In much of the Trefethen data in that book they spell the name Trefethern! The family data part uses that spelling. In the history part of the book there are some scattered uses of the Trefethen spelling. There was also an occurrence of Treferrin.
   A human eye search in a physical book spots the different spellings instantly - and recognizes them for what they are. But a digital search of the PDF file only shows what one asked for! Therefore a digital search using any of the full spellings misses a lot of the entries! So - a search for just "Tref" is required for the best results!

[The numbers in parentheses such as "(17)" refer to numbers in the Source book --Andrew Trefethen]

On page 552 of the "History of Rye, New Hampshire" it says that Albert Brackett Trefethen (24) was a son of Oliver Trefethen (17).  THAT  is  WRONG!
   That Albert Brackett Trefethen [on this page] was a son of Joseph (6) and Hannah (Berry) Trefethen (as shown in the Trefethen Family Database)..
   Yes - Oliver had a son named Albert B. Trefethen. See page 551 of the book.  But Joseph (6) also had a son named Albert B. Trefethen. See pages 348 - 349 of the book.
   Now look at the Trefethen Family Database. It (correctly) shows Albert Brackett Trefethen ⁰⁰⁸⁵ [this page] as born in 1835. And 1835 is confirmed on "Find a Grave" (which also includes a photo (although the last digit of his birthyear is hard to read) of his headstone).
   As Oliver (17) was born in 1826 (see page 551 in the "History of Rye, New Hampshire") - he would have only been 9 years old when Albert Brackett Trefethen ⁰⁰⁸⁵ [on this page] was born - and therefore couldn’t have been his father! (BTW: the dates work out fine for Albert Brackett Trefethen [on this page] to have been the son of Joseph (6).)
Oliver (17)'s son Albert B. Trefethen was born in 1857. (Per the Trefethen Family Database.)

                          Respectfully,
                                Allen E. Humphries