In watchmaking, the term spring doesn't describe just one component: it describes at least three distinct families with different functions and physics. Confusing them is the first mistake I hear, even from people who've worn watches for years.
The mainspring is the energy source of the movement. It lives inside the barrel, coiled upon itself. When you wind it — by hand or through an automatic rotor — it accumulates elastic energy; when it unwinds, it delivers that energy to the barrel wheel and then to the train. The physical problem is that the torque delivered is not constant: it's high when fully wound, declining progressively. A three-meter mainspring like the one mounted in the Honoris barrel, machined directly from the plate, maintains relatively stable torque across almost the entire power reserve thanks to thirty turns. The historical solution to torque variation is the fusée-and-chain transmission, which compensates for decay by modulating the lever arm along a pulley with varying diameter. The constant force escapement solves the problem downstream, stabilizing the force right at the entry to the lever. The bridle is the device that limits tension at the end of winding: it prevents the spring from overloading and breaking.
The hairspring is something else entirely. It's the heart of the regulator: it controls the oscillation frequency of the balance wheel and therefore the watch's rate. The most common form is flat; the cylindrical hairspring is wound vertically rather than flat, guaranteeing greater concentricity and stability, but requiring machining times ten times longer — H. Moser sculpts it by hand in the HMC 811 caliber, with two Breguet curves included. Material makes a difference: traditional steel is sensitive to magnetism and thermal variations. Silicon is non-magnetic and thermally stable. Nivachron — an alloy developed by Nivarox — occupies a practical middle ground: more resistant than ordinary steel to magnetism and shocks, less brittle than silicon. The dual hairspring mounted in certain tourbillons, like the H. Moser Streamliner, adds a second spring that generates an equal and opposite force, reducing positional errors related to gravity.
Rate adjustment is achieved in two ways: by moving the regulator's index, which lengthens or shortens the active length of the spring, or — in free-sprung balance wheels — by modifying the balance's own inertia through adjustable screws or weights. The second method eliminates the regulator and the microplay it introduces, but requires disassembly for each adjustment: it's not suitable for all watches or all technicians.
There's also the spring as a structural element of the case: the super-compressor caseback exploits external pressure to further compress the seal, creating a hydraulic seal that increases with depth. It's a spring working in the literal sense, not as an energy reservoir.