influence (n) : the act or power of producing an effect without apparent exertion of force or direct exercise of command
[Late Middle English: from Old French, or from medieval Latin influentia ‘inflow,’ from Latin influere, from in- ‘into’ + fluere ‘to flow.’ The sense ‘imperceptible or indirect action exerted to cause changes’ was established in Scholastic Latin by the 13th century, but not recorded in English until the late 16th cent.]