This "Say, brothers" version of the verse has the same rhythm as the "Glory, Hallelujah" chorus. Or in other words, in "Say, Brothers" the verse and the chorus have essentially identical melody and rhythm.
Expanding on this a little--the observant musicians among you will have noticed that the verse of Battle Hymn ("Mine eyes have seen the glory . . . " has the same exact melodic outline of the Chorus ("Glory, glory hallelujah . . . ").
In fact, really the melodies of the verse & the chorus of Battle Hymn are the same--the verse is a simple rhythmic variant of the chorus.
And the rhythmic variant generally boils down to this: The chorus often holds one note for a long time, the verse fills that same time by repeating the same note several times, generally with a dotted rhythm.
Example (key of C):
Verse: GG GG FE GC DE EE DC etc.The "Say, brothers" lyrics fit the melody (essentially the same melody/rhythm as the Chorus of "Battle Hymn") like this:
Chorus: G FE GC DE DC etc.
G F E G C D E D C etc.
Sa - ay Bro-thers will you mee - t us etc.