Thanks for pointing that out, Masato.
According to a documentary I saw on PBS or the History Channel, Bates's poem enjoyed widespread popularity right upon its first publication. Since it had no tune, people sang it to all sorts of extant melodies (including, I think, the tune we now use for Amazing Grace). By far the most commonly used one, during the first two years after the poem was published, was "Auld Lang Syne." Then someone discovered that Samuel Ward's already published "Materna" was a perfect fit for Bates's poem, and that became the accepted tune for the song.