Jesse Adair's grandson, C G Cleminshaw, was using "Jesse's" seal till he discovered that he shouldn't do so. Amelia Adair was C G's mother and she had obtained the seal from her father "Jesse". In a copy of a letter dated 1933: It was a fine seal, too,...a Saracen's head, with a spear through it. (From Lillian).
The Adairs of Genoch, Scotland, and the Adairs of Loughanmore, Ireland, appeared to have included the sword.