NationMaster - Encyclopedia: Slide rule

The slide rule (often nicknamed a "slipstick"^[1]) is a mechanical analog computer, consisting of at least two finely divided scales (rules), most often a fixed outer pair and a movable inner one, with a sliding window called the cursor. The slide rule was used primarily for multiplication and division, and also for "scientific" functions such as roots, logs and trig, but does not generally perform addition or subtraction.^[2] Image File history File links Download high resolution version (1566x880, 588 KB) Summary w:Slide rule, Pickett model N902-T simplex trig. ... Image File history File links Download high resolution version (1566x880, 588 KB) Summary w:Slide rule, Pickett model N902-T simplex trig. ... A page from the Bombardiers Information File (BIF) that describes the components and controls of the Norden bombsight. ... A slide-rule cursor Slide rules use as a cursor a sliding glass or plastic plate etched or painted with a fine line for aligning to the different scales. ...

Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but in the early to mid 1970s the electronic scientific calculator made it largely obsolete and most suppliers exited the business. A calculator is a device for performing calculations. ... A basic arithmetic calculator. ...

Despite their similar appearance, a slide rule serves a purpose different from that of a standard ruler: a ruler measures physical distances and aids in drawing straight lines, while a slide rule performs mathematical operations by using distances on nonlinearly-divided scales. A variety of rulers A 2 metre carpenters rule Retractable flexible rule A ruler or rule is an instrument used in geometry, technical drawing and engineering/building to measure distances and/or to rule straight lines. ...

This is a scan of a Pickett pocket slide rule, done by me, Benjamin Crowell, in 2005. ...

Basic concepts

In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers, common operations that can be time-consuming and error-prone when done on paper. More complex slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions. Logarithms to various bases: is to base e, is to base 10, and is to base 1. ...

In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result.

The user determines the location of the decimal point in the result, based on mental estimation. Scientific notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule. Scientific notation, also known as standard form, is a notation for writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. ...

Even the most basic student slide rules have more than two scales. Most consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change. Cursor of a slide rule I made the photo myself and I copyright it under GNU General Public License. ... Cursor of a slide rule I made the photo myself and I copyright it under GNU General Public License. ...

Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip, still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales. It was invented by William Oughtred.

Operation

Multiplication

A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules

log(x y) = log(x) + log(y)

and

log(x / y) = log(x) - log(y)

. Moving the top scale to the right 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. Because

log(x) + log(y) = log(x y)

, this position on the bottom scale gives

x y

, the product of

x

and

y

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 2×7. 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 2×7, but instead we calculated 0.2×7=1.4. So the true answer is not 1.4 but 14.^[3]

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.^[4]

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 (e^x) 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: Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ... In mathematics, the common logarithm is the logarithm with base 10. ... The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2. ... The exponential function is one of the most important functions in mathematics. ... Pythagoras of Samos (Greek: ; between 580 and 572 BCâ€“between 500 and 490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism. ... In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. ...

When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... Image File history File links Scales on a K&E 4081-3 slide rule, photographed by Benjamin Crowell, 2005. ... Image File history File links Scales on a K&E 4081-3 slide rule (back), photographed by Benjamin Crowell, 2005. ...

Roots and powers

There are single-decade (C and D), double-decade (A and B), and three-decade (K) scales. To compute

x 2

, 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. For

x y

problems, you can use the LL series of scales. There are often several, but we only need worry about the one with x on it. First, you align the leftmost 1 on the C scale with x on the LL scale. Then, you find y on the C scale and go down to the LL scale with x on it. That scale will have your answer. If y is "off the scale," then you can find

x y / 2

and square it using the A and B scales as described above.

Trigonometry

The S, T, and ST scales are used for trig functions and multiples of trig functions, for angles in degrees.

For angles from around 5.7 up to 90 degrees, sines are found by comparing the S scale with C. 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 or, for angles greater than 45 degrees, CI. Common forms such as k*sin(x) can be read directly from x on the S scale to the result on the D scale, when the C-scale index is set at k. For angles below 5.7 degrees, sines, tangents, and radians are approximately equal, and are found on the ST or SRT (sines, radians, and tangents) scale, or simply divided by 57.3 degrees/radian. Inverse trigonometric functions are found by reversing the process. Some common angles, measured in radians. ...

Many slide rules had S, T, and ST scales marked with degrees and minutes. So-called decitrig models used decimal fractions of degrees instead.

Logarithms and exponentials

Base-10 logarithms and exponentials are found using the L scale, which is linear. Some slide rules have a Ln scale, which is for base e.

The Ln scale was invented by an 11th grade student, Stephen B. Cohen, in 1958. The original intent was to allow the user to select an exponent x (in the range 0 to 2.3) on the Ln scale and read e^x on the C (or D) scale and e^-x on the CI (or DI) scale. Pickett, Inc. was given exclusive rights to the scale. Later, the inventor created a set of "marks" on the Ln scale to extend the range beyond the 2.3 limit, but Pickett never incorporated these marks on any of its slide rules.

Addition and subtraction

Addition and subtraction can be performed directly on a slide rule using two different techniques. ^[5]

The first method to perform addition and subtraction on the C and D (or any comparable scales) requires converting the problem into one of division. For addition, the quotient of the two variables plus one times the divisor equals their sum:

For subtraction, the quotient of the two variables minus one times the divisor equals their difference:

The second method utilizes a sliding linear L scale available on some models. Addition and subtraction are performed by sliding the cursor left (for subtraction) or right (for addition) then returning the slide to 0 to read the result.

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. [1] This article is being considered for deletion in accordance with Wikipedias deletion policy. ...

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. Rounding to n significant figures is a form of rounding. ...

A number of tricks can be used to get more convenience. Trigonometric scales are sometimes dual-labeled, 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.

Specialized 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. Emerson Electric Company was established in 1890 in St. ... These water valves are operated by handles. ...

Circular slide rules

Circular slide rules come in two basic types, one with two cursors (left), and another with a movable disk and a single cursor (right). The dual cursor versions perform multiplication and division by maintaining a fixed angle between the cursors as they are rotated around the dial. The single cursor version operates more like the standard slide rule through the appropriate alignment of the scales. Image File history File links Download high-resolution version (1126x1101, 103 KB) Description: Pickett circular slide rule Source: Scanned image of my personal property Date: 20 November 2006 04:55 UTC Author: (Dick107) File links The following pages on the English Wikipedia link to this file (pages on other projects... Image File history File links Download high-resolution version (1126x1101, 103 KB) Description: Pickett circular slide rule Source: Scanned image of my personal property Date: 20 November 2006 04:55 UTC Author: (Dick107) File links The following pages on the English Wikipedia link to this file (pages on other projects... Coordinated Science Laboratory at the University of Illinois File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Coordinated Science Laboratory at the University of Illinois File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The International System of Units (symbol: SI) (for the French phrase Syst me International dUnit s) is the most widely used system of units. ... The Imperial units are an irregularly standardized system of units that have been used in the United Kingdom and its former colonies, including the Commonwealth countries. ... Image File history File links Breitling-Navitimer. ... Image File history File links Breitling-Navitimer. ... Breitling logo Breitling is a brand of Swiss watches from the Canton of Jura. ...

The basic advantage of a circular slide rule is that the longest dimension was reduced by a factor of about 3 (i.e. by π). For example, a 10 cm circular would have a maximum precision equal to a 30 cm ordinary slide rule. At least one circular rule sacrificed some of the scales usually found in slide rules in order to obtain additional resolution in multiplication and division. It was the 8 3/8" in diameter Atlas slide rule, apparently made by Gilson in 1931, and was of the two-cursor variety. It functioned through the use of a spiral C scale, which was claimed to be 50 feet long and readable to five significant figures.^[6] 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. However, for non-cyclical non-spiral scales such as S, T, and LL's, the scale length is shortened to make room for end margins. When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ...

Circular slide rules are mechanically more rugged and smoother-moving, but their scale alignment precision is sensitive to the centering of a central pivot; a minute 0.1 mm off-centre of the pivot can result in a 0.2 mm worst case alignment error. The pivot, however, does prevent scratching of the face and cursors. 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. The main disadvantages of circular slide rules are the difficulty in locating figures along a rotating disc, and limited number of scales. Most students learned slide rule use on the linear slide rules, and did not find reason 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. 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. The front of a metal E6B. An E6B flight computer commonly used by student pilots. ... Face The 1930s (years from 1930â€“1939) were described as an abrupt shift to more radical and conservative lifestyles, as countries were struggling to find a solution to the Great Depression, also known in Europe as the World Depression. ... Look up aircraft in Wiktionary, the free dictionary. ... For other uses, see Aviator (disambiguation). ... Dead reckoning (DR) is the process of estimating ones current position based upon a previously determined position, or fix, and advancing that position based upon measured velocity, time, heading, as well as the effect of currents or wind. ... A compass (or mariners compass) is a navigational instrument for finding directions on the Earth. ... The Global Positioning System (GPS) is the only fully functional Global Navigation Satellite System (GNSS). ... Dead reckoning (DR) is the process of estimating ones current position based upon a previously determined position, or fix, and advancing that position based upon measured velocity, time, heading, as well as the effect of currents or wind. ... The principles of air navigation are the same for all aircraft, big or small. ... This is a list of types of calculators, many of which are obsolete but hoarded by legions of admiring collectors. ... The front of a metal E6B. An E6B flight computer commonly used by student pilots. ...

In 1952, Swiss watch company Breitling introduced a pilot's wristwatch (above, left) 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. Breitling logo Breitling is a brand of Swiss watches from the Canton of Jura. ... This page is about timekeeping devices. ... This article contains information that has not been verified and thus might not be reliable. ... This page is a candidate to be moved to Wiktionary. ... A kilometer (Commonwealth spelling: kilometre), symbol: km is a unit of length in the metric system equal to 1,000 metres (from the Greek words Ï‡Î¯Î»Î¹Î± (khilia) = thousand and Î¼ÎÏ„ÏÎ¿ (metro) = count/measure). ... A nautical mile or sea mile is a unit of length. ... The gallon (abbreviation: gal) is a unit of volume. ... The litre or liter (see spelling differences) is a unit of volume. ...

Cylindrical slide rules

There are two main types of cylindrical slide rules: those with helical scales such as the Fuller and the Otis King, and those with bars, such as the Thacher and some Loga models. In either case, the advantage is a much longer scale, and hence potentially higher accuracy, than a straight or circular rule. Image File history File links Download high-resolution version (194x1552, 53 KB) Scan of Otis King model K, by Richard Francis Lyon (user:dicklyon), contributed to creative commons with attribution required: photo by Richard Lyon. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev... Image File history File links Download high-resolution version (194x1552, 53 KB) Scan of Otis King model K, by Richard Francis Lyon (user:dicklyon), contributed to creative commons with attribution required: photo by Richard Lyon. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev... Otis Kings patent calculator, model K; Photo by Richard Lyon. ...

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. An example of Mahogany The name mahogany is used when referring to numerous varieties of dark-colored wood, originally the wood of the species Swietenia mahagoni, known as West Indian or Cuban Mahogany. ... This article is about the box tree. ... The steel cable of a colliery winding tower. ...

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 [2], and probably only a little earlier in Germany. Scales were made of celluloid or plastic. Later slide rules were made of plastic, or aluminum painted with plastic. Later cursors were acrylics or polycarbonates sliding on Teflon bearings. Diversity Around 91 genera and 1,000 species Subtribes Arthrostylidiinae Arundinariinae Bambusinae Chusqueinae Guaduinae Melocanninae Nastinae Racemobambodinae Shibataeinae See the full Taxonomy of the Bambuseae. ... Celluloid is the name of a class of compounds created from nitrocellulose and camphor, plus dyes and other agents, generally regarded to be the first thermoplastic. ... Aluminum is a soft and lightweight metal with a dull silvery appearance, due to a thin layer of oxidation that forms quickly when it is exposed to air. ... The acryl group is one of the functional groups sorted in the chemical class of acryl where one of four hydrogen atoms in ethene is replaced with a different functional group. ... Polycarbonates are a particular group of thermoplastic polyesters. ... Teflon is polytetrafluoroethylene (PTFE), a polymer of fluorinated ethylene. ...

All premium slide rules had numbers and scales engraved, and then filled with paint or other resin. Painted or imprinted slide rules were viewed as inferior because the markings could wear off. Nevertheless, Pickett, probably America's most successful slide rule company, made all printed scales. 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. This article does not cite any references or sources. ...

History

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. The first description of this scale was published in Paris in 1624 by Edmund Wingate (c.1593 - 1656), an English Mathematician, in a book entitled “L'usage de la reigle de proportion en l'arithmetique & geometrie”. The book contains a double scale on one side of which is a logarithmic scale and on the other a tabular scale. 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 and the prior claims of Wingate. Oughtred's ideas were only made public in publications of his student William Forster in 1632 and 1653. Portrait of William Oughtred, from http://www-groups. ... Portrait of William Oughtred, from http://www-groups. ... William Oughtred William Oughtred (March 5, 1575 â€“ June 30, 1660) was an English mathematician. ... For other people with the same name, see John Napier (disambiguation). ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Edmund Gunter (1581 - December 10, 1626), English mathematician, of Welsh extraction, was born in Hertfordshire in 1581. ... William Oughtred William Oughtred (March 5, 1575 â€“ June 30, 1660) was an English mathematician. ... Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...

In 1677, Henry Coggeshall created a two-foot folding rule for timber measure, called the Coggeshall slide rule. His design and uses for the tool gave the slide rule purpose outside of mathematical inquiry. In measurement, the Coggeshall slide rule, also called a carpenters slide rule, was a slide rule designed by Henry Coggeshall in 1677 to facilitate measuring the dimensions, superficies, and solidity of timber. ...

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. Peter Mark Roget (January 18, 1779â€“September 12, 1869) studied medicine at the University of Edinburgh and became a distinguished physician and lexicographer. ...

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.^[7],^[8] Engineering is the design, analysis, and/or construction of works for practical purposes. ... The Keuffel and Esser Co. ...

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. Robert Hookes microscope (1665) - an engineered device used to study living systems. ...

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 aluminum 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. The E6-B Flight Computer, a circular sliderule with added features is still used today in aviation, particularly by student pilots. Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki TÅjÅ Casualties Military dead: 17,000,000 Civilian dead: 33,000... The United States Navy (USN) is the branch of the United States armed forces responsible for naval operations. ... Look up aircraft in Wiktionary, the free dictionary. ... The front of a metal E6B. An E6B flight computer commonly used by student pilots. ...

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. Aluminum Pickett-brand slide rules were carried on five Apollo space missions, including to the moon, according to advertising on Pickett's N600 slide rule boxes [3]. Image File history File links Slideruleinuse. ... Image File history File links Slideruleinuse. ... This does not cite any references or sources. ... The 1960s decade refers to the years from January 1, 1960 to December 31, 1969, inclusive. ... Stethoscope The stethoscope (Greek ÏƒÏ„Î·Î¸Î¿ÏƒÎºÏŒÏ€Î¹Î¿, of ÏƒÏ„Î®Î¸Î¿Ï‚, stÃ©thos - chest and ÏƒÎºÎ¿Ï€Î®, skopÃ© - examination) is an acoustic medical device for auscultation, or listening, to internal sounds in a human or animal body. ... Wernher von Braun stands at his desk in the Marshall Space Flight Center, Huntsville, Alabama in May 1964, with models of rockets developed and in progress. ... Pickett is a surname, and may refer to Albert J. Pickett Bill Pickett Blake Pickett Bobby Boris Pickett Byron Pickett Cindy Pickett Cody Pickett George Pickett, of Picketts Charge James Edward Pickett Lucy Weston Pickett Philip Pickett Ryan Pickett Tim Pickett Wilson Pickett See also Pickett County, Tennessee Fort... Project Apollo was a series of human spaceflight missions undertaken by the United States of America (NASA) using the Apollo spacecraft and Saturn launch vehicle, conducted during the years 1961 â€“ 1975. ...

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.

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. [4] Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximating products using formulas from trigonometry. ...

Decline

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. The DEC PDP-8 minicomputer was introduced in 1965. Image File history File links Download high-resolution version (640x1090, 1090 KB) [edit] Summary [edit] Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): TI-30 ... Image File history File links Download high-resolution version (640x1090, 1090 KB) [edit] Summary [edit] Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): TI-30 ... The tower of a personal computer. ... Fortran (previously FORTRAN[1]) is a general-purpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ... IBM redirects here. ... IBM 650 front panel, showing bi-quinary indicators IBM 650 front panel, rear view The IBM 650 was one of IBMâ€™s early computers, and the worldâ€™s first mass-produced computer. ... The IBM 1620 was announced by IBM on October 21, 1959 and marketed as an inexpensive scientific computer. It was withdrawn on November 19, 1970. ... IBM 1130 Console, restoration in progress. ... BASIC (Beginners All-purpose Symbolic Instruction Code) is a family of high-level programming languages. ... DEC, dec or Dec may refer to: December - a month of the year in the Gregorian Calendar Department of Environment and Conservation Digital Equipment Corporation - a computer and technology company, now part of HP Declination - a term from astronomy Diethylcarbamazine - a drug commonly used to treat infections by filarial parasites... A PDP-8 on display at the Smithsonians National Museum of American History in Washington, D.C.. This example is from the first generation of PDP-8s, built with discrete transistors and later known as the Straight 8. ...

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 solved. 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." Fortran (previously FORTRAN[1]) is a general-purpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ... Three textbooks. ... Numerical Integration with the Monte Carlo method: Nodes are random equally distributed. ...

Another step toward the replacement of slide rules with electronics was the development of electronic calculators for scientific and engineering use. The first included the Wang Laboratories LOCI-2, ^[9] introduced in 1965, which used logarithms for multiplication and division and the Hewlett-Packard HP-9100, introduced in 1968. ^[10] Some consider the HP-9100 the first true scientific calculator because it had trigonometric functions (sin, cos, tan) in addition to exponentials and logarithms. The HP-9100 used the CORDIC (coordinate rotation digital computer) algorithm, ^[11] which allows for calculation of trigonometric functions using only shift and add operations. This method facilitated the development of ever smaller scientific calculators. A calculator is a device for performing calculations. ... Wang logo circa 1976. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... The Hewlett-Packard Company (NYSE: HPQ), commonly known as HP, is a very large, global company headquartered in Palo Alto, California, United States. ... In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. ... CORDIC (digit-by-digit method, Volder`s algorithm) (for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. ...

The last nail in the coffin for the slide rule was the launch of pocket-sized scientific calculators, of which the 1972 Hewlett-Packard HP-35 was the first. Such calculators became known as "slide rule" calculators since they could perform most or all of the functions on a slide rule. At several hundred dollars, even this was considered expensive for most students. While professional slide rules could also be quite expensive, drug stores often sold basic plastic models for under $20 USD. But by 1975, basic four-function electronic calculators could be had for under $50. By 1976 the TI-30 offered a scientific calculator for under $25. After this time, the market for slide rules dried up quickly as small scientific calculators became affordable. Somewhat ironically, most advanced high school mathematics classes now require graphing calculators that cost nearly $100 by the late 1990s as mathematics reform sought to leverage technology. The Hewlett-Packard Company (NYSE: HPQ), commonly known as HP, is a very large, global company headquartered in Palo Alto, California, United States. ... An HP-35 calculator The HP-35 was Hewlett-Packards first pocket calculator and the worlds first scientific pocket calculator (a calculator with trigonometric and exponential functions). ... The United States dollar is the official currency of the United States. ... The original TI-30 The TI-30 is a scientific calculator introduced in 1977 and manufactured by Texas Instruments. ... A typical graphing calculator. ...

Advantages

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. Look up fallacy in Wiktionary, the free dictionary. ... This article or section does not cite its references or sources. ... Rounding to n significant figures is a form of rounding. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... Symbols representing a single Cell (top) and Battery (bottom), used in circuit diagrams. ...

Disadvantages

In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. ... The word resolution has several meanings, depending on context. ...

Finding and collecting slide rules

For 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. The Keuffel and Esser Co. ... Faber-Castell logo Faber-Castell erasers Faber-Castell is a German manufacturer of writing instruments, art supplies and slide rules, founded in 1761 in Nuremberg by Kaspar Faber. ...

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, made of celluloid, tend to break down chemically over time. Celluloid is the name of a class of compounds created from nitrocellulose and camphor, plus dyes and other agents, generally regarded to be the first thermoplastic. ...

In many cases, an economical method for obtaining a working slide rule is to buy more than one of the same model, and combine their parts.

References in popular culture

Original crew photo. ... The Hunt for Red October was a 1990 film based on the best-selling novel of the same name. ...

Notes

^ Lester V. Berrey and Melvin van den Bark (1953). American Thesaurus of Slang: A Complete Reference Book of Colloquial Speech. Crowell.
^ The Binary Slide Rule manufactured by Gilson in 1931 performed an addition and subtraction function limited to fractions. See, http://www.sphere.bc.ca/test/circular-man2.html, instruction manual pages 7 & 8. Retrieved March 14, 2007.
^ Resetting the slide is not the only way to handle multiplications that would result in off-scale results, such as 2×7; 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.
^ 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.
^ AntiQuark: Slide Rule Tricks
^ See, http://www.sphere.bc.ca/test/gilson/gilson-manual2.jpg. A photo can be seen at http://www.hpmuseum.org/srcirc.htm. An instruction manual for the unit marketed by Dietzgen can be found at http://www.sliderulemuseum.com/SR_Library_General.htm All retrieved March 14, 2007.
^ The Log-Log Duplex Decitrig Slide Rule No. 4081: A Manual, Keuffel & Esser, Kells, Kern, and Bland, 1943, p. 92.
^ The Polyphase Duplex Slide Rule, A Self-Teaching Manual, Breckenridge, 1922, p.20.
^ The Wang LOCI-2
^ The HP 9100 Project
^ J. E. Volder, "The Birth of CORDIC", J. VLSI Signal Processing 25, 101 (2000).

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