This line is traced back to Edward Booth (a) (borne about 1695) who lived in Wainfleet, Lincolnshire, and his mother Catherine.
The family has a long association with the village of Friskney, Lincolnshire. Edward’s son Thomas was Vicar of Friskney, and then Thomas’s grandson Thomas Willingham became vicar there in turn. When he died, his daughter Edith Maria BOOTH married the incoming replacement Henry John CHEALS, and the tradition continued with their son John Pacey CHEALS becoming vicar in turn.
The Booth family form the link between the Franklin and Richardson lines.
There is an oral tradition in my family that these Booths are linked to General Booth, founder of the Salvation Army, but there is no evidence for that as yet.
The land mass in arctic Canada known as Boothia was named by the Franklin/Richardson expeditions, and can be reasonably expected to have been dedicated to Sir John Richardson’s wife Mary Booth. However, this dedication has also been attributed to Sir Felix Booth, a London distiller (of Booth’s Gin fame), who financed one of the expeditions that searched for Franklin. This suggests that there may be a connection between the distilling family and the Booths described here.
An overview chart of the ALINGTON BOOTH FRANKLIN REYNOLDS RICHARDSON lines is available as a .pdf diagram here.