It looks like Thompson is the correct last name.

In the 1940 census of Beat 1, Hinds, Mississippi:

head August Thompson M 46 Mississippi
wife L E Thompson F 40 Mississippi
dau Eva Thompson F 17 Mississippi
son Jessie Thompson M 16 Mississippi
dau Mary Thompson F 14 Mississippi
dau Katie Thompson F 12 Mississippi
son Augustus Thompson M 10 Mississippi
dau Thelma Thompson F 7 Mississippi
son Lee Thompson M 3 Mississippi

You can also find this family in the 1930 census, with August's name listed as Augusta. I haven't checked the other census records for the family, so let me know if you need help finding them.


Here is August's Social Security death record:

Name: August Thompson
SSN: 425-48-4970
Last Residence: 39209 Jackson, Hinds, Mississippi, United States of America
Born: 15 Jul 1893
Died: Jun 1978
State (Year) SSN issued: Mississippi (Before 1951)

He can also be found in "U.S., World War I Draft Registration Cards, 1917-1918", as well as "WWI Civilian Draft Registrations".

Hope this helps get you started! It looks like there are quite a few (at least 6 or 7) John Jones's in that area who are the right age to be the father...