From GFHS Marriage Index:
11 October 1835 Thomas WHITE married Elizabeth HAIL by Banns at Abenhall.

This Memorial at Christchurch Churchyard:
Headstone;
In Loving Memory/ of/ William White/ the beloved husband of Eliza White of Joyford/ who died Feb 9th 1910/ aged 66 years/ Also of the above Eliza White/ who died Nov 14 1934/ aged 86 years.

Following baptisms at Christchurch:
15 December 1842 Alice daughter of Thomas and Elizabeth WHITE.Joyford. Collier
5 July 1846 Tom son of Tom and Elizabeth WHITE, Christchurch. Collier
5 July 1846 Amelia daughter of Tom and Elizabeth WHITE, Christchurch. Collier.

I cannot see William born c 1844 listed.

19 December 1869 William WHITE, Collier, Joyford and son of Thomas married Eliza SMITH, Berry Hill, daughter of Edward SMITH deceased at Christchurch. Witnesses: Benjamin SMITH and Mary NELMES.

SMITH family in 1851:

2444 0309 033 Berry Hill SMITH Edward HD M 31 Collier GLS West Dean
2444 0309 033 Berry Hill SMITH Amealia WI M 24 - GLS West Dean
2444 0309 033 Berry Hill SMITH George SO U 6 - GLS West Dean
2444 0309 033 Berry Hill SMITH Eliza DA U 2 - GLS West Dean

Mike