William James, son of Paul and Ann, was christened in Derby in 1872.
The LDS pilot site has some likely children for him and Sarah Jane:
Richard Alfred GIBSON, christened Fairfield, Derbyshire, 2 Sep 1901
Edna Emily GIBSON, b. 30 Oct 1905 and chr. 21 Nov 1905 at St Michael's, Garston
Elsie May GIBSON, b. 15 Sep 1909 and chr. 12 Oct 1909 at St Michael's, Garston
(Mother's maiden name not given, but the time and place are right.)
Free BMD
http://freebmd.rootsweb.com has the births of 2 children with the surname GIBSON and mother's maiden surname MOORE in West Derby district:
Herbert H GIBSON, Mar Q 1912 (W.Derby 8b 1292)
Walter W GIBSON, Jun Q 1913 (W.Derby 8b 1336)
To "fill in the gaps", you would need to buy a few credits for the 1911 census, or use the advanced search facility on the free index to find people with the surname GIBSON living in Garston in the same household as James William.
Rambler
