slider ruler

1622 – New Development for Slide Rule

Moving forward from Napier Rods and Napier’s contribution to calculating sticks based on the gelosia, or lattice, multiplication method. In 1620 Edmund Gunter of London makes a straight logarithmic scale and performs multiplication and division on it with the use of a set of dividers, or calipers. In about 1622 William Oughtred, an Anglican minister recognized as the inventor of the slide rule, placed two such scales side by side and slides them to read the distance relationships, thus multiplying and dividing directly. He also developed a circular slide rule.

Slide Rule Evolution

A lot of prominent historical figures contributed to the evolution of the slide rule:  In 1675 Sir Isaac Newton solved cubic equations using three parallel logarithmic scales and made the first suggestion toward the use of the cursor. In 1677, two years after Newton invents the cursor, Henry Coggeshall perfected the timber and carpenter’s rule. Fast-forward 200 hears, and in the beginning in 1683, Thomas Everard popularized the gauging rule, used to determine the content of ale, wine and spirits barrels and to calculate the excise tax thereon. This design, first created by William Oughtred in 1633, found it’s way well into the 19th century. In 1722 John Warner, a London instrument dealer, used square and cube scales. By 1790 James Boulton and James Watt modified slide rules to improve their accuracy and usefulness. By 1799 their Soho slide rule helped to usher in the Industrial Revolution. It facilitated the design and manufacture of the the steam engine. In 1815 Peter Roget  inventeda log log scale, which he uses to calculate roots and powers to any number or fraction thereof. In 1851 Amedee Mannheim standardized a set of four scales for the most common calculation problems. His design and use of a cursor hastened the eventual widespread acceptance. Early in the 19th century the first slide rules came into use in the United States. President Thomas Jefferson had one, and Joseph Priestley recognized their advantages in his chemistry work, which includes the discovery of oxygen.

The slide rule’s importance to the Industrial Revolution, and the impact of the Industrial Revolution upon the slide rule, are demonstrated by the proliferation of designs: over ninety (90) designs are recorded in the first 10 years of the 20th Century.

Cylindrical calculators with extra long logarithmic scales are invented by George Fuller of Ireland in 1878 and Edwin Thacher of New York in 1881. Production of Thacher’s calculator was taken over by a Hoboken, New Jersey instruments company, Keuffel and Esser, which had previously imported slide rules for sale. A revolutionary linear slide rule construction with scales on both front and back and with a cursor referring to all scales simultaneously is patented in 1891 by William Cox, an invention he calls the “duplex slide rule”.

Log scales in three sections – a shape most familiar to us today – appeared about 1901, enabling very accurate calculation of powers and roots to any number or fraction.

Before the advent of the pocket calculator, Slide Rule 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 around 1974 the electronic scientific calculator made it largely obsolete.

Basic Concept of the Slide Rule

Today’s programming would not be here in the stage it is in if not for the advancements in the calculation methods – and the Slide Rule should proudly take a bow. The slide rule, also known as a slipstick in United States is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction. In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers. These common operations can be difficult  and human error factor is much higher when calculation are done on paper or “in your head”.

Most slide rules 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. More elaborate slide rules allow complex calculations, such as multiplication, duvision, exponentials, square roots and powers, logarithms, and trigonometric functions to be 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.

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 (which can usually be pulled out, flipped over and reinserted for convenience), 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. Scales may be grouped in decades – numbers ranging from 1 to 10 (i.e. 10n to 10n+1). Thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.

The PhotoCalcul website has an interesting collection of images of various slide rules, as well as Eric’s Slide Rule site