Slide rule





The slide rule is a mechanical precursor of the pocket calculator. It was
invented in 1625 by William Oughtred.

Once widely used for rapid, approximate scientific and engineering
calculations, a slide rule is an analog computer consisting of three
interlocking calibrated strips. The central strip can be moved lengthways
relative to the other two. A sliding cursor with an alignment line can
record an intermediate result on any of the scales.

One slide rule remains in daily use around the world, the E-6B. This is a
circular slide rule first created in the 1930s for pilots to help with
dead-reckoning. It is still available in all flight shops, and remains
widely used. While GPS has greatly reduced the use of dead-reckoning for
aerial navigation, the E-6B remains widely used as a backup device and all
flight schools demand its use.

Theory of operation

Slide rules calibrated on one side were called "simplex." Slide rules
calibrated on both sides were called "duplex."

Typically two significant figures of precision were possible, with three
being obtained by expert users who could estimate the fraction between
gradations. Some high-end slide rules had magnifying cursors that basically
doubled the accuracy, permitting a 10 inch slide rule to serve as well as a
20 inch.

Slide rules often have other mathematical functions encoded on other
auxiliary scales. The most popular were trigonometric, usually sine and
tangent, logarithm of logarithm (base 10) (for taking the log of a value on
a multiplier scale), natural logarithm and exponential scales. Some rules
included a pythagorean scale, to figure sides of traiangles, and a scale to
figure circles.

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.

A number of tricks were used to get more convenience. Trigonometric scales
were sometimes dual-labelled, in black and red, with complementary angles,
the so-called "Darmstadt" style. Duplex slide rules often duplicated basic
scales on the back. Scales were often "split" to get higher accuracy.

Circular slide rules had two basic types, one with two cursors, and another
with a moveable 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 π). For example, a 10cm
circular would have a maximum accuracy equal to a 30cm ordinary slide rule.

Circular slide rules were mechanically more rugged, smoother-moving and more
precise than linear slide rules, because they depended on a single central
bearing. The central pivot did not usually fall apart. The pivot also
prevented scratching of the face and cursors. Only the most expensive linear
slide rules had these features.

The highest accuracy scales were placed on the outer rings. Rather than
"split" scales, high-end circular rules used helical (snail-shell-shaped)
scales for difficult things like log-of-log scales. One eight-inch premium
circular rule had a 50 inch helical log-log scale!

Circular slide rules also eliminate "off-scale" calculations, because the
scales were designed to "wrap around."

A real disadvantage of circular slide rules is that less-important scales
are closer to the center, and have lower accuracies.

The main disadvantage of circular slide rules was just that they were not
standard. Most students learned on the linear slide rules, and never
switched.

Materials

The best older slide rules were made of bamboo, which is dimensionally
stable, strong and naturally self-lubricating. They used scales of celluloid
or plastic. Some were made of mahogany. Later slide rules were made of
plastic, or aluminum painted with plastic.

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.

Early cursors were metal frames holding glass. Later cursors were acrylics
or polycarbonates sliding on teflon bearings.

Magnifying cursors can both help engineers with bad eyes, and double the
accuracy of a slide rule.

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 light scrubbing
with steel-wool. For painted slide rules, and the faint of heart, use
diluted commercial window-cleaning fluid and a soft cloth.

History

Slide rules came into wide use in the 1850s, as engineering became a
recognized professional activity.

In World War II, bombardiers, navigators, and other warriors 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.

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. Some engineering students and engineers actually carried
5 inch pocket slide rules in their belts, in addition to using a 10 or
20Êinch rule for precision work at home or at the office. All this came to
an end in the 1970s, when the advent of miniaturised scientific calculators
made slide rules obsolete.

Most slide rules are now collectors' items. A very popular model is the
Keuffel & Esser Deci-Lon, a premium scientific & engineering slide rule,
available in tenÊinch "regular" and fiveÊinch "pocket" variants. Another
prized model is the eightÊinch Scientific Instruments circular slide rule.
At the turn of the millennium, the collectors' market still doesn't seem to
be drying up, and as recently as 2002, new slide rules were being located in
the back-shelves of university book-stores, even though production ended in 1973.