Marion J. Hatchett (in A Companion to The New Harp of Columbia, University of Tennessee Press, 2003, p. 199) says:

Music: This tune [i.e. PROSPECT] apparently first appeared in print in the 1835 edition of William Walker's SouH [Southern Harmony], where it is attributed to M.C.H. Davis and printed in three parts with the first stanza of this text [Watts' "Why should we start and fear to die?"]. In later editions of SouH PROSPECT was attributed to Graham. Walker's version was reproduced in SacH [Sacred Harp]. ... Jackson listed PROSPECT among the "Eighty Most Popular" (27).