Longitudinal development of muons in large air showers studies from the arrival time distributions measured at 900m above sea level

The arrival time distributions of muons with energies above 1.0GeV and 0.5GeV have been measured in the Akeno air-shower array to study the longitudinal development of muons in air showers with primary energies in the range 10 to the 17th power to 10 to the 18th power ev. The average rise times of muons with energies above 1.0GeV at large core distances are consistent with those expected from very high multiplicity models and, on the contrary, with those expected from the low multiplicity models at small core distances. This implies that the longitudinal development at atmospheric depth smaller than 500 cm square is very fast and that at larger atmospheric depths is rather slow.