Thanks for your reply. Unfortunately I don't have much more info than I have already posted on the forum:
My g-grandfather George Acheson (b. 1847 Tyrone - father Charles) emigrated to Australia. His home in Rockhampton, Queensland was called "Gosford". Siblings in Ireland may have been Jane, Andrew, Charles, John, Joseph, Margaret and Ann. I believe at least two of the brothers moved to the US - one to the East Coast and one to the West. John Acheson - I think - lived in California and lost his house in the great earthquake.