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A brief history of the slide rule
The slide rule made possible to design the world before computers.
This is just a brief history of the slide rule, the full version can be freely downloaded. A simple tutorial is at the end of this page.
"Houston, Tranquility Base here. The Eagle has landed"
with these words Armstrong announced the landing on the Moon.
One of the on-board computers was a pocket slide rule, supplied to all the Apollo missions.
Invented in 1622 this tool came in space.
Pickett N600 ES sliderule, in use on the Apollo's missions
INTEL 4004 microprocessor was designed by Federico Faggin in 1971.
1971: Gilson slide rule and 4004 processor signed by Faggin
In 1971 the 4004 was mounted on a cumbersome Busicom calculator, but already the following year appeared the HP 35, the first portable scientific calculator. The era of slide rules was over, let's see it briefly.
The slide rule
In 1617 John Napier revolutionized mathematics by discovering logarithms. Complex calculations could finally be carried out relatively quickly.
In 1620 Edmund Gunter drew the logarithmic scale
placing the numbers on a ruler at a distance from the origin proportional to the value of their logarithm.
Particolare di un righello di Gunter, ca. 1790
This instrument remained in use until the early 1900s, despite the fact that the slide rule had already been invented in 1622.
In 1654, just few years after the invention of Oughtred, Robert Bissaker made the "Gauging Rule", with 4 slides, specialized in measuring the contents of the barrels of wine, beer or spirits and calculate the tax burden.
The Gauging Rule, half of the eighteenth century
In 1677 Henry Coggeshall created the "Carpenter's Rule", mounted on two wooden rulers with the gradation in inches, the central sliding scale in bronze and several other scales to solve various problems.
Carpenter's Rule, ca. 1840
At the beginning of 1700 there were slide rules specific to all the needs of the time.
Gauging Rule, ca. 1820
Towards mid-800, however, there was a pressing need for computational tools not only specialized in tax or workshop use.
Charpentier, ca. 1880, one of the first generic slide rule
The golden age
In 1859 the French artillery lieutenant Amedee Mannheim perfected the scales introducing the movable cursor. the modern model was born.
With the Mannheim model appears the cursor, ca. 1860
Around 1920 the slide rule had assumed its final form.
The model preferred by Einstein, ca. 1930
In order to improve accuracy, proportional to the length of the scales, where produced models very large, also circular or cylindrical.
Fowlers, ca. 1910
Large cylindrical slide rule, ca. 1936
The slide rule in the war
The modern slide rule was made by the French lieutenant Mannheim to maximize the range of his guns.
Slide Rule to measure the exposure to radiation and sniper model
Slide rules were used by gunners to solve the problems of the shooting triangle.
They were also used in meteorology to analyze the data provided by the sounding balloons.
Preparation of the meteorological bulletin
Launching torpedoes requires a lot of calculations. Italians and Germans used a simple circular slide rule, the American electro-mechanical models to automatically found the best shooting solution.
US automated sliderule and the simple European model
Modern bombing required perfect determination of targets, often nocturnal or obscured by clouds.
Tactical calculations during the Battle of Britain
The needs of air navigation also led to the E6B aeronautical sliderule.
This instrument proved immediately irreplaceable and lived a long career.
The first E6B, the progenitor of a series still on the market
The twilight of the analog era
The first computers appeared around 1946, but they were huge and expensive, the same IBM planned to sell up to four a year, and the slide rule seemed irreplaceable.
Nobody imagined a world without the sliderules: they served to housewives in the kitchen, to tracing the routes on the ship "Star Trek". Appeared on the cover of Playboy, were also proposed as cufflinks and tie clips.
"Miss Slide Rule", ca. 1950
Walt Disney had a simplified model for the children, was built in Braille for the blind, with scales dedicated to solving statistical problems and also in hexadecimal, octal or binary for computer programmers.
Hexadecimal model for computer programmers
It was the laptop of the era, always sticking out of engineers' pocket. A true sign to identify the category.
In 1955, after 9 years of tests, one of the most revolutionary aircraft in history was delivered: the Boeing B52 Stratofortess, a long-range nuclear bomber jet.
The B52 and the slide rule used by Boeing
Approximating calculations for excess created the myth of the "Olde Good Things", but the modern structural analysis required now exact results, thus promoting the development of electronic calculators.
The latest slide rules had more than 30 scales
To provide economical and precise tools, were designed slide rules that projected a virtual logarithmic scale several meters long.
Salmoiraghi projection slide rule, probably
In 1969 the sliderule was used on the Apollo 11 landing on the Moon: a very long career which began more than 350 years before.
From the seventeenth century to the Moon, a really long career
Finally in 1972 the Helwett Packard, advertising it as "Innovative electronic slide rule", put on sale the first economic scientific calculator, 50 times smaller than the competitors and so modern that it is still on the market.
From 1972 only electronic in space
The HP 35 uses the logical principle of Reverse Polish Notation (RPN), designed in the '20s by Jan Lukasiewicz, which allows to describe any formula without the use of parentheses.
Try the Java simulation of the HP35, ©Neil Fraser
Calculate the hypotenuse of a right triangle with legs of 3.4 and 4.3 cm
The RPN eliminate the problems due to parentheses and operator precedence (first division, then the addition etc..).
The slide rule today
But our "hero", reliable and environmentally friendly, it is always necessary to pilots and military and perhaps the adventure is not over yet.
First computers were not powerful, but able to replace 150
Logarithms and the basis of the slide rule
The mathematician John Napier discovered in 1614 the logarithms, published in "Mirifici logarithmorum canonis descriptio", capable of expressing any positive number via powers.
To multiply two numbers just look out for their logarithms and add them together: the result is the number whose logarithm correspond to the sum.
With logarithms we are unable to work quickly as the consultation of the tables is very laborious.
Now we can try to construct the scale: the 1 is the starting point, the 2 is located at 3.01 cm, the 3 to 4.77 and so on up to 10.
How far it is possible, for reasons of space, we now add the minor divisions (logs between 1 and 99).
Instead of search the logarithms in the tables we can simply add them with the help of a compass.
The sliderule, being an analog instrument, replace the mathematical functions with linear measurements. To show how it works let's start to see how we can execute an addition using two common metric rules.
To add 2+6 we don't need to move again the rule (set on 2+), but just read the sum directly on the figure 6 of the B rule. To subtract, we use the opposite proceeding.
From the accuracy of the construction depends the precision of the results but, also dividing further the scales, it is not possible to operate with numbers greater than 100.
To perform 2 x 4 we align the 1 of scale B in correspondence of 2 in scale A and the result can be read on the same scale above the 4 of scale B.
We now have a tool that can perform multiplication. The previous picture also shows how to perform 8/4. Just put the 4 of scale B under the 8 of scale A and read the result on the same scale above the 1 in scale B.
The sliderule allows quick calculations thanks to the ease of adding logarithms by sliding two logarithmic scales over each other, but the first models invented by Edmund Gunter in 1620 were not so practical.
There are also some disadvantages. If we want process 4x3 the slides are positioned as follows:
The total is now located out of the scale. To solve this problem, we need to use the 10 of the rule B, instead of the previous 1:
So we obtain 1.2, but the right total is 12: the slide rule gives only the numbers and how to locate the dot or how to add ten or hundreds we must find by ourselves.
This was just a brief outlook, but the slide rule has many other scales and can reach the computing power of a modern calculator. His only flaw is the poor readability. The secret is: practice, practice ...
Practice with this slide rule emulator
Sliderule on Wikipedia
1972 Pickett ad: 5 lunar missions!
© 2004 - 2023 Nicola Marras Manfredi