The index maintained by rootsireland.ie that indexes baptisms has James Parker's parents as Patrick Parker and Mary Murphy. However, the copy of the register at the National Library of Ireland has his parents listed as ____ Parker and Mary Murphy, with a blank space for the father's given name.
My hypothesis is that the both the rootsireland.ie index and the microfilmed register at the National Library of Ireland are transcriptions (of different sorts) of the original register at Tubberclaire parish.