## Introduction: How to Use a Slide Rule

I was going to enter this into the "Party like it's 1929" contest because slide rules:

- Were used in 1929 (and earlier, but never at parties I'm afraid)

- Are an intrinsically easy to replicate technology; once you know how it works, you can trivially replicate it on any medium, such as soup cans, railway spikes, or discarded bills of hyperinflated currency.

- They work underwater, in a vacuum, in the sun, in the snow, in nuclear winter. Never runs out of batteries, and you can drop it off a building and it will still work. It is the ideal tool for the discerning scientist of the post-collapse-of-western-civilization world.

- Cannot be used to easily calculate compound interest far into the future, which no one should be depending on right now anyway, since real "wealth" gains are unpredictable in the face of uncertain inflation and prime interest rates in the short term.

Unfortunately I am both ineligible for prizes, and published this instructable way too long ago. Curses!

Slide rules are analog mechanical calculators. They were ubiquitous among engineers and scientists from their inception, to the development of cheap transistor calculators.

They allowed you to do quick calculations with an accuracy up to two or three significant figures. You can multiply, divide, perform exponential functions, square/cube roots, inverse functions, trigonometry, and others. You cannot add or subtract. (Actually you can but it's much harder than doing it in your head. Bonus points to whomever posts a method to do so as a comment.)

You do the math essentially by moving sticks around. If you learn how to use this, and actually do, expect to entertain questions from anyone under 40, and nostalgic comments from anyone 40 or over.

Now, all strangeness aside, I've found one situation where I really appreciated the slide rule: as a biologist doing field work.

In that special case, you know that nature is not so kind sometimes. You will freeze and burn, you will fall off things, you may be away from civilization for months. Storms can be pretty bad, and when they aren't, the countless insects scream for a blood meal. You will need to do math in absurd conditions.

So if you're part of that special group of people to whom this applies, this is a useful tool. In fact, you should never leave for the field without a slide rule and dice (for randomizing sampling and selection for treatment groups... "arbitrary" is just not good enough for proper statistics).

This photo is of the slide rule in its "start" position. The center plastic piece slides left and right, the plastic piece to the left (called the cursor) is also mobile. Most functions are accessed in this position... if you move the cursor so that it is centered on "2" on the bottommost scale, you will notice that it lines up with 8 on the X^{3} scale, and 4 on the X^{2} scale... which should come as no surprise.

But... it lands on 5 on the 1/X scale! This is our first lesson about slide rules. They do not indicate the decimal places. You need to remember that 1/2 is going to be less than 1, but more than 0.1... and thereby reason that the indicated 5 is actually 0.5. This sounds annoying but rapidly becomes trivial.

To perform the inverse of these functions, just look them up backwards. For instance, in this configuration, 6 on the X^{2} scale lines up nicely around 2.45 on the middle scale, which of course is the square root.

Next, we shall move to multiplication.

## Step 1: Multiplication

The middle part of the slide rule is mobile. You move it around mainly when you want to perform multiplication/division. It works because one of the scales is linear, the other logarithmic.... and as I hope we all know:

log(ab)=log(a)+log(b)

log(a/b)=log(a)-log(b)

Note that in this photo, the slide has been moved so that "1" on the center scale is lined up with "2" on the bottom scale.

Now, note that "2" on the bottom scale is lined up with "4" on the middle, 3 with 6, etc. If you had lined up 2.15... you would then get 4.3, and 6.45 lined up.

Division just works by looking at this backwards.

But what if you wanted to perform 2 by 7? It goes off the end of the scale! Just slide the rule the other way.

## Step 2: Multiplication 2

Just slide the rule the other way so that "2" on the bottom scale is lined up with the "1" *to the far right* of the middle scale, unlike this photo.

7 will nicely line up with 1.4, which we in our infinite wisdom know is actually 14.

Now, complex functions.

## Step 3: Complex Funtions

To be fair, these functions aren't complex at all. You can do them in your head if you teach yourself floating point math, eliminating the need for a slide rule totally. Then, you can convince people you're an idiot-savant. Not the best bar trick, I admit.

The center of the slide rule actually comes out completely. Flip it over and you will be delighted to see new scales.

They let you perform trigonometric functions and their inverse in the same fashion as you performed the functions described in step 1.

Finally, your slide rule may differ. It may offer more or less functions, or function to three decimal places instead of two. It may also be circular instead of linear. You may also trivially make your own slide rule given wood or paper, cutting implements, and preferably a measure of sobriety. It is after all only two sticks that move relative to each other!

There are also many more complex operations you can perform with a slide rule, which are beyond the scope of this text. None of these are random number generation, so don't forget to carry dice if you need to do this. Some hobbyists have some that have over 20 sides and come in bright colors, so generate substantial entropy per roll as compared to coin tosses... and are easier to find when you inevitably drop them into leaf litter while climbing a tree, while doing a field study.

## 17 Comments

14 years ago on Introduction

I remember doing math on a slide rule in 7th grade. It's still faster than working it out on a four-function most of the time. I also tend to spend less time wondering what the hell I meant to be figuring.

Reply 14 years ago on Introduction

I usually use a casio fx4000p programmable calculator when I need to know the numerical answer to something, which isn't terribly often. I was once able to do floating-point math mentally, which is arguably even more "old-school" than using a slide rule. It was slow though, cos(pi/7) for instance would have taken about 5 minutes (while sober, less while drunk). Recently one of my friends has shown me something called "vedic mathematics". There's some bizarre spiritualism associated with it, but that aside there are some good math functions in there. If you learn it well, you could probably make the slide rule obsolete! (/sarcasm) Good luck with your drunken slide rule!

Reply 13 years ago on Introduction

My first encounter with "Vedic Mathematics" (It gets its name from the Hindu Vedas) was in "The Daring Book for Girls".

Apparently the Vedas were non writen text books (from a pre Gutenberg era) locked against errors by poetic rhyme and meter.

Some are mathematical methods, other seem to be 'James Bond science fiction soap opreas' that describe the detonation and effects of two neuclear bombs ('Gurka's Arrow' and 'The Iron Thunderbolt'), and all sorts of aircraft (Amaya) from baloons to rocket craft and even flying saucers.

Oddly enough, Robert Oppenheimer, who was the top scientist at Los Alamos during the Manhatan Project was an expert on the Vedas and recited one of Shiva's quotes after the Trinity test. ("I have become death, The destroyer of worlds.")

Did you ever find a circular slide rule (designed for electronics work) with 24 equally spaced marks on the face? Resistors, capacitors and inductors are seperated by the roots of 10. (20% components are seperated in value by the sixth root of 10, 10% components by the twelfth root of 10 and 5% components by the twenty-fourth root of 10.)

14 years ago on Introduction

Slide rules can be used to calculate compound interest, by using the LL scales, which do exponentiation. There were even some slide rules made with LL scales but called "interest" scales, kind of an early version of the HP Business calculators: http://home.clara.net/sliderules/a-to-z/commercial/commercial2.htm

14 years ago on Introduction

http://www.sciam.com/media/pdf/Slide_rule.pdf

Scientific American ran this in a cool article a few years back "When Slide Rules Ruled" . I scanned then scaled up the page so it would be easier to "read between the lines". Fun and brings back memories of electronics class in High School. With the log function of a scientific calculator generate the numbers, mark them out with a (metric) rule and hey presto..! (Still stumped on how to make trig functions but I'm not a math whiz.) Did this once to make a log-scaled graph for capacitance/R computations- same principle applies for the rule, natch.

Reply 14 years ago on Introduction

Totally sweet! I think I may transfer the image to a PCB and use that to make a second slide rule for my lab. There are two ways to do trig on a slide rule... the hard way where you manually do floating-point calculations using a Taylor series, which lets you do most complex math functions even if they are not on the rule. You could probably even use them to calculate logarithms on the slide rule to higher accuracy than the slide rule normally allows, and then use those to calculate even more accurate logarithms... but I digress. The easy way to do trig functions is to have a slide rule that has a separate sliding part for them. When the rule is at the zero position, all the numbers line up to the sine, cosine or tangent of that number (of course the numbers are presumed to be in radians).

14 years ago on Introduction

Some slide rules had very long scales which were printed as spirals on disks or as helices on the surfaces of cylinders. Scales several metres long could be put on devices that could fit into a jacket pocket, enabling calculations to be done to 4-digit accuracy or even better. I had such a slide rule at high school. Its main problem was that other kids didn't recognize it, so it didn't have the "nerd-cool" effect that regular slide rules had.

14 years ago on Step 3

"preferably sobriety" rofl I know some folks who might try and make a slide rule when they got drunk. I'm one of them...

14 years ago on Introduction

My Dad has ten foot long slide rule in our basement from a navy ship.

Reply 14 years ago on Introduction

Sweet, that thing is probably a valuable antique now. The slide rule pictured is a humble 6 inches. My first book on electricity was actually a NAVPERS 10086 Navy Training Guide in Basic Electricity. I finished it and started a biochemistry textbook using the free time I gained by refusing to attend religion class in high school. Ah, good times.

Reply 14 years ago on Introduction

It's called a demonstration slide rule because instructors would teach math calculations on it at the front of a class. It's probably still worth a couple hundred bucks because they are very rare. Last I saw, a yellow 8 foot rule went for around 500 on eBay.

Reply 14 years ago on Introduction

Haha, brilliant! Looks like our friend here has a profitable restoration project in his cards!

Reply 14 years ago on Introduction

Cool! Thanks for the tips. I will look into restoration. ;)

Reply 14 years ago on Introduction

It probably is not worth that much because it is missing the slide itself. A shame but it still looks cool on the wall.

14 years ago on Introduction

This is great! A video would be nice, but you'd need about 720p HD to see the numbers clearly enough to be useful. Maybe a Flash animation.

Reply 14 years ago on Introduction

Instructables auto-resizes the images... click on the little "i" in the upper left hand corner of the image, then on the link below the image that says "1024x768". Then, you will actually have better than 720p! Thank you for pointing that out, I forgot that it was nontrivial to view the image in its original format.

Reply 14 years ago on Introduction

No, no, no...not what I meant. The images are just fine. I meant that it would be nice to have a video to further explain how it worked, but the standard crappiness you get from the average webcam would be far too blurry and compressed to see the numbers. Also, you couldn't put it on YouTube: the compression would kill it unless you cleverly added &fmt=18 to the end of the URL.