In watchmaking, a differential is a gear — or a system of gears — that receives energy or information from two sources and calculates their average, or that distributes a single impulse toward two destinations. It is not a single concept: there are at least three distinct families, and confusing them leads to evaluation errors.
The first family is that of differentials for dual oscillators. Philippe Dufour codified it in the Duality with a central differential that coordinates two independent balance wheels; François-Paul Journé adopted the same principle in the Chronomètre Résonnance. Greubel Forsey employs in the Double Balancier a spherical differential that averages the rates of two oscillators tilted at 20°, theoretically halving the error margin on frequency. Ulysse Nardin in caliber UN-251 uses a patented vertical differential — claimed to be the world's smallest — on ball bearings, which harmonizes two inclined silicon balance wheels. The fundamental distinction from resonance: in the differential the two oscillators remain independent and their average is calculated mechanically; in resonance they synchronize through physical proximity, without intermediary gears.
The second family is that of differentials for winding and transmission. Bovet has patented a three-dimensional spherical differential that duplicates every winding action on the crown, reducing the number of rotations needed to accumulate ten days of power reserve and protecting the train. Ferdinand Berthoud uses a differential mechanism that separates the winding path from transmission to the mainspring, allowing continuous running during manual winding. Hamilton, on a much smaller scale, adopts a friction-controlled differential in the power reserve indicator of the Khaki Field Mechanical, with a slip spring that synchronizes the hand during winding.
The third family is that of differentials for display and distribution. Vacheron Constantin's Twin Beat uses a differential to transmit to the hands the correct speed depending on the active train — 5 Hz or 1.2 Hz — without the perpetual calendar losing count. The Big Bang Meca-10 employs two opposed discs connected by a spiral spring for a power reserve display. The Winnerl Heart Return activates its own reserve in discrete steps every seven hours through a differential with a finger on the dial side.
A point I often see overlooked: the position of the differential in the train matters as much as its presence. If it averages rates at the center wheel rather than the seconds wheel, the precision benefits are noticeably reduced. David Candaux in the DC12 MaveriK solves this with a flying planetary differential mounted on a spring, integrated with a damping spiral that absorbs disturbances when the two balance wheels require energy simultaneously.