The mainspring is the energy reservoir of any mechanical watch: a piece of tempered steel ribbon coiled inside a barrel that stores torque during winding and releases it progressively to the gear train. From the bench, I've seen every type of failure, and most precision problems start here, not at the escapement.
The barrel is not merely a container. Its dimensions directly determine the length and thickness of the spring, and therefore the power reserve and torque curve. A 35 mm barrel with three meters of spring and thirty turns, like the one in the Honoris machined directly from the plate, delivers relatively stable torque throughout almost the entire reserve. A double barrel, on the other hand, sums the energies of two springs in parallel or in series: Grand Seiko's caliber 9SA5 reaches eighty hours while maintaining a thickness of just over five millimeters. More barrels also mean that torque peaks dampen, because each spring works over a more limited unwinding interval.
The central problem of the mainspring is nonlinearity: it delivers high torque when fully wound, declining torque as it nearly empties. This variation is transmitted to the balance wheel and reads as amplitude variation, then as rate variation. Historic manufacturers responded with the fusée-and-chain transmission: a chain connects the barrel to a conical pulley of variable diameter, mechanically compensating for the decay of torque. Berthoud marine chronometers and British naval instruments made it a standard. Today you find it on haute horlogerie pieces like the Tourbograph Perpetual by A. Lange & Söhne. The remontoire d'égalité and the constant-force escapement work on the same principle but downstream, uncoupling the escapement from direct transmission and metering uniform impulses to the anchor at fixed intervals.
The stop-works mechanism, often a Maltese cross, cuts off the extremes of the curve instead: it blocks the last quarter and first quarter of unwinding, where torque is respectively too high or too low. You lose nominal reserve, but gain in effective linearity. The power reserve indicator shows where you are on this curve: a useful tool not just for convenience, but for understanding in which torque zone the movement operates at any given moment. The 2002 Royal Oak Concept Dymograph took this concept further, displaying the spring's instantaneous torque directly. Seiko's Spring Drive technology solves the problem another way: it uses a traditional mainspring but regulates the release with a batteryless electromagnetic brake, achieving one second per day on a constant basis. I don't know whether this solution will find widespread heirs outside Seiko.