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The Collaborative International Dictionary
To go across the country

Across \A*cross"\ (#; 115), prep. [Pref. a- + cross: cf. F. en croix. See Cross, n.] From side to side; athwart; crosswise, or in a direction opposed to the length; quite over; as, a bridge laid across a river.
--Dryden.

To come across, to come upon or meet incidentally.
--Freeman.

To go across the country, to go by a direct course across a region without following the roads.