Maybe I can help you.William was a name passed down from generation to generation in the Allardyce, Allerdice family.I show a William Allardyce born in 1818.His father was William Allardyce, fifth son of William Allardyce.But I have a feeling that your William's father was the brother of a William.Your William's father's name could be Joseph Allaryce. b. 1769;John Allardyce, b. 1772; Archibald Allardyce, b. 1773; or Samuel Allardyce, b. 1775.Please be aware that none of this is final, just suggestions so you might research further.It would be a big help if you had any historical data on your William.Good luck. Also, I have noticed that for no apparent reason several Allardyce's changed the spelling to Allerdice/Allerdyce, etc.