Only found the songs which begin "Come fellows, let us raise a song" and "Dear Old Dartmouth give a rouse," both from the 1890s. Neither "Carmina Collegensia," 1868 nor College Songs, 1860, have anything that approaches al alma mater. The "Academy Song-Book" of 1895 ignores Dartmouth.
The only reference I have is the use of "Old Dartmouth" as an air for "Jubilate" in 1860.
Any green men from Dartmouth out there?