At the close of “Home Again” (For All Mankind, S1E6), NASA engineer Margo Madison gifts the precocious daughter of a NASA janitor, Aleida Rosales, with a slide rule. It’s a personal moment that highlights the awe I feel for the engineers who sent men into space and to the moon using 350-year-old technology.
Those NASA engineers (and astronauts) joined a distinguished group of inventors such as Sir Isaac Newton, James Watts, Thomas Jefferson and Albert Einstein. All used slide rules, a tool integral to “nearly every invention, every design of a historic structure and in every significant scientific development for nearly 350 years.”
Slide rules, analog computing devices, made complex math easier to compute. They may have basic arithmetic operations (addition, subtraction, multiplication, and division) or they might have scales for logarithms, square and cube roots, exponents or trigonometric functions. Align the slide to make your computation.
Slide rules were the principal technology for making mathematical calculations from the late 1800s to until 1972. Electricians, engineers, navigators, scientists and math students used them regularly.
According to Larry Mullins, a NASA aerospace engineer, there were rooms were full of human calculators in the 1960s space era. It might take three months to calculate a launch trajectory. Today a (digital) computer can calculate that trajectory in a blink.
An early 17th century technology
But first, the log scale. 1614.
Scottish mathematician and astronomer John Napier is credited with discovering the logarithm, “which allows transforming complicated multiplications and divisions into simple additions and subtractions.” He published A Description of the Wonderful Table of Logarithms in 1614, setting the stage for the analog computer known as the slide rule.
In about 1622, William Oughtred invented the slide rule “in its present form.” The Anglican minister used it for multiplication and division. Newton used three parallel logarithmic scales in 1675 to solve cubic equations.
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. From 1625 to 1800, the first 175 years after its invention, a total of 40 slide rule types, including circular and spiral designs, are recorded. The next 100 years, from 1800 to 1899, saw the creation of 250 slide rule types and manufacturers. Over 90 designs are recorded in the first 10 years of the 20th century.
World War II spurred development of large scale computers. In the December 1951 of Fortune, IBM ran this ad for the IBM 604 Electronic Calculating Punch which it developed in 1948: the machine was like adding 150 engineers with slide rules!
Enter the electronic calculator
In 1972, Hewlett-Packard challenged the slide rule when it introduced the HP-35.
When an engineer or a scientist needs a quick answer to a problem that requires multiplication, division, or transcendental functions, he usually reaches for his ever-present slide rule. Before long, however, that faithful ‘slip stick’ may find itself retired. There’s now an electronic pocket calculator that produces those answers more easily, more quickly, and much more accurately.
It was the “world’s first scientific pocket calculator.” Unlike other personal calculators of the time, it could perform trigonometric and exponential functions. It was also costly at $395 ($2,775 in 2022 dollars). But it brought the slide rule era to an end.
Keuffel & Esser (K&E) Corp. produced its last slide rule, which it presented to the Smithsonian, on 11 July 1976.