It isn't that symbolic, actually, but a set of meanings barely beneath the surface. This is Anthony talking to Cleopatra. These are famous lovers. He is Rome to her Egypt, a land related to and defined by its rivers. Most simply he is saying, I don't care—let huge amounts of...
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time pass, and he won't do anything, because he doesn't care. He just wants to hold Cleopatra. But we also talk about passion and lovers being hot, so he's saying things are hot—and perhaps that his Roman firmness is going to "melt" into her (they will have sex, and his erection will melt).