Thomas: Thank you for your reply and your explanation regarding the various Federal census.
I have the 1850 and 1860 census for James S. and the 1880 census for Henry S. I also have the WWI registration for Norman H. The 1850 & 1860 census matches a birthdate for Henry S as 1833 which matches the information on Norman H. birth certificate. This does not match the age for Henry S on the 1880 census although the age for Eliza does match her 1844 birth year. I question if there is a transcription error on Henry's age on the 1880 census?? will need to research that more. James S' death is recorded in 1869 in Yell, Ark, which explains why he would not appear in the 1870 or 1880 census data.
You asked how I had a b/c for Norman in year 1882 because birth records in Ark only go back to 1914. Please see the following
Name of Child: Norman Hudson Heath DOB: 26 Jan 1882 @ 10:00 PM Location: Wooster, 10 miles north of Conway, Faulkner Co., Arkansas Father: Henry S. Heath; Age: 49; Born: Gibson Co., Tenn. Occ.: Farmer Mother: Eliza Jane Campbell; Age: 38; Born: Gibson Co, Tenn.; Occ: Housewife Number of children born to this mother including this child: 7 Number of children living at time of this birth: 5 Detail Certificate of Birth; State of Arkansas; State Board of Health; Bureau of Vital Statistics; Cert. No. 1147 Date 14 Jul 2010 Other information Request No. 199717136 Arkansas Prior Birth Records Year - 1943 Binder - 2 Volume - 063 Certificate No. 004301147 Mother's Maiden Name: Eliza Jane Campbell
Recorded 1943, Binder 2, Vol 063, Cert # 1147. Source: Vol 3, p 379 Title Arkansas Prior Birth Index. Author Arkansas Genealogical Society. Pub Info: Hot Springs, AR: Arkansas Genealogical Soc. 2002
With Norman's birth in 1882, this would explain why he is not shown in the 1880 census data or earlier.
I have not been able to find any census information for either Henry S or Eliza J. after 1880. Possible reasons could be death of Henry S and remarriage by Eliza J.Eliza could have gone to live another relative and I have just not been able to track that yet. Needs more research and time.
Thank you again for all the information. Very much appreciated.