Hi there,
These are both unusual surnames here. I did a quick check on the Irish Times ancestor page to see where these names might have been found (if at all) and what other variant spellings there might be (mid-19th century). There were no Hearsts here, however, there were Hersts, and guess where they were found? Yes... Monaghan! I also checked Purdy, which is also less common here. When I checked for the two names, the place where both names were found was... Monaghan! You can look at this here: http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&UserID= and here http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Surname2&UserID=
It is more difficult to find information without a more precise place of origin. There are a number of places where you can start your research:
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at. Tithe Applotment Books (1823-38). Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS).
You could check for Robert Hearst in the UK National Archives here: http://www.nationalarchives.gov.uk/
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Sinead Cooney
Genealogist (Ireland XO)