4. ruleth—Greek, "presiding over."
his own house—children and servants, as contrasted with "the church" (house) of God (1Ti 3:5, 15) which he may be called on to preside over.
having his children—rather as Greek, "having children (who are) in subjection" (Tit 1:6).
gravity—propriety: reverent modesty on the part of the children [Alford]. The fact that he has children who are in subjection to him in all gravity, is the recommendation in his favor as one likely to rule well the Church.