My Great Grandfather was William Doherty from Cloone, Co. Leitrim (born 1855). He joined the RIC so he was posted to Cork, which is where died in 1926. His father was Peter Doherty and we believe his father was Michael. Peter was born about 1817.
It appears that there were 2 separate Doherty families who came down from Donegal, and while they are related it goes way further back to their "link up" point (joint ancestor).