Henry Phipps's story is one with which many people, particularly in contemporary America, can probably identify: someone who spent his life making a lot of money for other people, though this deed provided him with no spiritual fulfillment. When he converted to Christianity, he thought that his newly found righteousness would save him. God, he believed, would reward him with longer life for his sacrifices, at the very least. Alas, this was not Henry's fate.
Henry worked with important people and maintained positions of leadership, though in rather unglamorous roles:
I was the Sunday school superintendent,
The dummy president of the wagon works
And the canning factory,
Acting for Thomas Rhodes and the banking clique;
My son the cashier of the bank,
Wedded to Rhodes' daughter,
My week days spent in making money...
He was not the actual president "of the wagon works / And the canning factory," but only a "dummy," a puppet figure who made appearances, but no actual decisions. He "[acted]" for others. His son, it seems, was also destined to a subordinate role. Though he is married to Rhodes's daughter, he is a mere cashier. Thomas Rhodes, whom we meet earlier in the anthology, is a thoughtless, insensitive man only concerned with accruing wealth. Henry acted in his service during the week, but his Sundays were spent "at church and in prayer," making it clear that he was devoted to spiritual fulfillment.
He was a man who did his duty, without questioning any of it, as he was cleansed of possible wrongdoing by his faith:
In everything a cog in the wheel of things-as-they-are:
Of money, master and man, made white
With the paint of the Christian creed.
Finally, the bank was destroyed. In its dilapidated state, it was revealed to be a thoroughly rotten machine, sullied and broken constantly from within and showing signs of shoddy patchwork:
The wheels with blow-holes stopped with putty
The rotten bolts, the broken rods;
And only the hopper for souls fit to be used again
In a new devourer of life, when newspapers, judges and money-magicians
Build over again.
The "newspapers, judges and money-magicians" are the manipulators who lazily maintained the bank, who rendered Henry a mere cog within it, and who find new "souls" to feed it.
Henry was one such soul, "stripped to the bone," though he now lies "in the Rock of Ages." This line seems to refer to his commemoration in immortality. Perhaps, on his epitaph, there is a note dedicated to all of his hard work -- not that this matters to Henry, for he "[sees] now through the game" and is "no longer a dupe." His faith convinced him (using Proverbs 2:21 and 10:27 as inspiration) that his moral uprightness would be rewarded with long life, while the lives of those like Thomas Rhodes would be shortened.
Henry experiences a sort of existential crisis and lapse of faith when Dr. Meyers "discovered a cancer in [his] liver":
I was not, after all, the particular care of God!
His senses of singularity and justness are diminished by the revelation. He could stand to be a "cog," knowing that God took an interest in his existence. He discovered, on his deathbed, that this was not true.
He characterizes his life as a climb. On the cusp of death he is "standing on a peak." His mortal struggles are "the mists through which [he] had climbed." Alas, he is ready for "larger life in the world," or some discovery of meaning which will remain with him in the after-life. Instead, "eternal forces / Moved [him] on with a push." The "push" here seems not to be one of encouragement, but dismissal. Poor Henry is as neglected in death as he was in life.