'Bonaparte Crossing The Rhine was published in O'Neill's Music of Ireland in 1850 in the Marches and Miscellaneous section.'

To avoid further confusion, O'Neill's Music of Ireland was published in 1903. The 1850 refers to the number of tunes included in the collection and is used as a shorthand to distinguish it from the later collection of dance music which had the subtitle '1000 gems'. So you have O"Neill's 1850 (MoI) and O'Neill's 1000 (DmoI).