However , Frederick betrothed Elizabeth to Henry Julius , Duke of Brunswick . He promised the Scots instead that `` for the second ( daughter ) Anna , if the King did like her , he should have her . '' Scottish ambassadors had at first concentrated their suit on the oldest daughter , but Frederick betrothed Elizabeth to Henry Julius , Duke of Brunswick , promising the Scots instead that `` for the second ( daughter ) Anna , if the King did like her , he should have her . ''