The Breguet invention patented in 1801 that uses a rotating cage to reduce positional errors is the tourbillon.
Abraham-Louis Breguet developed the tourbillon for pocket watches, whose stationary positions could cause gravity-related timing differences. The escapement and balance are mounted inside a rotating cage, traditionally completing one revolution per minute, so positional errors are distributed over time.
Breguet received the French patent on 26 June 1801, although the invention took years to develop and commercialise. The mechanism was especially relevant to pocket watches because they were commonly carried in a vertical position.
A tourbillon does not automatically make every watch more accurate than every non-tourbillon watch. Modern manufacturing, regulation, and wearing patterns also affect precision. The mechanism is now valued both for its horological purpose and for its visible mechanical artistry.