Green’s Dictionary of Slang

dignity.

1871		L.H. Bagg Four Years at Yale 44: Dig, [...] an abbreviation for dignity.
1906		Sun. Times (Perth) 18 Feb. 4/7: I ’ad a nappointment with me girl. Jim coulder come too [...] But ’e stood on ’is dig.
1909		J. Ware Passing Eng. of the Victorian Era 109/1: Dig (Mid. Class, Elegant). Abbreviation of ‘dignity’; e.g., ‘So I stood upon my dig, and told him his room was nicer than his company.’ Sometimes ‘otium dig’ (from ‘otium cum dignitate’; e.g., ‘Come and see me in my summer-house; there I am in my otium dig.’.
1915		Bulletin (Sydney) 5 Aug. 47/2: ‘That’s no way fer a gentleman ter speak ter a lady,’ says May, on ’er dig. at once.