A Device You Can Count On
If California’s energy crisis turns computers into pricey paperweights and makes AA batteries as scarce as vacuum tubes, Tom Wyman will still be able to perform vital calculations such as finding the square root of 144 or figuring the value of 2 to the power of 10.
That is, if he can decide which of his approximately 450 slide rules to use.
Long before there were pocket calculators, scientific calculators, PC desktop calculators, graphing calculators, wristwatch calculators and Palm touch-screen calculators, there was the humble slide rule.
For nearly 350 years, these simple mechanical devices were used by scientists, engineers and all manner of technical tradesmen (and perhaps a very few tradeswomen) to make complex calculations.
But in 1972, Hewlett-Packard introduced an electronic pocket calculator called the HP-35, and the slide rule’s fate was sealed.
“Unlike the typewriter, which is still being phased out, it went out overnight,” said Wyman, a retired petroleum engineer and shipping manager in his mid-70s who lives in Palo Alto. “When I got my HP-35, it was: ‘Goodbye slide rule!’ ”
Nearly three decades later, the slide rule is enjoying a renaissance of sorts among engineers and others who have fond memories of their younger years.
In a world where technological change often comes at a frighteningly quick pace, slide rules evoke a nostalgia for a simpler time. Those were the days when technology was more hands-on, when scientists carried boxes of punch cards to program their computers and future engineers spent their summer vacations building radios by hand.
Slide rules are even tugging the heartstrings of a handful of folks who had scarcely learned to count by the time the devices began their precipitous decline. For the young, slide rules exert a kind of ancient mystique.
“Believe it or not, I have used it once or twice in the lab when I couldn’t find my pocket calculator,” said Eric Marcotte, a 32-year-old neuroscientist at McGill University in Montreal. “My calculator disappears a lot, but oddly, no one ever takes my slide rule.”
An Episcopal minister and mathematician named William Oughtred first described how slide rules would work in his 1632 book, “Circles of Proportion and the Horizontal Instrument.” Some historians believe that Oughtred built his first slide rules a few years earlier.
The devices were based on a mathematical breakthrough--John Napier’s discovery of logarithms in 1614. The discovery made it possible to carry out complex calculations using basic mathematical operations such as addition and subtraction. Slide rules use logarithms to mark off distances, and calculations can be made by comparing those lengths.
Slide rules come in a variety of shapes and sizes. Most are rectangular, but some are made of concentric circles. A few are cylindrical with dials that rotate like a bicycle lock. The smallest rules can fit in a breast pocket, and the largest ones used to be mounted over classroom chalkboards so that students could follow along as the teacher made calculations.
The most common slide rules are about the size of a bumper sticker and divided into thirds. The top and bottom are held in place by metal brackets, and the middle section slides back and forth between them. Each part contains several “scales” consisting of hash marks and numbers calibrated for specific tasks, such as multiplication and division.
To multiply, for example, you first find one of the factors on the D scale. Then you slide the middle section of the rule so that one end of the C scale lines up with the first number. Finally, you slide the cursor--the clear plastic window with the faint red line--over the other factor on the C scale. Follow the red line down to the D scale, and the number you see is the answer you’re looking for.
It might sound complicated, but it’s really nothing more than adding two lengths together to find their total distance.
(Want to play along at home? Visit https://ds.dial.pipex.com/nib/card rule.htm to print out a pair of scales, then paste them on a piece of cardboard and cut it down the middle to create a simple, bare-bones slide rule. More complicated recipes for homemade slide rules are available at https://calclab.math.tamu.edu/~fulling/m152/sliderul.html and https://icarus.physics.montana.edu/math/csr.html.)
Throughout the centuries, slide rules became quite specialized and advanced. Hydraulics experts used them to calculate the flow of sewage in sewer systems. Machine gunners relied on them to help them aim their weapons. Even Sir Isaac Newton toiled with slide rules (and invented one as well) as he formulated the basic laws of physics in the 17th century.
As analog devices, slide rules weren’t absolutely precise, but they were good enough. After all, they were used by the engineers who built the Brooklyn Bridge and the scientists who sent a man to the moon.
Just a few decades ago, slide rules were indispensable. Techies kept them strapped to their belts in leather cases like scabbards. They fixed their identities in large part based on whether they used a Kueffel & Esser or a Post brand rule. They even competed in spelling-bee-style contests to see who could perform complex calculations the fastest.
Though slide rules simplified things for scientists, they weren’t necessarily easy to employ. After adjusting the bars and sliding the cursor to get a number, users still had to figure out where the decimal point should go. (Multiply 4 by 5 on a slide rule and the answer is 2, not 20.)
“When you’re using a slide rule, it’s necessary to figure out whether you’re talking about 250 cubic feet of concrete or 25.0 cubic feet,” Wyman said.
Slide rule enthusiasts actually see this as an advantage. Unlike calculators, slide rules force their users to really think about the equation they are trying to solve and understand the mathematics behind it.
“You do have to know some math,” said Craig Watkins, a math and physics lecturer at MIT who teaches a no-credit course called “How to Use a Slide Rule.” “When you use a slide rule, you learn not to rely on machines to give you perfect results because it’s just garbage in, garbage out.”
In a time of incredible technological complexity, the simplicity and elegance of the slide rule has helped make it an item worth preserving and collecting for tech aficionados.
Bob Otnes was so proud of his slide rule collection that he put his specimens on display at the Palo Alto Library in 1991. They caught the attention of Rodger Shepherd, and the two men decided to organize a meeting of slide rule collectors. Today, their group--called the Oughtred Society--claims 375 members around the globe.
Since the 69-year-old Otnes retired as an electrical engineer last year, he has devoted his time to producing the Oughtred Society’s biannual journal, arranging the group’s annual West Coast meeting later this month and preparing a trip to Germany for a meeting of the Oughtred Society’s European members. He also tends to his collection of about 300 slide rules, which occupy a place of honor in his home.
“About the only advantage I can think of about being a widower is that here in my dining room, I have two display cases filled with slide rules and calculators,” said Otnes, whose wife passed away in 1993.
Since slide rules went by the wayside in the early 1970s, anyone who used them regularly probably is at least 50 years old today. Wyman, the Oughtred Society’s president, is trying to make the devices appeal to younger folks so that they don’t die out with the last of the middle-aged techies.
“This has become an integral part of the history of mathematics and the calculation,” Wyman said. “In a sense, it will never be forgotten. But whether there’s sufficient interest to keep groups together, that remains to be seen.”
It will depend on people like Marcotte, the McGill University neuroscientist. His interest in slide rules dates back to childhood, when he watched his older brother use one in school. By the time he reached high school, hand calculators already were pervasive.
Undaunted, Marcotte looked for slide rules in antique shops and stationery stores but always came up empty. Then the World Wide Web came to his rescue.
“I typed in ‘slide rule’ on EBay and 250 hits came up,” he said. “People don’t realize what they are. They figure they’re not worth anything.”
A mere $1,300 later, Marcotte’s slide rule collection contains about 70 specimens. On his Web site devoted to slide rules (https://www.slide rule.ca), he warns that the devices could end up following in the footsteps of the Dodo bird. To prevent that from happening, he sometimes hands out slide rules as gifts.
“They’re really big hits,” Marcotte said. “People are quite tickled with them. They didn’t know these things were still around.”
More than 500 slide rule enthusiasts ranging in age from 15 to 80 maintain an active e-mail discussion group on the Internet. (To sign up for the group, go to https://groups.yahoo.com/group/sliderule.)
Popular topics include the care and maintenance of slide rules, how to determine the value of a slide rule and how to solve particular problems using a slide rule. Sometimes, said list moderator Michael O’Leary, the discussion revolves around such questions as: “What make and model slide rules were used in the space program by the astronauts?”
Plasma physicist Barrie Ripin of Bethesda, Md., still remembers laying hands on his first slide rule in the summer of 1960 before heading off to college. At $35, the expenditure was the equivalent of buying a low-end PC today.
“I remember spending many an hour with talcum powder to make it slide perfectly,” he recalled.
The Kueffel & Esser mahogany device still holds a place of honor strapped to his computer monitor with a sign that reads “Emergency Use Only.”
“Even after I got that calculator, the slide rule was very useful, and it’s faster for most things,” Ripin said. “It’s almost like the epitome of analog processing. There’s just something about having it in your hands and moving that slide back and forth. It gives you a closer connection to what you’re doing.”
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Times staff writer Karen Kaplan covers the Internet.
