Trying to read place names

I think it’s probably Ballinvrinsig. Likely family in 1911 census:

http://www.census.nationalarchives.ie/pages/1911/Cork/Inishkenny/Ballinvrinsig/383211/

To add to the Post by Elwyn, it was the practice that the birth was notified by the midwife or some relative, to the local Registrar who would have been the local dispensary doctor.

Regards, 

The modern spelling is Ballinvarosig (spellings often change over time, but that might also be what those entries say).  You can see more info about it at this link:

https://www.townlands.ie/cork/kinalea/carrigaline/kilpatrick/ballinvaro…

There's an interactive map at that link showing the townland as just to the south of the town of Carrigaline (which is south of Cork city).  If you compare what that map shows with what Google Maps shows (if you search for Carrigaline), it looks as though there are only a half dozen homes left in the townland, so someone there or in Carrigaline could probably give you more info, if you plan to visit.

I am not sure what the town name is but at the top of the page I think Ballygarvan is identified. Ballygarvan is part of Ballinhassig Parish and south of Cork City. I could not find William's and Mary Bermingham's marriage record. I did find in the 1901 and 1911 censuses a William Murphy living with his family in Ballygarvan. In 1911 he was 21. He was a postman and his parents were James Murphy and Julie Horgan. Per Irishgenealogy, he was born in Ballygarvan on Nov 9, 1888. Ballygarvan borders on Ballycranig, maybe that is the name on Eileen's record??

Regards- Mary

The first reply is the correct place Ballinvrinsig  which is near Waterfall south of city. Ballinvrinsig townland is  situated between the Bandon road and Waterfall village.  

Sorry, I missed that one on the list.  Here's a link to the page about Ballinvrinsig:

https://www.townlands.ie/cork/cork/inishkenny/inishkenny/ballinvrinsig/

Based on Elwyn's 1911 census, per Irishgenealogy, Walter was born in 1904 (High St., Cork) and William in 1909 (93 High St., Cork)  I couldn't find Nora. 

Mary

Many thanks to everyone that answered my query it has been so helpful to me. Thanks again