Isaac Murphy Letter said; "Wm moved to Georgia"...

William White Jr. 
(Son of Wm & Elizabeth White)
Born: abt. 1815 Union Co SC
Died: Unknown
Buried: Unkn...
(1840 Census indicates age between 20 & 30)

Married: Unknown 
(is married in 1840 - wife between 20 & 30yrs)

Known Children: None listed on 1840 Census

"Mystery Child"

William White is one of the mystery children of Wm & Elizabeth.

William is spoke of in two letters written by grandsons of Robert 
White Sr:  Isaac P. Murphy and his brother Jason Wiley Murphy, 
for which an abstract is listed below:

In a Family Letter dated March 17, 18__ (probably 1870's)
From Jason Wiley Murphy to his sister Edy Jackson:

"...Father White lives his upper plantation near Thompsons cross 
roads is well. Cousin Ginna Coggins live at the same place. Sally & 
Susan lives at the old place. Backael? at the Village. Betsy married 
Lipskum lives on Jocher Creek has no children. Wm in Georgia.  
Lucy dedd. Samuel in Alabama. Susan has one son married. Rachael 
two daughters, Lucy one. I don't know how many Ginny has married..." 

Note: All of the Children mentioned above are William & Elizabeth's.

Comments:

There were several William White's in Union county, at the time of 
Wm Sr's death, in 1829, William Jr. was only a teenager, so cannot
be any of the Wm's on the 1830 census, for Union Co SC. 

At least in the 1830 Census, Wm is living with his immediate family,
or a guardian, as was commonly ruled  by the courts, of the time...

There maybe a Guardianship record hidden somewhere at the Union
County Court house. It is not mentioned in Wm's Estate record. An
inspection of the Count Minutes for 1829 may reveal this information.

Census Records: 

The 1840 census is the most revealing for Wm White Sr's boys 
James and Wm, living very close to each other and relatives. Have
sorted out  the White's, this James & Wm  and these can only belong 
to Wm & Elizabeth White Sr. 

1840 Union Co SC Census Page 197a

The Neighborhood 

James White - Males: 0000010000000 - Femls: 0110010000000
                                 (Son of Wm & Elizabeth)
Hannah Fincher
Jesse Boatman -        Males: 0000020000000 - Femls: 0100100000000
                                (Uncle of James & Wm, brother of their mother)

              Union Co SC Census Page 198a
William White - Males: 0000100000000 - Femls: 0000100000000 
                                 (Son of Wm & Elizabeth)
James Gibbs -            Males: 0000100000000 - Femls: 0000100000000
                                 (Brother of Elias White's wife Anne)
William Hays
James Browning         Males: 2100010000000 - Femls: 0111100100000
                                 (Brother of James White's wife Nancy Browning)
Joseph  Robinson
Monroe Robinson
Churchill Gibbs -      Males: 0101010000000 - Femls: 0100100000000
                               (Brother of Elias White's wife Anne)
Elias White -    Males: 2110201000000 - Femls: 1121001000000
                               (Uncle to James & Wm)