“What is a circular slide rule for, and how do you use it?”
The slide rule was once an indispensable tool in upper-level math classes, yet today it is largely unknown to most students – and to many watch enthusiasts as well. Even so, mechanical luxury watches with a slide rule function are still being made. And fans of Breitling watches in particular know full well the practical value a pilot's chronograph with a calculating function can offer in everyday life. In this article, we introduce slide rule watches and take a look at their history and how they work.
Wristwatches for calculating – popular for decades
Ever since wristwatches came into wider use around the time of World War I and, by the 1920s at the latest, began their triumphant march to replace the pocket watch, manufacturers have continually sought to increase their usefulness to the wearer through additional functions. One of the best-known results of this development is surely the chronograph, which lets you time specific intervals and is needed above all in sports, the military and science. And even though most watch owners probably use this function rather rarely in everyday life, chronographs – especially among men's watches – rank among the most popular models of all. Another useful complication of mechanical wristwatches, though less widespread by comparison, is a circular slide rule.
The first watches of this kind came onto the market only a few years after the first chronographs and were intended primarily for pilots and air navigators. The renowned Swiss luxury watch manufacture Breitling is one of the brands that specialized early on in developing and producing pilot's watches, and it remains one of the leading names in this segment to this day. No wonder, then, that Breitling's current collection still includes models with a slide rule function. Since the arrival of electronic calculators in the 1970s, which were quickly integrated into quartz watches and are now available on practically every cell phone, mechanical circular and linear slide rules have lost much of their importance. Yet they still offer a helpful alternative to electronic devices – especially since they need neither sunlight nor battery power.
How do circular and linear slide rules actually work?
For most people today, a calculator is the tool of choice when it comes to performing more elaborate calculations or sparing themselves complex mental arithmetic. But well into the 1970s, many people had no access to these electronic helpers. To simplify and speed up calculations, mechanical aids were used instead. For many decades, the slide rule – sometimes also called a slipstick – was part of the basic kit of engineers, scientists and upper-grade students. It is a so-called analog computer, meaning a calculating aid that works without any electronic components whatsoever. What exactly it can be used for depends on its design, particularly on the type and number of scales available.
Which calculations are possible
Slide rules are used primarily for multiplication and division. Depending on the design, they can also handle other operations such as squaring, extracting roots, logarithms, trigonometric calculations or parameterized conversions. The slide rule is based on the principle of graphically adding or subtracting specific lengths on logarithmic scales. These scales are located on both the fixed and the movable part of every slide rule. A variation on this principle is the circular slide rule, which differs only in that the scales are arranged in a circle rather than running side by side in a straight line.
Who invented it?
The essential groundwork for building and using slide rules was laid with the development of logarithms, above all by the Scottish mathematician John Napier and the Swiss watchmaker Jost Bürgi. Working independently of each other, both developed the first known systems for calculating logarithms. Napier's first publication on the subject appeared in 1614, and as early as 1624 Edmund Gunter (1581-1626), an English theologian and mathematician, published his thoughts on logarithmic numbers.
He developed a rod with a logarithmic scale on which lengths could be picked off with a pair of dividers, making it possible to perform multiplication and division.
This, however, still proved very laborious. All the more significant, then, was the idea presented in 1632 by the Englishman William Oughtred, who proposed using two congruent logarithmic scales, which could run either straight or in a circle. For this reason, Oughtred is regarded as the inventor of the slide rule and the circular slide rule in the true sense.
From the first prototypes …
In the first two centuries after their invention, slide rules were used relatively little, and their use in watches was still unthinkable. That changed only when James Watt rediscovered their potential toward the end of the 18th century, and as the Industrial Revolution and rapidly accelerating technical progress required more and more technical and scientific calculations. At first, the various slide rule models were usually made of wood, brass, bamboo or ivory; later, models made of aluminum, plastic and stainless steel prevailed. For calculations beyond multiplication and division, they were often fitted with additional scales. In some cases, individual slide rules even carried more than 30 scales.
… to the slide rule chronograph
The idea of combining a chronograph and a circular slide rule in a wristwatch arose in connection with the development of pilot's chronographs. In the pre-computer era, pilots and air navigators depended on being able to measure time reliably and perform certain calculations quickly and accurately, both when planning and preparing flights and when navigating en route. Slide rule watches offered several advantages here.
With this new development, only a single combination instrument had to be carried – one that could conveniently be worn on the wrist and was therefore always close at hand.
The Breitling Navitimer – the legendary pilot's chronograph with aviation slide rule
Breitling's Navitimer line is probably the best-known mechanical watch line with a slide rule function. Its series, which include the Navitimer 01, Navitimer 1884 and Navitimer World, among others, are today the favorite watch of many pilots and aviation fans. Breitling launched the first model as early as 1952. To this day, the slide rule scales are visible at first glance around the outer edge of the dial, giving these prestigious pilot's watches their distinctive “face.” The outer scale ring is adjusted by rotating the bezel, with the knurled edge making it easier to operate.
The Navitimer chronograph is based on a predecessor called the Breitling Chronomat, which the US Army Air Force officially adopted in 1942 as the standard chronograph for its pilots and which was already a slide rule chronograph. For the Navitimer pilot's watches, the bezel was made somewhat more complex. The refined pilot's chronograph now made it easy to calculate rates of climb or descent, average speeds and fuel consumption – and it still does so today, even though cockpit calculations are now almost exclusively done electronically.
In the aircraft, slide rule watches therefore serve pilots more as backup instruments. But even for those who are neither aviation nostalgics nor professional or hobby pilots, Breitling slide rule watches have a charm all their own. After all, they are also excellently suited to everyday calculations such as currency conversions and other rule-of-three problems. During a business negotiation, for example, you can quickly and discreetly work out certain figures – at least as a rough estimate – with a few seemingly playful movements on your watch, without frantically tapping away at a calculator or phone.
