Slide Rule

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 a rotating bezel with a 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 is where the tradition comes from.

Not all manufacturers set up the scales in the same way. Hamilton, on the Khaki Aviation Converter, inverts the Navitimer's approach: it positions simple scales on the rotating bezel and complex ones on the fixed dial. The result is better readability, even though it requires a moment of adjustment for those coming from Breitling. The Gallet Excel-O-Graph follows similar logic: a rotating bezel functioning as a circular slide rule for operations on distance, speed, and fuel consumption, designed for aviation and navigation.

The typical calculations the slide rule permits: speed relative to distance covered, fuel consumption as a function of distance, conversions between imperial 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 detail that is not secondary, because continuous rotation without clicks allows more precise positioning than click-stop bezels.

There is also a specific variant for diving: the unidirectional bezel of diving watches with a no-decompression time scale. The principle is different — not logarithmic but linear — but the function is analogous: a passive and mechanical calculating instrument that requires no power and cannot fail from software issues.

A curiosity: the Juvenia Arithmo mounted a double-domed crystal — called a refrascope — that magnified the slide rule scales to improve readability. It worked, but it made the watch difficult to photograph without distortion. From the workbench, I have seen few examples in good condition: the double crystal tends to yellow and the cost of replacement 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 is a detail often lost in service: many original bezels have been replaced with examples lacking that marking, reducing the historical value and functionality of the instrument.