There is one in every research project, the man with the common name who disappears in the records.
In the Madden genealogy that man is Michael Murphy. Michael was supposedly born in Ireland to James Murphy and Mary Brien about 1833.
No record of that birth has been found. One possibility is a christening record for Michael Murphy, the son of Edanus Murphy and Mary Brien. He was born 21 Apr 1833 and christened the next day in the parish of Ballycullane (Tinturn), Wexford. This is in the diocese of Ferns.
Edanus is considered a latin form of Aidan, a diminutive form of Aodh. The name means "fire" and is sometimes anglicized as Hugh ... not James.
Could it be the right record? Michael Murphy is such a common name, but it is the right year and the right mother.
Another possibility is Michael Murphy the son of Cons Murphy and Mary Brien baptised 29 Dec 1833 in Rosnacaharach, Muintervarra, Cork.
There are others, but I have not found one with James Murphy and Mary Brien and birth dates get further from an age of 28 which he gave when he married.. In fact the only mention of his parents names is the marriage record of Michael and Bridget.
I have not been able to find the family of Michael in Canada. I believe I have found him as a servant age 25 in the 1861 census in Stratford, but with no other names to check, this it might not be him. The record of his marriage just a few weeks later says that he lives in Stratford. The census would put his birth in 1835/6 but 25 is one of those nice round ages that an employer might give. Like many Irish his age is inconsistent in nearly every record.
It is my hope that some record might miraculously appear and give a few more clues.