Hi Kim,
I was at school with a Francis Patrick Hamilton between 1948-52 but his family lived in Co. Down. It looks as though your Samuel Francis lived in the Fermanagh and Tyrone area most of his life unless he returned to the area when he retired.
You asked for a fit in your first message. Sometimes you are lucky and find an immediate fit. Other times you have to keep posting messages on a regular basis so that people do not forget about you. This way they notice you have a keen interest in the subject and are making the effort. If you find a friendly person who posts a bit of useful information to you, no matter how small, you will find others tend to join in, do some searching for you and send some information. They are drawn to your posts because a friendly atmosphere is being created. I have looked at other boards where a message has been posted asking for information and two or three years may pass without a reply. Stark information with bare facts is OK but the more dressing up that is done to your posts the better, a bit of colour never does any harm and attracts people.
What religious persuasion was followed by your Hamilton family? I am guessing Presbyterian with a Scottish planters background.
As a matter of interest where are you located Kim?
Your thanks are appreciated but it is a pleasure to assist you in your search, Chris