The line repeated in Hamilton's musings is "on the other side."
We can arrive at this answer because:
When he starts thinking about his life and everything he has witnessed, he starts repeating the line "on the other side," as he starts thinking about the important people in his life who have died and are no longer on the material side of the world.
The repetition of that line demonstrates Hamilton's desire to go to the other side and find the people he misses.
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