  Theoretical and experimental developments in the 1920s that accompanied the
birth of coincidence methods, as well as later crucial applications during the
1930s and 1940s are presented. In 1924 Walther Bothe and Hans Geiger applied a
coincidence method to the study of Compton scattering with Geiger needle
counters. Their experiment confirmed the existence of radiation quanta and
established the validity of conservation principles in elementary processes. At
the end of the 1920s, Bothe and Werner Kolh\"orster coupled the coincidence
technique with the new Geiger-M\"uller counter to study cosmic rays, marking
the start of cosmic-ray research as a branch of physics. The coincidence method
was further refined by Bruno Rossi, who developed a vacuum-tube device capable
of registering the simultaneous occurrence of electrical pulses from any number
of counters with a tenfold improvement in time resolution. The electronic
coincidence circuit bearing Rossi's name was instrumental in his research on
the corpuscular nature and the properties of cosmic radiation during the early
1930s, a period characterized by a lively debate between Millikan and followers
of the corpuscular interpretation. The Rossi coincidence circuit was also at
the core of the counter-controlled cloud chamber developed by Patrick Blackett
and Giuseppe Occhialini, and became one of the important ingredients of
particle and nuclear physics. During the late 1930s and 1940s, coincidences,
anti-coincidences and delayed coincidences played a crucial role in a series of
experiments on the decay of the muon, which inaugurated the current era of
particle physics.
  PACS numbers: 96.50.S-, 84.30.-r, 96.50.S-, 95.85.Ry, 29.40.-n, 13.35.Bv,
45.20.dh, 12.20.-m, 91.25.-r, 29.40.Cs, 13.20.-v, 14.60.Ef, 14.60.Cd, 78.70.Bj,
20.00.00, 95.00.00, 01.60.+q, 01.85.+f, 01.65.+g
