Floyd Co. Birth Records list W.S.C.P. Phillips (male), b. 10-24-1866, father Mahlon, occ: farmer, mother Rachel.

A child born in Oct 1866 would be 3 in Aug 1870, and there is no death record for any child of Mahlon and Rachel between 1866 and 1870. So pending further evidence, I am going to assume that this birth record is for the Noah C. Phillips who appears as age 3 in the 1870 census.