Measurement methods for determining the critical current of ionisation waves in gas discharge tubes are examined in detail. The conventional visual method which finds the current at which the waves disappear is erroneous since the criterion, 'observable', depends on the observing conditions. In the rigorous method it is defined as a current at which the linear growth rate of waves is zero. For the measured upper critical (Pupp) current of argon gas, close agreement is found between Cooper and Oleson (1961), Venzke (1970), Wojaczek (1971) and the present author over a wide range of pressure-radius product 0.3 approximately 60 Torr cm.