The hymn is sung to the tune "Helmsley." Here's the first musical phrase:
In the first verse, the text here is (of course) "Lo! He comes with clouds descending." "Descending" is sung with a descending melisma (F# E D C B), giving a sense of its meaning. "Comes" is also sung with a melisma (G F#), providing something of a sense of movement; appropriate for the context, these notes also descend, although only a half-step.
In the second verse, the text is "Ev'ry eye shall now behold Him." The words "ev'ry eye" are sung with melismas (G B D | G F#), giving a sense of entirety or number.
In the fourth verse, the text is "Yea, amen, let all adore Thee." Similar to the above, "all" is sung with a melisma (E F# G), lending a sense of entirety.
This same musical phrase is repeated as the third phrase, and in the first verse, the text here is "Thousand thousand saints attending." The words "thousand thousand saints" are sung with melismas (G B D | G F# E D | E F# G), providing a sense of that multitude.
In the third phrase of the third verse, the text (describing the "dear tokens of His passion" from a previous line) is "Cause of endless exultation." The words "endless exultation" are both sung with melismas (G F# E D | E F# G F# E D C B), and since they're stretched out, there's a sense of the duration of "endless."
Here's the second musical phrase:
In the fourth verse, the text here (describing "Thee" from the previous line) is "High on Thine eternal throne." Like "endless exultation," the words "eternal throne" are sung with melismas (A B D C B | B A), giving a sense of that duration.