There are 3 titles associated with this firm.

Mayne, Frances. An introduction to the reading of the Holy Bible. By a lady. London: Francis Knight, 1775.
Mayne, Frances. An introduction to the reading of the Holy Bible. By a lady. London: Francis Knight, 1785.
Unknown, [Woman]. The deserter. A poem, in four cantos: describing the premature death of a youth of eighteen, who perished through ill-timed severity in Dover-Castle on the 5th of March, 1788. ... By a young lady. London: Thomas Hookham [New Bond Street], John Debrett [178 Piccadilly], Francis Knight, J. Robinson, J. Faulder, Thomas Davies [St. John's Street], Botyter, 1788.