I am not sure that your William H is Hiram's son, but it is a possibility.Try a search at RootsWeb on Hiram Durham who married Matilda Caledonia Mills for more information. The site was down when I tried to check a few minutes ago, but there were several hits.I personally haven't done any research other than on our direct connection to Emmaline "Emma".
Hiram Durham Family 1860 Madison County AL censusson William age 2 born MS
Hiram Durham Family1870 Lincoln County TNson William age 10 born MS
Hiram Durham - 1880 Lincoln County TNWilliam is not in the household
However I found this -
W H Durham 21 AL AL AL, Mary C. 22 AL AL NC, son Eli V 10/12 (July) TN AL AL 1880 Lincoln County TN
I wish I could be of more help.Good luck with your research & if you do find there is a connection, please contact me.I am willing to share information about our Emma's line if you are intersted.