As you will have gathered, this is the hairspring: a tiny spiral spring, as fine as a hair, whose beats keep a watch running steadily. The celebrated hairspring is a true Archimedean spiral, coiled in the horizontal plane into 12 to 15 equally spaced turns about 0.03 mm thick. Coupled to the balance wheel, the spring turns first one way, then the other: it oscillates about its equilibrium position. The regularity of this "breathing"—in other words, the isochronism of its oscillations—allows the passage of time to be measured precisely and reliably (see Tangente 179).
A watch hairspring