Is the slide rule now a tool only for calculating collectors? - CSMonitor.com Is the slide rule now a tool only for calculating collectors? By Rick Leopold, Special to The Christian Science Monitor April 7, 1987 Save for later Saved Boston — IT'S a tool that engineers who built the Golden Gate Bridge, now 50 years old, would not have been without. Once upon a time, it was used in planning almost all buildings, bridges, tunnels, and other engineering projects. What tool, so universal a short time ago, is hardly seen anymore? The slide rule. In recent years, it's become increasingly difficult to buy an old-fashioned slide rule. In the early '70s, electronic slide rules - better known as pocket calculators - made manual slide rules almost obsolete. Fifteen years ago, Hewlett-Packard came out with the HP-35 - reportedly the first small calculator to perform engineering functions. In the following years, mass production of calculators sent prices plummeting. The slide rule was almost forgotten. Recommended: Could you pass a US citizenship test? Parsippany, N.J., is home to Keuffel and Esser, formerly one of the largest manufacturers of slide rules.

Hank Haase, manager of sales administration and a 40-year veteran with the company, which manufactures drafting films and paper, has seen the rise and fall of the slide-rule business. During the 1960s, Keuffel and Esser produced 5,000 slide rules per month. In 1975, they produced their last slide rule. Mr. Haase says it was the Cadillac of the slide-rule industry - the ``Log Log Deci Trig,'' made of seasoned mahogany and precision engraved. During the earlier days of production, it took many craftsman to fashion one of these instruments. Haase notes that the United States Naval Academy and West Point were large users of the ``Deci Trig,'' as were mathematical engineers. Though they're no longer produced, the company still stocks around 1,200 or so and occasionally gets an order for some. Photos of the Day Photos of the day 02/08 Why would anyone still want to buy a slide rule, when inexpensive calculators are so readily available? According to Haase, slide rules are better suited to some functions than are calculators.

He explains that if you're doing quotations and bids, markups and markdowns, a slide rule lets you ``see down the road.'' For example, if you set your slide rule on a certain factor to determine, say, a 30 percent margin on the sale of your pet rocks, at a glance you can see what price you would have to charge for a 45 percent margin. This is not possible on a calculator, where you need to make a new mathematical calculation to find the figure for the 45 percent margin. Despite this isolated advantage over the calculator, Haase does not expect the slide rule to make a comeback. Neither does Arthur Orans of Philomath, Ore. Nostlalgia and genuine appreciation for this relic of our recent past led him to found the Philomath International Slide Rule Society. Begun in 1983 after he found an ``orphan'' slide rule at a flea market, his organization now boasts more than 400 members worldwide. Periodic newsletters are sent to members, and the society maintains manuals for slide rules with special uses - such as those for chemical, integral, and naval engineering. Many sympathetic to his cause have sent slide rules to Mr.

Oran - from high-tech to big classroom models. In turn, he has donated many of these ``specimens'' to the Oregon Museum of Science and Industry in Portland. For a $7 membership fee, one can join up with fellow slide-rule enthusiasts. The mention of slide rules evokes a poignant memory for Mark Schuster, an assistant professor at the Massachusetts Institute of Technology. He remembers the giant, six-foot-long slide rules hanging over the classroom chalk boards during his student days at MIT. He says he laments the passing of the slide rule because students have lost the ability to estimate in a creative way. With slide rules, the user has to figure out the correct placement of the decimal points. Students are now using calculators or computers to solve complex mathematical problems. Their tendency is to simply trust the answer their calculator has given them without thinking about whether or not the answer is reasonable. Although it seems that everyone has become accustomed to the decimal points and push-button ease of calculators, most of those contacted for this article do not believe that slide rules are collectors items. But who would have thought that Superman comic books - or even the Ford Edsel - would become collectors items?

Philomath International Slide Rule Society, Box 892, Philomath, Ore. 97370. Next up Slide Rule Operation Multiplication The figure below shows a simplified slide rule. It consists of two scales that can move with respect to each other. A numeral x is printed on each scale at a distance from the "index" (the left side number 1) equal to its base-10 logarithm (logx) times the length of the scale. Tick marks between each numeral are similarly placed according to logarithmic distance. A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules log(xy) = log(x) + log(y) and log(x / y) = log(x) - log(y). Sliding the top scale rightward by a distance of log(x) aligns each number y, at position log(y) on the top scale, with the number at position log(x) + log(y) on the bottom scale. Since log(x) + log(y) = log(xy), reading this position on the bottom scale gives xy, the product of x and y. The illustration below shows the slides arranged for multiplication of 2 with any other number.

The index on the upper scale is aligned with the 2 on the lower scale. This shifts the entire upper scale rightward by log(2). The numbers on the upper scale line up with the multiplication-by-2 result on the lower scale. For example, the 3.5 on the upper scale is aligned with the product 7 on the lower scale, the 4 with the 8, and so on: Operations may go "off the scale". For example the diagram above shows that the slide rule has not positioned the 7 on the upper scale above any number on the lower scale, so it does not give any answer for 2 x 7. In such cases, the user may slide the upper scale to the left, effectively multiplying by 0.2 instead of by 2, as in the illustration below: Here the user of the slide rule must remember to adjust the decimal point appropriately to correct the final answer. We wanted to find 2 x 7, but instead we calculated 0.2 x 7 = 1.4. So the true answer is not 1.4 but 14. (see note 1) Division The illustration below demonstrates the computation of 5.5/2.

The 2 on the top scale is placed over the 5.5 on the bottom scale. The 1 on the top scale lies above the quotient, 2.75. (see note 2) Other operations In addition to the logarithmic scales, some slide rules have other mathematical functions encoded on other auxiliary scales. The most popular were trigonometric, usually sine and tangent, common logarithm (log10) (for taking the log of a value on a multiplier scale), natural logarithm (ln) and exponential (ex) scales. Some rules include a Pythagorean scale, to figure sides of triangles, and a scale to figure circles. Others feature scales for calculating hyperbolic functions. On linear rules, the scales and their labeling are highly standardized, with variation usually occurring only in terms of which scales are included and in what order: A, B The scales on the front of a K&E 4081-3 slide rule The scales on the back of a K&E 4081-3 slide rule Roots and powers There are single-decade (C and D), double-decade (A and B), and three-decade (K) scales.

To compute x2, for example, we can locate x on the D scale, and read its square on the A scale. Inverting this process allows square roots to be found, and similarly for the powers 3, 1/3, 2/3, and 3/2. Care must be taken when the base, x, is found in more than one place on its scale. For instance, there are two nines on the A scale, and to find the square root of nine, we must use the first one; using the second one gives the square root of 90. Trigonometry For angles between 5.7 and 90 degrees, sines are found by comparing the S scale with C or D. The S scale has a second set of angles (sometimes in a different color), which run in the opposite direction, and are used for cosines. Tangents are found by comparing the T scale with C, D, or, for angles greater than 45 degrees, CI. Sines and tangents of angles smaller than 5.7 degrees are found using the ST scale. Inverse trigonometric functions are found by reversing the process.

The ST scale could also be used to convert between degrees and radians and was sometimes labeled SRT for this reason. Logarithms and exponentials Base-10 logarithms and exponentials are found using the L scale, which is linear. For base e, the LL scales are used. Physical design Standard linear rules The length of the slide rule is quoted in terms of the nominal length of the scales. Scales on the most common "10-inch" models are actually 25 cm in length, as they were made to metric standards, though some rules offer slightly extended scales to simplify manipulation when a result overflowed. Pocket rules are typically 5 inches. Models a couple of meters long were sold to be hung in classrooms for teaching purposes. Typically the divisions mark a scale to a precision of two significant figures, and the user estimates the third figure. Some high-end slide rules have magnifying cursors that make the markings easier to see. Such cursors can effectively double the accuracy of readings, permitting a 10-inch slide rule to serve as well as a 20-inch. A number of tricks can be used to get more convenience.

Trigonometric scales are sometimes dual-labelled, in black and red, with complementary angles, the so-called "Darmstadt" style. Duplex slide rules often duplicate some of the scales on the back. Scales are often "split" to get higher accuracy. Specialised slide rules were invented for various forms of engineering, business and banking. These often had common calculations directly expressed as special scales, for example loan calculations, optimal purchase quantities, or particular engineering equations. For example, the Fisher Controls company distributed a customized slide rule adapted to solving the equations used for selecting the proper size of industrial flow control valves. Circular slide rules A simple circular slide rule, with only inverse, square and cubic scales. On the reverse is a handy list of 38 metric/imperial conversion factors. Circular slide rules come in two basic types, one with two cursors, and another with a movable disk and a cursor. The basic advantage of a circular slide rule is that the longest dimension was reduced by a factor of about 3 (i.e. by p). For example, a 10 cm circular would have a maximum precision equal to a 30 cm ordinary slide rule.

Circular slide rules also eliminate "off-scale" calculations, because the scales were designed to "wrap around"; they never have to be re-oriented when results are near 1.0 - the rule is always on scale. Circular slide rules are mechanically more rugged, smoother-moving and more precise than linear slide rules, because they depend on a single central bearing. The central pivot does not usually fall apart. The pivot also prevents scratching of the face and cursors. Only the most expensive linear slide rules have these features. The highest accuracy scales are placed on the outer rings. Rather than "split" scales, high-end circular rules use spiral scales for difficult things like log-of-log scales. One eight-inch premium circular rule had a 50 inch spiral log-log scale! Technically, a real disadvantage of circular slide rules is that less-important scales are closer to the center, and have lower precisions. Historically, the main disadvantage of circular slide rules was just that they were not standard. Most students learned slide rule use on the linear slide rules, and never found reasons to switch. One slide rule remaining in daily use around the world is the E6B.

This is a circular slide rule first created in the 1930s for aircraft pilots to help with dead reckoning. With the aid of scales printed on the frame it also helps with such miscellaneous tasks as converting time, distance, speed, and temperature values, compass errors, and calculating fuel use. Breitling Navitimer Montbrillant wristwatch with circular slide rule. The so-called "prayer wheel" is still available in all flight shops, and remains widely used. While GPS has reduced the use of dead reckoning for aerial navigation, and handheld calculators have taken over many of its functions, the E6B remains widely used as a primary or backup device and the majority of flight schools demand that their students have some degree of its mastery. In 1952, Swiss watch company Breitling introduced a pilot's wristwatch with an integrated circular slide rule specialized for flight calculations: the Breitling Navitimer. The Navitimer circular rule, referred to by Breitling as a "navigation computer", featured airspeed, rate/time of climb/descent, flight time, distance, and fuel consumption functions, as well as kilometer-nautical mile and gallon-liter fuel amount conversion functions.

Materials Traditionally slide rules were made out of hard wood such as mahogany or boxwood with cursors of glass and metal. As noted below, at least one high precision instrument was made of steel. In 1895, a Japanese firm, Hemmi, started to make them from bamboo, which had the advantages of being dimensionally stable, strong and naturally self-lubricating. These bamboo slide rules were introduced in Sweden in the fall of 1933, and probably only a little earlier in Germany. Scales were made of celluloid or plastic. Later slide rules were made of plastic, or aluminium painted with plastic. Later cursors were acrylics or polycarbonates sliding on Teflon bearings. All premium slide rules had numbers and scales engraved, and then filled with paint or other resin. Painted or imprinted slide rules are inferior because the markings wear off. Premium slide rules included clever catches so the rule would not fall apart by accident, and bumpers so that tossing the rule on the table would not scratch the scales or cursor. The recommended cleaning method for engraved markings is to scrub lightly with steel-wool.

For painted slide rules, and the faint of heart, use diluted commercial window-cleaning fluid and a soft cloth. History William Oughtred (1575-1660), inventor of the slide rule. The slide rule was invented around 1620-1630, shortly after John Napier's publication of the concept of the logarithm. Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale, which, with additional measuring tools, could be used to multiply and divide. In 1630, William Oughtred of Cambridge invented a circular slide rule, and in 1632 he combined two Gunter rules, held together with the hands, to make a device that is recognizably the modern slide rule. Like his contemporary at Cambridge Isaac Newton, Oughtred taught his ideas privately to his students, but delayed in publishing them, and like Newton, he became involved in a vitriolic controversy over priority, with his one-time student Richard Delamain. Oughtred's ideas were only made public in publications of his student William Forster in 1632 and 1653.

In 1722, Warner introduced the two- and three-decade scales, and in 1755 Everard included an inverted scale; a slide rule containing all of these scales is usually known as a "polyphase" rule. In 1815, Peter Roget invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents. This was especially useful for fractional powers. Modern form The more modern form was created in 1859 by French artillery lieutenant Amédée Mannheim, "who was fortunate in having his rule made by a firm of national reputation and in having it adopted by the French Artillery". It was around that time, as engineering became a recognized professional activity, that slide rules came into wide use in Europe. They did not become common in the United States until 1881, when Edwin Thacher introduced a cylindrical rule there. The duplex rule was invented by William Cox in 1891, and was produced by Keuffel and Esser Co. of New York.

(see notes 3 and 4) Astronomical work also required fine computations, and in 19th century Germany a steel slide rule about 2 meters long was used at one observatory. It had a microscope, attached giving it accuracy to six decimal places. In World War II, bombardiers and navigators who required quick calculations often used specialized slide rules. One office of the U.S. Navy actually designed a generic slide rule "chassis" with an aluminium body and plastic cursor into which celluloid cards (printed on both sides) could be placed for special calculations. The process was invented to calculate range, fuel use and altitude for aircraft, and then adapted to many other purposes. Engineer using a slide rule. Note mechanical calculator in background. Throughout the 1950s and 1960s the slide rule was the symbol of the engineer's profession (in the same way that the stethoscope symbolized the medical profession). As an anecdote it can be mentioned that German rocket scientist Wernher von Braun brought two 1930s vintage Nestler slide rules with him when he moved to the U.S. after World War II to work on the American space program.

Throughout his life he never used any other pocket calculating devices; slide rules obviously served him perfectly well for making quick estimates of rocket design parameters and other figures. Pickett brand slide rules were the standard in the Apollo program; Pickett's slide rules of the era often included a NASA or Apollo logo to promote the fact. A Pickett N600-MES (6 inch, magnifying cursor, "Eye-Saver" yellow) was standard equipment on all Apollo flights. Some engineering students and engineers carried ten-inch slide rules in belt holsters, and even into the late 1960s this was a common sight on some campuses. Students also might keep a ten-or twenty-inch rule for precision work at home or the office while carrying a five-inch pocket slide rule around with them. Another mechanical pocket calculator, the Curta a.k.a. "pepper grinder", was also popular among scientists. In 2004, education researchers David B. Sher and Dean C. Nataro conceived a new type of slide rule based on prosthaphaeresis, an algorithm for rapidly computing products that predates logarithms. There has been little practical interest in constructing one beyond the initial prototype, however.

Demise The importance of the slide rule began to diminish as electronic computers, a new, but very scarce resource in the 1950s, became widely available to technical workers during the 1960s. The introduction of Fortran in 1957 made computers practical for solving modest size mathematical problems. IBM introduced a series of more affordable computers, the IBM 650 (1954), IBM 1620 (1959), IBM 1130 (1965) addressed to the science and engineering market. John Kemeny's BASIC programming language (1964) made it easy for students to use computers. Wang Laboratories introduced desk-sized calculators starting in 1965. The DEC PDP-8 minicomputer was introduced in 1965. Computers also changed the nature of calculation. With slide rules, there was a great emphasis on working the algebra to get expressions into the most computable form. Small terms were approximated or dropped. Fortran allowed complicated formulas simply to be typed in from textbooks. Numerical integration was often easier than trying to find closed form solutions. More difficult problems could be attacked.

The young engineer asking for computer time to solve a problem that could have been done by a few swipes on the slide rule became a humorous cliché. Many computer centers had a framed slide rule hung on a wall with the note "In case of emergency, break glass". The last nail in the coffin for the slide rule was the launch of scientific pocket calculators; i.e., models featuring trigonometric (sin, cos, ...) and logarithmic functions, of which the Hewlett-Packard HP-35 was the first, in 1972. By that time slide rules were mostly used in schools, where textbook and exam problems were designed to be solved on them. That market dried up quickly once scientific calculators became affordable. Advantages A slide rule tends to moderate the fallacy of "false precision" and significance. The typical precision available to a user of a slide rule is about three places of accuracy. This is in good correspondence with most data available for input to engineering formulas (such as the strength of materials, accurate to two or three places of precision, with a great amount - typically 1.5 or greater - of safety factor as an additional multiplier for error, variations in construction skill, and variability of materials).

There's an old saying in engineering, "if you care about the third significant digit of tensile strength, you are already in trouble". When a modern pocket calculator is used, the precision may be displayed to seven to ten places of accuracy while in reality, the results can never be of greater precision than the input data available. A slide rule requires a continual estimation of the order of magnitude of the results. On a slide rule 1.5 x 30 (which equals 45) will show the same result as 1,500,000 x 0.03 (which equals 45,000). It is up to the engineer to continually determine the reasonability of the results: something easily lost when a computer program or a calculator is used and numbers might be keyed in by a clerk not qualified to judge how reasonable those numbers might be. When performing a sequence of multiplications or divisions by the same number, the answer can be often determined by merely glancing at the slide rule without any manipulation. For example, using the ruler pictured above, the user can compute virtually any multiple of two just by looking, leaving the user's hands free.

This can be especially useful when calculating percentages, e.g., for test scores. A slide rule does not depend on batteries. Slide rules, unlike electronic calculators, are highly standardized, so there is no need to relearn anything when switching to a different rule. One advantage of using a slide rule in addition to an electronic calculator is that an important calculation can be checked by doing it on both; because the two instruments are so different, there is little chance of making the same mistake twice. Finding and collecting slide rules For the reasons given above, some people still prefer a slide rule over an electronic calculator as a practical computing device. Many others keep their old slide rules out of a sense of nostalgia, or collect slide rules as a hobby. A popular model is the Keuffel & Esser Deci-Lon, a premium scientific and engineering slide rule available both in a ten-inch "regular" (Deci-Lon 10) and a five-inch "pocket" (Deci-Lon 5) variant. Another prized American model is the eight-inch Scientific Instruments circular rule. Of European rules, Faber-Castell's high-end models are the most popular among collectors.

Although there is a large supply of slide rules circulating on the market, specimens in good condition tend to be surprisingly expensive. Many rules found for sale on online auction sites are damaged or have missing parts, and the seller may not know enough to supply the relevant information. Replacement parts are scarce, and therefore expensive, and are generally only available for separate purchase on individual collectors' web sites. The Keuffel and Esser rules from the period up to about 1950 are particularly problematic, because the end-pieces on the cursors tend to break down chemically over time. In many cases, the most economical method for obtaining a working slide rule is to buy more than one of the same model, and combine their parts. Notes Note 1: Resetting the slide is not the only way to handle multiplications that would result in off-scale results, such as 2 x 7; some other methods are: (1) Use the double-decade scales. (2) Use the folded scales. In this example, set the left 1 of C opposite the 2 of D. Move the cursor to 7 on CF, and read the result from DF. (3) Use the CI scale.

Position the 7 on the CI scale above the 2 on the D scale, and then read the result off of the D scale, below the 1 on the CI scale. Since 1 occurs in two places on the CI scale, and one of them will always be on-scale. Method 1 is easy to understand, but entails a loss of precision. Method 3 has the advantage that the it only involves two scales. Note 2: There is more than one method for doing division. The method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the 1 at either end. Note 3: The Log-Log Duplex Decitrig Slide Rule No. 4081: A Manual, Keuffel & Esser, Kells, Kern, and Bland, 1943, p. 92. Note 4: The Polyphase Duplex Slide Rule, A Self-Teaching Manual, Breckenridge, 1922, p.20. The Slide Rule: A Computing Device That Put A Man On The Moon : NPR Ed : NPR Instagram Twitter The protractor and the Bunsen burner. Playing the recorder in music class.

Drawing arcs and circles with a compass in geometry. These tools of the education trade become part of our lives for a semester or two and then we move on. Today, NPR Ed begins a new series examining these icons of the classroom. We start off with a device that once was essential to higher-level math, in school and in the workplace, but now has all but disappeared: The slide rule. "Take your batteries out," Jim Hus says, watching his pre-calculus students remove the AA batteries that power their calculators. "Let's do those multiplication problems again." For the next calculations, Hus's juniors and seniors at Highland High School in Highland, Ind., will use a different tool: A tool that dates back 400 years. Before the smartphone, the laptop and the graphing calculator, there was the slide rule. It's a powerful mechanical computing device, often no larger than a 12-inch ruler, marked with numbers — but part of it slides in an out to to show relationships between different sets of numbers. Source: NPR Credit: LA Johnson That seemingly simple tool has a serious resume. NASA engineers used slide rules to build the rockets and plan the mission that landed Apollo 11 on the moon.

It's said that Buzz Aldrin needed his pocket slide rule for last-minute calculations before landing. Article continues after sponsorship "The slide rule is an instrument that was used to design virtually everything," says Deborah Douglas, the director of collections and curator of science and technology at the MIT Museum in Cambridge, Mass. The museum just ended a three-year exhibit on slide rules. "The size of a sewer pipe, the weight-bearing ability of a cardboard box, even rocket ships and cars." So, What Is A Slide Rule? Slide rules are typically rectangular and about the size of a ruler. They are divided into thirds, the top and bottom are fixed in place, but the middle section slides back and forth. Each section has scales — numbers and line marks for calculations. The first one was built by William Oughtred, a cleric teaching math in England in the 1600s. It was based on John Napier's discovery of logarithms. In its simplest form, the slide rule adds and subtracts lengths in order to calculate a total distance. But slide rules can also handle multiplication and division, find square roots, and do other sophisticated calculations. For generations of engineers, technicians and scientists, the slide rule was an essential part of their daily lives.

Until, all of a sudden, it wasn't. In 1972 Hewlett-Packard came out with the first handheld electronic calculator. Practically overnight, the slide rule had become obsolete. "The death of the slide rule was pretty instantaneous," says Bob De Cesaris, who oversees chip manufacturing at Intel and has one of the largest collections of slide rules in the country. De Cesaris estimates his collection has nearly 4,000 slide rules. He is also the president of the Oughtred Society — a group of 400 slide rule collectors and enthusiasts seeking to preserve the device's history (and where you can find out all sorts of information about them). And yet, despite the calculating power these days in even your handheld phone, the slide rule isn't quite dead. Sample Problem: 2x2 Step 1: Line up the C scale and D scale on the left index. Previous Step 2: Slide the C scale index to the D scale number 2 Previous Step 3: Locate the C scale number 2 Previous LA Johnson/NPR Hide caption Step 4: Now look at the D scale underneath the C scale 2 to find your answer!

Previous i View slideshow Here and there, teachers like Jim Hus still use them in the classroom. Sister Paula Irving, a nun at the Community of Jesus in Orleans, Mass., teaches a computer programming course to homeschooled high school students. And when she covers the history of the computer, she teaches students how to use a tool she remembers watching her father use as he calculated their family's finances. More than a thousand miles west, Laurie Emery, a math teacher at South Winneshiek High School in Calmar, Iowa, will teach her junior pre-calculus class how to do intricate calculations without a calculator. There's even a freshman seminar about the slide rule at the University of California, San Diego, that Professor Joe Pasquale has been teaching since 2003. "We live in this age when computing is getting exponentially more powerful but we often don't even think about the calculations being made," says Pasquale. "We just let our computer do all the work." In the seminar, Pasquale says his students are often amazed that the slide rule's answers make sense. Thinking About The Math "The nice thing about a calculator is you don't have to think – but it's also a bad thing," he adds.

"When you're using a slide rule you have to be engaged. You have to be thinking about math." And that's one of the main reasons some teachers still hang on to the old "slipsticks." MIT's Debbie Douglas says that even though the slide rule isn't as precise as a calculator, students can understand the idea of what it's doing. "It really makes one engaged with the process." Jim Hus still remembers deciding to invest $400 in a calculator and abandoning his slide rule during his freshman year at Purdue, back in 1974. But it's a device he'll never forget and he hopes his students at Highland High School in Indiana won't either. He's planning to have his students build a classroom slide rule. "I joke it will be the largest slide rule in the world," he says, laughing. "But this way, I'm not just handing the students a tool, we're learning how it operates so we can access higher math concepts." Last slide rule manufactured, July 11, 1976 | EDN Last slide rule manufactured, July 11, 1976 In 1976, EDN was in its 20th year.

What else was happening in 1976?: The first commercial Concorde flight took off on Jan 21. Apple Computer was formed on April 1. No joke. Viking 2 landed to explore Mars on Sept 3. NASA unveiled Space Shuttle Enterprise on Sept 17. EDN published " This 30-ppm scale proves that analog designs aren't dead yet ," by Jim Williams on Oct 5. Microsoft registered with the Secretary of State of New Mexico on Nov 26. The first laser printer is introduced by IBM (the IBM 3800 ). Diffie–Hellman key exchange cryptography was proposed. Read all of our coverage of EDN's 60th anniversary here . William Oughtred, as well as others, developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Slide rules became increasingly popular in the 1950s and 1960s, before beginning to fall out of favor to pocket calculators, which, by the mid 1970s, had become affordable and were considered significantly easier to use by the masses than slide rules.

The last slide rule manufactured in the United States was produced on July 11, 1976. Although some overseas companies continue to make slide rules and retailers like Think Geek offer replica models, these are often sold for nostalgia or are far more advanced than actual slide rules, some including electronics. Keuffel & Esser (K&E) Corporation had the honor of producing the last slide rule. The company presented it to the Smithsonian . Despite the end of slide rule manufacturing, many such tools can be found on engineers’ benches and in cubes today, decades after the end of production. Also see: David Crate's Quality Slide Rules Link to Site Map Inexpensive, Unused Pic kett Slide Rules Pickett was the leading maker of educational market slide rules in the U.S. Their low-cost rules were not necessarily a joy to behold or use, but they got the job done and cheaply. Today, when slide rules are no longer manufactured (anywhere in the world, as far as I've been able to determine), Luddites like me (and, perhaps you, since you're reading this) can benefit from the large reserve of unused Pickett rule sets still extant in office supply warehouses and school district auctions across the country.

The Pickett rules offered here for sale are arranged (more or less) in order of increasing complexity. All Pickett rules in this section are unused product. They are complete as they came when you could buy them in the college bookstore. All have instructions, case and original packaging (the one exception is the N3 Powerlog, it comes with the case, only). Plastic Pickett Rules Pickett 160C, Available in white (160C-T) or "eye-saver" yellow (160C-ES, depicted above). The 160C comes in a clear, rigid case labeled: "BREAK GLASS IN CASE OF EMERGENCY CAUSED BY COMPUTER POWER FAILURE. (Sorry, this item currently unavailble.) Pickett Model 115T. Aï¿½nice, simple slide rule, perfect for the beginner. Complete with instruction manual. $79. ï¿½ Pickett Model 115 Slide Rule Set Pickett Model 140. This is, perhaps, Pickett's nicest rule, (unless you prefer aluminum). Highly functional and easy to use and read.

Mint-in-Box w/ all orig. pieces / accessories: case, manual. Available with black scales, only. Also available with scales in both black and red (sorry, black and red scale version is sold out.) for improved readability (inverse scales are in red, please see photo just below). - SORRY, THIS ITEM IS SOLD OUT. Pickett Model 140 Slide Rule Set The Pickett Model 140, 22-scale log-log rule is the perfect choice for cost-conscious pedagogical applications where full-functionality, as well as consistency and completeness (manuals, cases) are desired. Scales on the 140 are: (front) LL02, LL03, DF, CF, CIF, L, CI, C, D, LL2, LL3, (back) LL01, K, A, B, Cos S, Sec T ST, T, C, D, DI, LL1. $119. Pickett Model 125. Idenitcal to the 140 but lacking log log scales. Complete, new-condition set: $59.

Pickett "All-Metal" Rules Pickett's touted their aluminum rules as a rough-and-ready replacement for "frail" wooden counterparts. May have been a little "specmanship" going on, but Pickett's pricing was more considerate of student's budgets. Pickett N300 Slide Rule Pickett N300 , 5" "eye-saver" yellow aluminum technical rule. Complete set includes manual, warranty card, and box. (Also available in boring white). $149. This Just in ... Pickett N500 Slide Rule Set Pickett N500-ES, Yikes. It's pretty cool, after all these years, to find such a thing. 10" aluminum log-log engineering rule. Complete set includes leather case, manual, warranty card, and box. $149. (Currently available only in WHITE color). Pickett N600 Slide Rule Set ï¿½ Pickett N600, These are really nice:ï¿½small format but able to perform all the calculations of the N500. Complete set includes leather case (with handy pocket clip), manual, warranty card, and box.

$195. Available in yellow and white. Pickett N3p Slide Rule Set ï¿½ Pickett N3p, The ultimate rocket for you pocket. Complete set includes leather case (with handy pocket clip), manual, warranty card, and box. $249.. Pickett N3/N600 "Combo" Slide Rule Set Pickett N3/N600 - you need one,ï¿½I mean, two. Complete set includes leather cases (with handy pocket clip), manual, warranty card, and box. $395.. Pickett N515-T . Cleveland Institute of Electronics special version. These rules were often seen in the evening, after dinner was cleared, on the kitchen table, where many an aspiring electronics technician would burn the midnight oil to get a new career so they could quit that menial job at the grocery. These are great for anyone doing work with electrical calculations involving reactances and/or resonant frequency (special scales). The reverse side is devoted to formulae, constants, and a special decimal point finder (should be helpful to all of you calculator addicts!).

The rule is new-condition; leather case (gold-tone embossed "Cleveland Institue of Electronics") has a couple of small scuffs. Includes belt loop. $129. Pickett B1 . The only bamboo rule that Pickett ever sold. Made in Japan by the same folks who brought us the wonderful Lafayette rules. Ths rule has a great scale layout. Condition is new. Exquisite specimen. Quite rare. $795. Eugene Dietzgen Co. Slide Rules Dietzgen Cat. No. 1773 System Darmstadt Pocket Rule. Superb, German-made slide rule with remarkable functionality for a 'quasi-simplex' format. It has the basic Arithmetic scales (C, D, C-inverse), Trigonometric scales, and three decades of Log Log scales (reverse of slide). In addition, it is equipped with the Squared and Cubed scales (A, B, K), a Pythagorean scale, a ruler on the obverse top edge, a metric rules on the reverse top edge, and special gauge marks on the indicator for pi/4 and power calculation. All of it is explained in the manual (included). It comes with a nifty pigskin slipcase.

The set is complete, although the box is quite worn, the rule and case are like new. (Sorry, this item is not available under terms of Slide Rule Express except for established customers.) $225. ï¿½ï¿½ Dietzgen Cat. No. 1776 Duplex Redi-Rule Set. Very handy little model. Complete set, including case with pocket clip, instruction manual and original box. (This item is not available under terms of Slide Rule Express.) $175. Dietzgen Cat. No. 1771 Redi-rule. Really neat and very practical 5-inch plastic rule. 11-scale Mannheim layout features inch and mm straightedges. Beautifully made; high-quality production is evident in the level of detail and accuracy of the paint-filled marking and even the leather case. Complete set with instructions, leather slipcase, trademark Dietzgen orange, two-piece box. The enitre set is in new condition. Instruction booklet is creased from fitting into box. Made in U.S.A. $99. Dietzgen Field Book.

"Field book manufactured of high grade 50% Rag Paper having a Water Resisting Surface and is sewed with Bing Special Enamel Waterproof Thread. Made in U.S.A." 16 pages of mathematical reference tables and diagrams in the back. The rest is blank - for your "field data". Approx 4 3/4" x 7 1/4". Attractive "Dietzgen" embossed cover. $36. Dietzgen Cat. No. 1767 "National" Slide Rule Set. A good, quality, basic-function slide rule. Complete set, with case, instruction manual and original box. (Click HERE for close-up image of rule.) $39. SORRY, THIS ITEM IS SOLD. Keuffel and Esser Slide Rule Sets - All items are limited availability and subject to prior sale. (K+E sets are not available under terms of Slide Rule Express ) K+E 68 1622 Polyphase (old 4053-3). Complete, mint set (photo above) includes slide rule, hunter-green case, manual, care booklet and box - like new. $325. K+E 4053-2.

Very rare, 8-inch version of the popular 4053. Very good condition, lightly used. (no case) $195. K+E 4161-1 Polyphase Pocket Slide Rule (photo above). New condition (box has a missing flap and a small spot where the green surface was torn off, apparently when a price sticker was removed). This is a relatively rare version, in the late-style packaging. Complete set includes leather case (with pocket clip), instruction manual. $279. K+E 68 1287 Log Log Duplex Decitrig Pocket Slide Rule (old 4181-1C). This is actually a 4181-1 under K+E's re-vamped model numbering scheme; in fact the rule is marked "4181-1" on the end, just as they were before the new scheme was introduced. It took K+E a few years to make the numbering-system change-over, and by the time they had, slide rules were considered obsolete! HERE is a better photo of the rule, itself.

This is a complete NOS set, including the green leather case with handy pocket clip, manual and care booklet in original box (box does exhibit some reasonable wear). (Sold) K+E 68 1215 Log Log Duplex DeciTrig Slide Rule (old 4081-3S). Complete mint set (photo above). This is the mainline K+E workhorse slide rule, the final, copyright 1947 scale set, used by technical professionals throughout the world, realized in mahogany and celluloid. Complete set, with case, manual, and care booklet. Everything is in mint, unused condition - rule is factory-sealed (box does show some wear). $1650. K+E 68 1318 Log Log Duplex Trig Slide Rule (old 4080-3S). Complete mint set (photo above). This is the reincarnation of the venerable 4080, much like the decitrig, but with the trig scales marked in units of degree, minutes and seconds instead of decimal degrees. Beautiful, mahogany construction. Complete set, with case, manual, and collateral paperwork.

Mint, unused condition (box does show some wear). A rare and truly remarkable, historic item. $4000. K+E 68 1100 Deci Lon - Their "flagship" rule, in perfect condition. Complete, mint set includes Deci Lon slide rule, original box, chamois-lined leather case, belt-clip attachment, hardcover manual, and care booklet (Sold). K+E 68-1130 5-inch Deci-Lon Slide Rule, (photo above). This is pretty much the Holy Grail (if you will) of slide rule collecting: K+E's slide rule apotheosis, in pocket format, unused-in-box. The box is a little marked-up and scuffed-up, but the contents are PERFECT. How many of these can there still be on this earth? These sets didn't come with a manual, but one is included for your reference. (I suppose the rationale for not including the manual was that the pocket rule was adjunct to the 10-inch model, which did come with a manual.) Price includes over-night shipping to any U.S destination. Your Satisfaction is Guaranteed.

(Sold.) K+E 4185-7 Clip-on Indictor Magnifier (photo above). Mounts on the indicator of any of these K+E 10" duplex rules, to provide better visibility and precision. Mounting clips fold up when not in use. Felt pouch, box. $95. (back to top of page) - Frederick Post Slide Rule Sets - Versalog Slide Rule No. 1460. This slide rule is a genuine classic and deservedly so, with one of the best scale layouts ever devised for professional technical work. The construction is bamboo, a wonderfully stable, mildly lubricious material. This set is unused and immaculate (the box is a little worn). It is complete with leather case, belt hook attachment, hardcover manual and warrany/care insert. $495 Versalog II Slide Rule No. 1460.

The epitome of the Versalog's exemplars; this was the final iteration of the rule with several improvements including the addition of the "A" scale, extension of R2 scale to reduce the need to reset indices, the addition of radian identification on trigonometric scales allowing direct conversion of radians to degrees and vice-versa, color-coded (3rd color, green) trig scales, mathematical notations on scale labels to clarify fnctionality, and several others. This is a flawless, like new, specimen of the model and includes the manual , which is even harder to find than the rule! $375. "Pocket" Versalog Slide Rule No. 1461. Amazing! This a complete, boxed set of the pocket version of the 1460, and exactly replicates the wonderful scale set. It is also bamboo and celluloid. This set is unused and in beautiful condition (box has a few dings). It is complete with pocker-clip leather case, softcover instructions and warrany/care insert. Hardbound Versalog Slide Rule Instructions will be included, upon request. $750. Chemistry Slide Rule No. 1491.

Has special scales for various chemistry-related calculations including molar concentrations / ratios, atomic weights, molecular weights, water boiling / condensing points versus pressure and temperature, and more. Click HERE to see a close up of the front of the rule and click HERE to see the back. Complete set includes case with removable belt clip, instruction manual, case booklet and box. Rule and case are in new condition. Manual and box show some slight wear. $1750. (back to top of page) - Sun Hemmi Slide Rule Sets - Sun Hemmi #266 Electronics Slide Rule , Sun Hemmi #266 "Electronics" Slide Rule is designed with the electrical/electronics engineer in mind, equipped as it is, with numerous scales (one side of this duplex rule is completely devoted to special scales) for the straightforward calculation of of numerous parameters presumably of interest to Electrical Engineers and their ilk, including R-L-C time constants and 3-dB points, complex impedances, surge impedances (transmission lines), parallel / series network impedances, resonant frequencies / wavelengths, dB ratios, phase relationships, and the like.

A special extension of the standard log-log scales enables calculations into the range of 10^-9, for working with nanoseconds, etc.; a nice very touch. Construction is classic Hemmi bamboo and celluloid with engine cut, paint-filled graduations. The rule has some 24 scales, many multiple use, in navy, red and green colors. Rule is marked "SUN HEMMI JAPAN NO. 266" and "ELECTRONICS". Cursor is nickel-plated brass, with glass indicators. Set includes unused slide rule, leather case, copy of instruction manual. Please note that this rule suffered some rust-staining while in storage, mostly affecting just one end, around the plated steel brace. (Sorry, this item is not available under terms of Slide Rule Express.) (Sold). Sun Hemmi #269 Civil Engineering Slide Rule , specialized rule facilitates various problems encountered by Civil Engineers including trig/survey calculations, triangle solutions, stadia and curve setting calculations, hydraulics and water head. With manual and brown leather case. Unused condition. Hemmi Bamboo and celluloid. $465. - Scientific Instruments Inc. - SIC No. 1610.

One of the most awesome circulars ever made, double-sided, with independently rotating "slide" disk on front side. Scales are: (obverse) E1, CI, C, D, A, K, LL0, LL1, LL2, LL3, (reverse) DI, D, T, S, T, S, T, ST, LL0', LL1', LL2', LL3'; Construction is robust aluminum plate with thick plastic facing on each side. Scales and numerals are deep-cut and paint-filled. Indicator has ball bearings on perimeter to facilitate smooth indicating. Rule only. (This item is not available under the terms of Slide Rule Express .) $495 (back to top of page) - Lafayette - Lafayette 99-7099 Decimalog - This is of my personal favorite slide rules. Well laid-out scales, nice looking, compact! Click HERE for another photo. $395. (back to top of page) - Staedtler - Steadtler Mars 544 28 Technical Slide Rule - This is an exquisitely beautiful and wonderfully capable rule. Complete set includes leather case, manual and box.

(Sold) The Appeal of Slide Rules - For Use and as Collectables. 'Micscape Lite' Article - Microscopy Enthusiasts Sharing Their Other Interests The Appeal of Slide Rules - For Use and as Collectables by David Walker, UK I have a fond affection for slide rules�when studying the sciences at high school and college in the early 70s onwards, they were still a common tool before their rapid demise in the mid 70s when electronic calculators became affordable for all. I bought my first scientific calculator in 1975 (a Decimo 2001E, 'Electronic Slide Rule') and my 'analogue calculator' rapidly gathered dust. It was only about two years ago that I renewed a latent interest in them and started to explore the many superb resources available, which prompted me to purchase a selection. I wouldn't describe myself as a collector, I bought one example each of styles and of makers that particularly interested me and my 'collection' has stopped at eleven. Making examples from published templates is also fun.

Some of these are illustrated below and, given the wealth of authoritative material available on the makers and models, I just add some comments on why they appeal to me and point out some major features. A selection of Web and other resources are offered at the end which discuss their history, manufacture, use, makers and their models. Examples of early 70s models Four typical models spanning a basic to a most advanced example available in the 70s are presented below. The standard slide rule used 25 cm (some 10 inch) long scales� the top one extends the scales. Their relative sizes and weights can clearly vary quite widely, dependent on the model style, materials and number of scales. The last is half the weight of the first example. From top to bottom: Faber-Castell 2/83N Novo-Duplex: Size 38 x 7 cm, 30 scales, plastic. This model is regarded by some as one of the finest slide rules ever made. Its combination of size, build, sophistication of scales offered and attractive use of colour gives a slide rule that impresses!

It became more widely known when Cliff Stoll published his excellent article ' When Slides Rules Ruled ' in 'Scientific American' May 2006 where it was highlighted. This is the only duplex model of the four shown, i.e. it has an equally comprehensive set of scales on the back (single sided are simplex rules). Used versions of the 2/83N crop up regularly on eBay and new old stock is available. The Faber-Castell 2/83N Novo-Duplex upper face�serious firepower on a slide rule! Rubber strips on metal brackets allow desktop use and a rubberised grip on ends of slides also aids use. This, like other rules with screwed brackets, allows retensioning of the slide to suit and realignment of upper and lower stators if required. This rule uses extended scales, i.e. beyond the 25 cm norm, this can aid calculations where an answer 'overflows'.

The typical positions for the C and D scales (1-10-100 scale for x�) as shown in the Hemmi below are replaced by so-called 'folded scales' CF and DF, typically folded around pi or root 10; these are also useful for some calculations. Studies have shown that a typical 25 cm model's C&D scales can be read to three significant figures to a consistent accuracy of ca. 0.5% across its length. As many writers have commentated, this was more than sufficient to design and build most of man's creations before the advent of electronic computers. Some rarer specialist rules can command high prices amongst collectors. A Faber 2/84 Mathema which featured advanced maths functions, sold at the time of writing for over $1200 on eBay. British Thornton AD 150 Advanced: Produced 1973+, simplex, 12 scales, plastic. This is a less sophisticated but typical 'advanced' rule with trig and hyperbolic scales, but my overall favourite in use for handling, practicality and feel, selling for a few pounds on eBay.

It was a widely available model when I bought the Hemmi below in the early 1970s. The plastic is thicker than many giving it a stiffness comparable to wooden stock models. The large indented brackets allow a good push pull action to set the slide accurately. A subtle feature that works well on this rule is the plastic strip rather than metal spring as cursor tensioner. This gives just sufficient tension to maintain cursor alignment but not too much to compress stators and make slide movement stiff. Some rules with metal springs if not perfectly adjusted can give too much tension giving a stiff slide, especially when cursor is near rule centre. The size and modest number of most likely used scales combined with British Thornton's reputation for precision also visually give the impression of a very crisp easy to read rule, more so I think than the 'busy' Faber above. See Resources below for a paper on the multiple complex steps which this company used to make high precision slide rules. Sun Hemmi P280: 10 + 3 scales. This Japanese made rule is the original bought in my teens when studying the sciences at high school.

Slide rules weren't mandatory, log tables were more commonly used, but some of my fellow students and I did use them, particularly for physics and chemistry, where the three significant figures was more than sufficient. This typical model with a dozen or so scales can handle most of the likely calculations a slide rule would be used for. At the time, a choice of slide rules were still commonly sold in any high street stationers such as W H Smiths and Boots the Chemist (the latter who had their own branded range). I unknowingly purchased a model which, although now joined with ten more in recent years, I still feel is hard to beat. The use of brackets only on the rear face gives a clean uncluttered look (but are rather fragile if dropped), the plastic is whiter than most giving high contrast scales, the pastel blue of the slide and a comprehensive but not overwhelming range of scales gives what I think is an elegant and easy to use 'sports car' of slide rules. Detail of the Sun Hemmi P281. The scale codes presented on the left were standardised across makers. The simplest rule may just have the A, B, C and D scales and probably the Cl for multiplication and division..

This is an example of a 'self indicating' rule because the function of each scale is given on the right; not all rules featured this. The slide when closed does not extend beyond the edges of the stock. Some makers extended the slide (e.g.Unique) (or indented the stock, e.g. British Thornton) to allow more precise control, especially when slide was nearly closed. Functions such as squares, square roots, cubes, cube roots and trig values can be read off for a value of x by just using the cursor. Exponential (or log log) scales are on the reverse of the slide. Pickett N902-ES: Size 31 x 4.3 cm, simplex, 9 scales, aluminium. Pickett were one of the main US makers and whose later models made extensive use of aluminium to give a lightweight but rigid rule. The 'ES' in the model name denotes their 'Eye Saver' yellow finish (560 nm), the benefits of increased visual acuity of scales and reduced eye strain are described in the accompanying leaflet. (Models were typically available both in traditional white or the yellow).

Acquiring 'New in Box' (NIB) examples of models is one aspect that appeals to some collectors. This is the Picket N902-ES 10 inch rule (NIB) bought off US eBay for less than $25. I've only bought two NIB models. I prefer to acquire the well used but still fully functional models (preferably with its box and manual albeit likely tatty) where they can often attract barely a few pounds. A well used example, often inscribed with owner's name, can be part of their appeal. Examples of earlier wooden / bamboo models Three typical mid 20th century or later wood based slide rules and one bamboo example are shown below. When handling wooden/bamboo slide rules, there is an immediate impression of rigidity, not always experienced with some later lightly built plastic rules, or some of the largest plastic rules that can sag somewhat under their own weight. The earlier rules engraved or stamped the scales on the wood (I don't possess an example); the examples shown adopt a variety of scale manufacturing methods using celluloid attached to the stock. Even for the cheapest school rules, precision scales were of course vital to be of use.

From top to bottom: The first two were made by the British company Unique based in Brighton. The first is the 'Brighton' model with mahogany stock, the most sophisticated they made; the second is their basic 'Log Log' model. Both use a scale method unique to the company of celluloid strips protecting printed paper scales. The 'USRC' logo dates the Brighton to 1955 or later. The third is a Hemmi 257 which I bought partly because it was an example of their use of bamboo, a self lubricating material. The end sections have a very distinctive look of bamboo and is my prize possession for a reason I'll return to later. Hemmi used two letter date codes, this one 'FG', which allows it to be dated to July 1955 using published lists. The last is a Castell, the 1/92 made of pear wood with a metric rule on its upper edge, which was quite a common feature. Unlike the Unique models, both the Hemmi and Castell use engraved scales on the celluloid itself bonded to the stock. End views of the four slides rules comparing design features of cheap to more expensive models.

L to R: Unique Log Log, Unique Brighton. Faber-Castell 1/92 and Sun Hemmi 257. The Unique Log Log, a cheap model, has no tongue and groove and relies on the celluloid strips overlying scales for placement. The first three from left to right are simplex rules, they only have scales on the front face and the cursor designs reflects this. The Hemmi 257 far right is a duplex with a bamboo stock with the distinct texture seen in end view. Metal strip inserts for stability and also as a base feature on the Castell and were typically used in 'closed rules'. Others used end brackets without a base like the Hemmi, an example of an 'open rule'. The first three have so-called 'railway track scales', a feature I like as keeps each scale distinct on a busy rule and can aid reading off values. It's not a design seen on most later rules, possibly because of the added complexity of manufacture if engraved scales rather than printed. Pocketability The 25 cm scale was used in typical 'full size' models but a variety of reduced scale models were available for pocketability.

The German Reiss 3212 model below has a typical 12.5 cm scale, this has a basic set of functions but some models crammed a lot of features into the format, e.g. the electronic rule below. I'm not sure if it caught on elsewhere, but many US models (both pocket and 25 cm) were available in leather holsters for the belt�the analogy with the Wild West hasn't escaped commentators on the slide rule's heyday�quickest on the draw maths perhaps for competing engineers tackling a thorny problem! See Dan Winters' delightful article in Discover Magazine, ' The First Nerd Tool' . Reiss 3212 pocket model, plastic with 12.5 cm scales. The Picket N600-ES 5 pocket model became famous as 'the slide rule that went to the moon' and was used on five Apollo missions. Examples in the Apollo themed presentation box are very collectable (but beyond my budget!). The original used by Buzz Aldrin on Apollo 11 sold for $77 675 in 2007.

Cylindrical and circular rules - three examples The slide rules illustrated so far are linear with typical 25 cm (or 10 inch) scales. For greater precision, models with linear scales of 50 cm or more were available but they can start to become impractical. Wrapping the scales spirally around a cylinder was adopted by some makers and I own one very common example, the 'Otis King Calculator', a British model whose production spanned from ca. 1923-1972 (shown right, model K, type B, serial no. N7055). It has scales equivalent to a 66 inch linear rule, although this is modest compared with some. The Fuller rule used a much larger cylinder with spiral scale 42 feet long. The Thacher rule used 20 linear scale bars mounted on a rotating cylinder scales equivalent to a ca. 60 foot linear rule. These are very collectable and attract healthy prices. The Otis calculators are readily available on UK eBay and a good boxed example of a common variant can be acquired for ca. �20+. Mine lacks the original leather case.

They have been widely studied; dating the serial numbers and styles throughout their production attracting particular interest. Perhaps familiarity in use will attract greater appreciation and it's a fascinating collectable, but I much prefer to use a linear rule where the complete scales are immediately visible. The extended scales can require 'hunting' to set a given value and don't feel that the single hand twisting action to set a precise value is as ergonomic as the linear rule where there's potential for both hands to work in opposition and hands kept off the scales. The 'K' model illustrated is also only capable of multiplication and division cf the multi function linear rules. Writers have remarked that the extended scale does not consistently give an additional significant figure cf the typical 25 cm linear rule. The calculator is ca. 10 inches fully extended and ca. 6 inches closed, diameter ca. 1 inch. A single cycle scale is on the left and a double cycle on the right. Manipulation of the sliding black cursor and rotating one scale with respect to the other provides the calculation. The scales on this example are coated paper (later models used celluloid).

Considering in use the scales are being handled all the time (unlike a linear rule), possibly in a grubby working environment, this example as do others, survive well. White scales on a black background were also available. Circular rules offered a more portable design and also much larger scales than a linear model if the scales were spiral. A wide range of specialist rules were, and some still are made, and used today for example in aviation. A very modest Time Life branded Concise 28N model (a Japanese maker still offering rules), shown right; most more advanced examples have been outside my budget to date. One of the finest models was the Faber-Castell 8/10 12 cm diameter, it's a stunning looking rule with subtle use of colour and advanced scales. The Gilson Atlas was ca. 8 inches in diameter, one type had a 46 foot spiral scale equivalent to a linear rule with a 71 foot scale! My homemade example of the Atlas from a downloadable template is shown below. The plastic simplex Concise 28N shown right (8.4 cm in diameter) was a promotional example from Time Life and uses circular scales. The outer are comparable to a ca.

21 cm linear rule, but become less precise as move towards the centre (innermost scale ca. 12 cm). A Russian KL-1 circular rule with a pocket watch type design is shown below. Its ca. 3.7 cm diameter outer scale makes it equivalent to a ca. 11.6 cm (4.6 inch) pocket linear rule. They are well made, very tactile and a pleasure to use and make excellent unusual presents for the 'techie folk' amongst family and friends (this example was a present to my brother for Christmas 2012.) A range of makers made rules to this design, including the English maker Fowler, with their 'Magnum' models being particularly impressive. See the page devoted to the watch style of slide rule at the International Slide Rule Museum . Russian KL-1 pocket watch style slide rule. Overall diameter 5 cm. There are log scales one side and trig. scales on the reverse so can perform the more common functions of a slide rule. One knob rotates the dial on the log side with respect to a small fixed needle (seen just below lefthand knob aligned with '1'). The other knob rotates the red needle.

They are regularly available on eBay, this one was bought from the Ukraine for �14 with original box and Russian instructions (dated 1969). (English instructions are available online, they are easy to use.) Specialist rules - two examples, a 'chemical' and an 'electronic' A wide range of specialist rules for a variety of trades and professions were made and are well documented. Many were less common than the standard rules and can attract higher prices. Electronic MK rule. IWA 0272, German made for the Dutch company De Muidekring N.V.: This belongs to my brother Ian, an electronics engineer. In his teens, being a keen electronic hobbyist, he won it in a competition run by a components supplier seeking a catchy sales line. We missed the top prizes but were chuffed with any prize. We still recall the corny sales line entered, 'Don't Bypass BuyPack for the Best Buys' ! The face showing the electronic scales of the IWA 0272. It is a duplex pocket slide rule with 20 cm scales but packs in a lot of features.

(The other face has typical maths functions.) The slide is a plastic strip sandwiched between two riveted faces; this design allows additional slide scales to be displayed, although gives a rather stiff feel. The rule employs a good use of limited colour and scales are crisply presented �a pocket rocket! The company IWA still makes specialist rules. Sun Hemmi P257 'Chemical rule'. The manual states 'especially designed for use by chemical engineers'. My own work background is in the petrochemicals industry and was keen to own an example. The more advanced models such as this one, aren't that common and often fetch three figure sums, but was lucky to acquire one on UK eBay for a modest two figure sum, possibly because the box was incomplete and lacked the original manual. As remarked earlier it was also my example of a rule with bamboo stock. It's a fascinating collectable but as a chemist I'm unsure how practical or widely used some of the features on this type of rule may have been with its 52 elements, 18 functional groups and given addition is needed to work out molecular weights, requiring calculations away from the rule.

The molecular weights of compounds in use would be readily to hand (container label, catalogue, 'Rubber Handbook') and for atomic weights a periodic table would never be far away. Conversion factors between temperatures, pressures etc would be to hand if required and using a mix of pressure units or temp. scales would often be limited in a given lab / industrial environment to avoid mix ups. Detail of the scales for the chemical engineer (or chemist) on the Hemmi 257. 25 cm scales, celluloid on bamboo, duplex scales. Placing the cursor over an element or chemical group on the upper scales allows the atomic / molecular weight to be read on the D scale on other side. They are arranged in order of their significant figures, i.e. H - Ag - Cd - B equivalent to 1008 - 1079 - 1081 - 1124 with Mo on far right - 9594. The position and presence / absence of a bar for each indicates decimal point location. A final thought - go retro and/or make one!

Going retro is becoming common, notably in hi-fi where the keen eared may appreciate the analogue sound to digital�valve amplifiers, vinyl LPs and analogue radios have made a big comeback. Slide rules, the analogue calculator, are cited by some as being obsolete, but why not a gentle revival to complement calculators (slide rules aren't designed to add or subtract of course). As often remarked, slide rules make the user think about their calculations, they only give the significant figures and the decimal point has to be quickly determined. Many of the calculations we do daily are simple multiplication and division without the need for the 8 decimal places a typical calculator will deliver, e.g. currency conversions, proportions, percentages or calculations for buying items around the home etc and can be readily done with little expertise on the main scales of a basic slide rule, a 5 inch pocket model could suffice. They're fun and an ideal way for students to really learn about the power of logarithms and to understand their calculations. A slide rule user may attract a bit of attention, perhaps even start a conversation or two if used in public.

A youngster may ask "what is that?", some of a certain generation may comment, "Hey you're using a slide rule, I haven't seen one of those for a while!". Or make one: There's no need to buy one for a user of any age to get started. It's fun and instructive to make a slide rule from one of the templates available online. The rule below was made in a few minutes from a print out, scissors and two pieces of clear adhesive tape. Good enough to appreciate how they work with a number of functions offered. A stiff paper slide rule made from the template in Cliff Stoll's Scientific American article. The above is a fun demo' design but with modern printers and some craft and/or wood making skills, some very fine slide rules can be made, linear and circular models in particular with a range of templates available. There's a good selection at the International Slide Rule Museum website, including an ingenious circular rule using a CD case by Ying Hum, see below. After a buying or making a slide rule, if the original manual isn't available online (many are), there's a superb illustrated tutorial on slide rule use (pdf download) offered on the Oughtred Society website (see Resources).

For a more ambitious homebuild project, some enthusiasts have built fully working replicas of large cylindrical rules like the Thacher . The above, based on the Concise 270 model, was made to Ying Hum's design using an inkjet printer, stiff glossy photo paper and clear acetate for cursor. Using his supplied high quality scales and a compass cutter for central holes as well as borders gives a high degree of concentricity between the two scales and cursor, producing a precise and usable slide rule. The large central pivot reduces the wear cf smaller fastenings that can introduce errors with wear. My homemade example of the Gilson Atlas Model III 8 inches in diameter, extending the ingenious DVD case design of Ying Hum (the flat base with pivot was cut out of case) and using a superb template based on the Model III by Wayne Harrison available to members of Yahoo 'The International Slide Rule Group' (in Files). The main scale is a single spiral scale, unlike the circular scales in the Concise model above.

Printed on glossy stiff photo paper using an old Epson 740 1200 dpi inkjet printer (much for better for hi-res work than my 600 dpi modern LaserJet) with acetate sheet cursors. A compass cutter cuts the centre and border for a neat, accurate working rule. The originals had a slipping clutch for the cursors, as during a calculation the cursors have to be held in position relative to each other. With above design the DVD pivot holds the cursors firmly and the card is moved with respect to cursors avoiding need for a clutch. Scale detail shown right. These rules are capable of at least four significant figure results, i.e. equivalent to four figure log tables. OK, I'll get off my slide rule soapbox!

Question: What made the slide rule obsolete?
Answer: Calculators