Thought I'd answer your post as well as our past communication in case others are interested.
In the 1900 census, Alonzo and Kate Fernald are in Boston, MA. His age is listed as 41 and birth day is listed as Oct 1859. Alonzo was born in Mass. and his parents are listed as born in ME. Kate is Irish age 35 born 1864. also in this household are son James age 20 born May 1880, dau. Nellie (your Helen)age 14 born Aug 1885, Alonzo age 11 born Oct 1888 and son in law Joseph Thompson 21 born 1879 with wife Annie 16, born July 1883 and their son Harold Thompson 1 month old born in April 1900. (census has 1890 by mistake.)This would probably confirm that your Alonzo is the son of Thomas and Dorcas Fernald. I have Dorcas maiden name as Elwell dau of Robert Elwell and Dorcas Day. Thomas Fernald supposedly died Nov 16,1864 and Dorcas remarried April 3 1864 to Otis Whipple. i suspect his death date may be a year off.
Alfreds son Alonzo was born about 1843. Alfred and Thomas are both living in Quincy MA in 1860.
Thomas Fernald was born in Maine his age is listed as 35 in 1860 and Dorcas is 27 from Mass. dau Orina is 7 and Alonzo is listed as being 4.
it looks like your Fernald line goes:
Helen A. Fernald and Thomas Francis Barry Alonzo Fernald and Catherine Boyle Thomas Fernald and Delia Dorcas Elwell Daniel Fernald and Phebe Trefethen Joseph Weeks Fernald and Catherine Chandler Jonathan Fernald and Sarah Weeks Ebenezer Fernald and Patience Mendum William Fernald and Elizabeth Langdon Renald Fernald and Joanna Warburton