The tourbillon

A tourbillon carries the balance and escapement in a cage that turns continuously, so that the errors a watch makes in each vertical position are averaged out.^1, 2

It was meant for the pocket watch, which hung upright in a waistcoat for most of the day, where gravity distorted the hairspring's behaviour.^1, 2

Breguet’s history records that the patent of 26 June 1801 ran for ten years.¹

Wikipedia says the idea was conceived by John Arnold and developed by Breguet; Breguet himself gave Arnold's son in 1808 an early Arnold chronometer rebuilt with a tourbillon, its plate calling it his first tourbillon regulator joined to one of Arnold's first works.^2, 4

Breguet's own records count 35 tourbillons sold between 1805 and 1823, with two experimental pieces before.¹

Breguet says that at the 1806 national exhibition it was described as keeping the same rate whatever the watch’s position.¹

Wikipedia counts fewer than a thousand made between 1801 and 1945, many for observatory chronometer trials.²

Wikipedia says the first wristwatch tourbillons appeared in the mid-twentieth century, in small numbers, from Patek Philippe, Lip and Omega.²

Wikipedia credits Audemars Piguet’s calibre 2870 of 1986, an automatic tourbillon wristwatch, with starting the modern revival.²

Wikipedia lists the variants that followed: double-axis (Anthony Randall, 1977), flying tourbillons supported from one side only (Alfred Helwig, 1920) and multi-axis designs since the 2000s.²

Does it help?

Wikipedia notes that whether a tourbillon ever made watches more accurate is debated among horologists; a modern wristwatch, which changes position constantly, does not need one to keep good time, and it is valued chiefly as a display of skill.²