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The Collaborative International Dictionary
Morganatically

Morganatic \Mor`ga*nat"ic\, a. [LL. matrimonium ad morganaticam, fr. morganatica a morning gift, a kind of dowry paid on the morning before or after the marriage, fr. OHG. morgan morning, in morgangeba morning gift, G. morgengabe. See Morn.] Pertaining to, in the manner of, or designating, a kind of marriage, called also left-handed marriage, between a man of superior rank and a woman of inferior, in which it is stipulated that neither the latter nor her children shall enjoy the rank or inherit the possessions of her husband.
--Brande & C. -- Mor`ga*nat"ic*al*ly, adv.

Wiktionary
morganatically

adv. In a morganatic manner.