Personification in The Love Song of J. Alfred Prufrock

Eliot uses personification here to describe the yellow fog as a cat-like figure that rubs up against the window panes and lingers in the shadows. This results in a familiar, comforting image that stands in stark contrast against the pollution of the fog.

The "eternal Footman" is a personification of death. A regular footman is a servant who generally admits and waits on guests—the suggestion being that if death is holding your coat, then you've entered a place where either you're not likely to come out or are on death's doorstep.