The word 'steadily-running' is a compound formed from 'steadily' (from 'steady' + '-ly') and 'running' (present participle of 'run'). 'Steadily' comes from Old English 'stede' meaning 'place' or 'firmness', and 'running' from Old English 'rinnan' meaning 'to flow' or 'to run'.

'Steadily' evolved from Old English 'stede' to Middle English 'stedi', and 'running' from Old English 'rinnan' to Middle English 'rennen', eventually forming the modern English words. The compound 'steadily-running' is a modern formation.

Initially, the components meant 'in a firm manner' and 'moving quickly on foot', but together as 'steadily-running', it now means 'operating or moving in a continuous, stable way'.