The balance spring

A balance spring, or hairspring, is a fine coiled spring fixed to the balance wheel. It pulls the balance back each time it swings out, so the balance oscillates at its own steady rate and controls the speed of the whole watch.^1, 2

Huygens's 1675 description: a spiral fixed at the centre to the balance arbor and at its outer end to the watch plate, whose coils alternately close and open as the balance swings.^2, 6

The idea was claimed by Huygens, Hooke, Hautefeuille and Thuret; which of them came first is still disputed.^1, 3, 7

Wikipedia's articles even disagree on the date: 'around 1657' and 1658 in some, the mid-1670s in others, with Hautefeuille and Huygens shaping the spiral in 1674 in one.^1, 8

Early balance springs had few turns: an early Tompion quarter-repeating movement in the Clockmakers’ Museum has a spring of five turns.^1, 9, 10

A regulator alters the working length of the spring to make the watch gain or lose. The rack-and-pinion type was long called the Tompion regulator; the lever type now used was patented by Joseph Bosley in 1755 but did not displace it until the early 1800s.^1, 11

A spring that kept equal time however wide the swing would make the watch independent of the mainspring's pull. Huygens hoped his spiral would do this; with the verge escapement of his day it could not.^11, 12

Warmth weakens a steel spring, so watches lost time in heat. Wikipedia records that Ferdinand Berthoud measured in 1773 that a brass balance with a steel spring lost 393 seconds a day for a rise of 60°F, 312 of them from the spring.⁸

Harrison's compensation curb, a bimetallic strip, altered the working length of the spring as the temperature changed; Mudge used a second hairspring as a curb in a watch of 1755.^1, 4, 13

The compensation balance of Pierre Le Roy, perfected by Earnshaw, put the correction in the balance rim instead and became the standard.^1, 4, 14

Makers learned to shape the spring for even timekeeping: John Arnold patented a helical spring with incurved ends in 1776, and Breguet's overcoil, which lifts the outer coil above the rest, became the common method.^1, 15

Wikipedia says early springs were of soft steel, which weakened, and that Harrison used hardened and tempered steel, which remained standard until the twentieth century.¹

Charles-Édouard Guillaume's Elinvar alloy, from about 1900, kept its elasticity with temperature and made compensation balances unnecessary; silicon springs followed in recent decades.^1, 8