The tune of both comes from the old gospel (spiritual?) "When the Chariot Comes," printed 1899, if not some earlier song that is not identified. Posted in this thread by Masato (09 Feb 02) and by Richie in thread 4947, 13 Nov 02.
Possibly the tune is descended from one of the variants of "Ship of Zion," Sacred Harp (?) and old spirituals, but this is strictly speculative.