Hello John,
My maiden last name is Syme and my parents were from Scotland (Glasgow area). My great grandfather's name was William Syme and my grandfather's name was Albert Baird Frew Syme. I have no information about whether or not there were siblings. My father's name was Albert Finlayson Syme.
I'm not sure if this could possibly be the same William Syme?
Best, Gillian