BAC3 has carried out a lot of research on the Parkhurst boys.see https://www.rootschat.com/forum/index.php?topic=884524.msg7574951#msg7574951
https://www.ancestry.com.au/search/collections/8812New South Wales, Australia, Hospital & Asylum Records, 1840-1913Definitely written as "came by ship Acme in 1849"