The Book of Dow deals with the family name Dow, not with Dows or Dowse. None of your family is listed in that book. The names Dow and Dows(e) are not connected. Dows(e) is a Norman name that was originally Douce from the word "dulcis." Dow and Doue are from Dove.
BTW, the name Dowson refers to a son of Dows, not son of Dow, so that name is also not related to Dow (as some may have thought).