From the details you mentioned, this looks like his birth on the SP index:
PATRICK MULHERN
1910
501/ 446
Old or West Kilpatrick
I think they are still in Scotland for the 1911 census. Just from the index, you need to check the original on SP, this looks like the family at Old or West Kilpatrick area:
Arthur 34
Annie 28
Patrick 2
John 1
Monica