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In "My Last Duchess," what situation brings the Duke and the agent together?

The Duke has apparently invited the representative of the Count upstairs to see part of his art collection. But the real reason was so the two men could meet alone in order to discuss the matter of the dowry the Duke will receive when he marries the Count's daughter. Evidently the Duke does not want to bring up the subject immediately for fear of appearing too mercenary. Instead he invited the visitor to look at a portrait of his last wife. While he is talking about this beautiful girl, now presumably dead, he reveals his true character as a cruel, selfish, arrogant, vulgar man incapable of loving anyone but himself. He makes such a bad impression on the Count's representative that the man jumps up and starts to retreat down the stairs to the room below where the Count himself and and a number of relatives of the Count and the Duke are gathered. It would appear that the Count's representative intends to warn the Count against allowing his daughter to marry the Duke under any circumstances. The Duke is alarmed because they have not gotten around to discussing the dowry. In the last lines of the poem he shows his real interest and the real reason he and the Count's representative are there together.



Will't please you rise? We'll meet
The company below, then. I repeat,
The Count your master's known munificence
Is ample warrant that no just pretence
Of mine for dowry will be disallowed,
Though his fair daughter's self, as I avowed
At starting, is my object.


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