Presumably the William Priestley Richardson a brother of the great architect Henry Hobson Richardson.
HH Richardson’s mother was Catherine Caroline Priestley, daughter of William Priestley, of St James, Louisiana, and grand-daughter of Joseph Priestley, the discoverer of oxygen, and father of modern chemistry

See his entry on rootsweb.com

http://worldconnect.rootsweb.com/cgi-bin/igm.cgi?op=GET&db=timnenno&id=I23865

ID: I23865
Name: William Priestley Richardson
Surname: Richardson
Given Name: William Priestley
Sex: M
Birth: Sep 1840 in Lousiana
Death: 28 Sep 1910 in Lousiana
Change Date: 21 Aug 2005 at 23:56:13

Father: Henry Dickenson Richardson b: in Bermuda
Mother: Catherine Caroline Priestley

Marriage 1 Mary Ellen Aubert
Children
Catherine Priestley Richardson b: 2 Jan 1882 in New Orleans, Louisiana