The slide rule integrated into a watch is not an ornament: it is a functioning analog instrument, based on the same physical-mathematical principle as the linear slide rule. The scales are logarithmic, which means the physical distances between numbers are not uniform — and precisely for this reason multiplications, divisions, and conversions become operations of visual alignment, not mental calculation.
The most common form is the rotating bezel with logarithmic scale opposed to a fixed scale on the dial. By rotating the outer ring you align values on the two scales and read the result at a third point. This is exactly the principle of the E6B flight computer, developed in the 1930s and remaining in operational use for decades. The Breitling Navitimer adopted it in 1952, bringing it to the wrists of AOPA pilots. That's where the tradition comes from.
Not all manufacturers set the scales the same way. Hamilton, on the Khaki Aviation Converter, inverts the Navitimer approach: it positions simple scales on the rotating bezel and complex ones on the fixed dial. The result is better readability, though it requires a moment of adjustment for those coming from Breitling. The Gallet Excel-O-Graph follows similar logic: rotating bezel as a circular slide rule for operations on distances, speeds, and fuel consumption, designed for aviation and navigation.
Typical calculations the slide rule enables: speed versus distance traveled, fuel consumption as a function of distance, conversions between Anglo-Saxon and metric units — feet/meters, gallons/liters, nautical miles/kilometers. On the Sinn 903 St the logarithmic scale is integrated into the bidirectional continuously rotating bezel: a technical detail that matters, because continuous rotation without clicks allows more precise positioning than click-stop bezels.
There is then a specific variant for diving: the unidirectional bezel of diving watches with no-decompression time scale. The principle is different — linear rather than logarithmic — but the function is analogous: a passive, mechanical calculation instrument that requires no power and cannot fail due to software.
Fun fact: the Juvenia Arithmo mounted a double-domed crystal — called a refrascope — that magnified the slide rule scales to improve readability. It worked, but made the watch difficult to photograph without distortion. From the bench I've seen few specimens in good condition: the double crystal tends to yellow and replacement cost is prohibitive.
On a vintage Navitimer, the reference to the boxed 10 — the number 10 surrounded by a red box on the bezel — serves as an anchor point for calculations. It's a detail often lost during overhauls: many original bezels have been replaced with specimens lacking that marking, reducing both the historical value and functionality of the instrument.