Hi Again
I see Henry Joseph registerd in the civil registry for Dublin South, Rathmines, 21 Leinster Road West, mother Kelly born 1st March 1901 and Mary Josephine Booth mother Josephine Kelly born 4th October 1908. Same address. See the father is called Hamilton, this surname is associated with Balrothery and Balbriggan if there is some connection. his occupation is given however as a solicitors, the census of Ireland for 1901 and 1911 are free to view online, default is 1911. The family are there in 1901, Hamiltons age is transcribed as 57 but looking at the form it is 37, she is 27 and they have a servant, his birth county is given as Kings County which is now Offaly, he died in 1911 in February at 33 Buckingham Street, from the 1911 census taken after hsi death they are living here, this suggests the family fortunes suffered, although she appears to be living with her sister also widowed. Buckingham Street would not have been the best area at the time I think, edges of a red light area, famed in story and song, If you are so inclined you can look up the area known as the Monto, large Wikipedia entry so possibly this is why if the chance offered they were off.
The census is here http://www.census.nationalarchives.ie/search/ search under Hamilton Booth for 1901 and Josephine Booth for 1911, both in Dublin. He was Church of Ireland (Protestant) she was a Catholic.
I assume these are your people who it appears to me have suffered both a loss of work and residence, it appears he had acute pneumonia in his R. and not sure of word, could be lobe, so right lobe.
This appears to me to be the correct family, his been Cof I and from Kings county is interesting if you wanted to find his birth on Irish Genealogy use, he is born in 1864 in Parsonstown registry district, south Offally main town Birr, his father was a clergy man so another reason she went to Chile, the mothers name I cannot make out other than Christian name, you could of course search for siblings and see if the writing is any clearer, father is Thomas, Birr is famous for its castle and telescope if you are of a mind to look it up, also the church of Ireland library will have info on the father and I have always found them helpful, come back if you want the link.
A great aunt of mine married a Booth man in Leitrim, he was a widower with children when she married him, no more children tohugh.
Regards and hope I have not confused the issue,
Pat