more precise and the less clutter in the process of arriving at an answer the better.

7. Jul 21, 2008

### robertm

Thanks for the replies.

I would certainly not be using the rule 24/7 or for mass calculating (I do of course have an appropriate calculator), but I am thinking that when I would benefit from being more involved in the number crunching process then taking the time to learn the operation and spending the money would be worth my while. I.e. More efficient than writing out huge operations, but not just punching in digits either. Sound like a viable reason (again, I haven't ever used one, so I am speculating)? I guess I have already established some what of a bias from drooling over them for some time now. :!!)

If you think I really might be wasting my time or making some dire mistake please say so! BobG, If you have any more suggestions on what model might be appropriate for the mathematics I will be doing in the next few years (physics undergraduate level) please let me know, many thanks for the link and the ideas.

8. Jul 21, 2008

### Integral

Staff Emeritus
Remember that slide rules are great at multiplication but do not add, that you must do on paper.

Just for the record, multiplication and division are the same operation, likewise, addition and subtraction.

9. Jul 21, 2008

### BobG

You can't do addition or subtraction directly, but you can do it. Multiplication on a slide rule is actually done by adding logarithms and division is done by subtracting logarithms. If you take the antilog of the two numbers you want and multiply or divide, the log of the result will be the sum or difference you want.

Most slide rule users just do the addition or subtraction in their head, since you're only dealing with 3 or maybe 4 digits at the most. It's not that the addition and subtraction are impossible - it's that the procedure is usually more trouble than it's worth (unless you're really bad at adding and subtracting numbers in your head).

Einstein and Werner Von Braun's both liked the Nestler 23R, which is an extremely basic slide rule. That's mostly due to the era they grew up in. Hemmi popularized the more exotic duplex slide rules in an attempt to rebuild its customer base after World War II. Hemmi was a Japanese company and it took a long time for Japanese products to become popular again after the war. Engineers have probably always been suckers for exotic gadgets, so Hemmi's duplex rules were extremely successful at rebuilding their customer base.

If you go with a duplex rule (which is hard to resist), the Post Versalog (Post 1460) is a good option. It's a general purpose mechanical engineering slide rule that's very good for general physics. It was also incredibly popular, meaning there's tons of them on e-Bay and the price is never very high unless the slide rule is still new in the box or in extremely pristine condition. Keuffel & Esser's 4080/4081 and 4180/4181's are equivalent to the Post Versalog and are also extremely popular. The Pickett N500ES was also equivalent and was extremely popular.

The main difference: Post slide rules were manufactured by Hemmi out of bamboo. K&E made theirs out of wood. Pickett made theirs out of aluminum. The bamboo has a very pleasing feel even though any slide rule you pick up will be 30 to 50 years old. Bamboo doesn't lose it's character for around 75 years. Obviously, the aluminum slide rules hold up equally well provided they've been kept dry, but the metal slide rules just don't have that same feel to them. The wood slide rules can have almost as good a feel as the bamboo slide rules, but results may vary depending on how the wood slide rules were stored.

The plastic slide rules also maintain the same feel they had when new, but there's very few American plastic slide rules that really compare in feel. Plastic slide rules from Europe are usually a lot more popular than American plastic slide rules. In America, plastic was used for cheapness and other materials were used for quality. Slide rules made of high quality plastic seemed to be appreciated more in Europe than in America. The Faber Castell 2/83N (from Germany) is plastic and is still one of the more expensive slide rules (and is an extremely good slide rule as well). Aristo and Deitzgen also made some good slide rules out of high quality plastic.

10. Jul 21, 2008

### BobG

When I think about it, addition and subtraction cause problems on a slide rule for a completely different reason. If you're multiplying sums or differences, you sometimes run into a problem that all of your significant digits have disappeared. $$5.21*(3.174 - 3.173)$$ doesn't give you a very accurate answer. $$5.21*(5.18 * 1.80 - 2.59 * 3.61)$$ would give an even less accurate answer. $$5.21 * (1.29 * 7.25 - 2.59 * 3.61)$$ gives an extremely inaccurate result when done on a slide rule.

Physics professors are funny. They teach you all about significant digits in your first chapter and then they ignore them when they run into the problem of multiplying sums or differences (solving problems for wave superposition or interference, for example). At best, they realize the conflict and make some comment like "Assume these values are exact to 10 significant digits" or some equally bizarre level of precision. Electronic calculators exist and it's as hard for professors to resist those extra digits as it is for the students. Even when teaching significant digits, most professors will tell you not to drop any of the digits along the way - only round off at the very end.

In reality, most of the situations where you run into these types of problems don't yield very accurate results in the real world either, but it would be hard to give full credit on a test when the student's answer is off by 16% or worse (especially if they're confronted by multiplying 5.21 times zero).

11. Jul 21, 2008

### lisab

Staff Emeritus
Sure, you can add and subtract with slide rules!

For example, to perform 9 - 7: place 9 slide rules on a table. Now take away 7 of them. Count the remaining slide rules. Works great!

12. Jul 21, 2008

### BobG

:rofl::rofl::rofl:

13. Jul 21, 2008

### robertm

I'll have to try that, thanks for the tip!

Thanks again BobG, I've got a few good ones picked out on ebay now. Including a versalog 1460 in exquisite condition for just a few bucks; I will post pictures when the catch is reeled in!

Do you have any suggestion on the best way to correctly learn the operation? Should the manual and some practice suffice?

14. Jul 21, 2008

### BobG

If it has the original book, it's a huge plus. Versalog put out a hard copy book with some of their slide rules that was probably the best around. It went beyond just the basics and covered how best to set up problems for the quickest solution, etc. The book can be bought on e-Bay as well.

Slide Rule Universe has electronic versions of several manuals and is a good source on how to use slide rules and how to maintain them. Most slide rules are very similar in that if you know how to use a scale on one slide rule, you know how to use it on every other slide rule. The most popular scales are included on just about all types of slide rules. The arrangement can vary and some have one or two special scales not commonly found, but one manual will teach you most of what you need for any type of slide rule.

15. Jul 21, 2008

### Chi Meson

My dad was particularly good at the slide rule while at the Naval Academy. I have his old K&E 4081 "Log Log Duplex, Decitrig" slide rule (with manual and sheath). When he gave it to me, ten years ago, I also thought I would learn to use it to "get a better feel for numbers" etc etc etc.

Never happened. I can do a basic multiplication, but that's it. It looks nice, though, out on the book case, next to the abacus.

16. Jul 21, 2008

### OrbitalPower

I would just get a normal, Mannheim type slide-rule to start off with. I found one on ebay with A-B-C CI - D - K and S - T - L scales for about 10 bucks or so. It came with instructions in a box which explained how to do the calculations, which it claims are rather easy to learn:

"The art of operating a slide rule is easy and can be learned readily by anyone. Any personal called upon to do much numberical calculation will find it profitable to invest the the small amount of time necessary to learn this art. The slide rule will save hours of mental strain for those engaged in business or engineering calculations."

The best book on Slide Rules is probably A Manual of the Slide Rule by J.E. Thompson.