Father of William Gayer and Sir John Gayer

From "Gayre's Booke, being A History of the Family of Gayre" Vol. IV by Lteut.-Colonel Robert Gayre and R. L. Gair (London: 1959), p. 62, in reference to the Humphry who m. Miss Sparke of Plymouth, gives evidence that his son John died without progeny and the line of Humphry ended in co-heiresses.
p. 64 of the same volume says that Dr. A.E. Gayer erred in making Sir John Gayer of Bombay a descendant of Humphry. Sir John's will mentions his brother, William in Nantucket. According to these authors, there is no such brother among the children of Humphry Gayer, or among those of any of his other (than Sir John Gayre of London) brothers.