Sons of Elias Emigh from Dutchess County New York migrated to Crawford County in western Pennsylvania
The Eighmy brothers (note spelling change) Peter, Isaac, Clark and Stephen all went west from New York to Crawford County, Pennsylvania. Clark's son Charles B. Eighmy (b. 1829-d. 1863) was born in New York, so the migration to Crawford County, Pennsylvania must have occurred after 1829.
Try Googleing Eighmy, History of Crawford County, Pa., and Eighmy, Springboro, Pa.
If this sounds like your family let me know and I'll provide family details.