I search for ADAMS in Liverpool. Base point of (William, Emily, Florence, Albert, Bertram, Sarah Harriet, & others, birth ranges 1872-1895, lived various parts of Liverpool).
Their father was Nathaniel Adams of Anfield Rd, Anfield, Liverpool, and who supposedly ran a ships chandlers/provisioners store in Liverpool, and whose siblings were (Susannah, Emma, John, Nathaniel, Thomas?, George/Joseph?, born circa 1850. A couple of this line went to USA & France (assume around c1870 +/-). Family talk has it they came from a farm called "Hillhead" some 6 miles from Lisburn, County Antrim, Nth Ireland.
Liverpool family inter-marriages comprise SHAW (Sir Edmund Buckley), CAINE, KINRADE, Rev. Wiliiam WILKINSON (Methodist, & time in Manx & Nth Yorkshire), CALLISTER (m Wilkinson in Manx), ASHTON, & CUTTS.
Regards, Mike Adams, mkradams@optusnet.com.au.