In these lines, Eliot indirectly compares the fog that covers the streets at night to a cat; it is an indirect comparison because he never directly states the word cat. However, if you look close at the details and put them all together like a puzzle, the clues are pretty clear. For example, he uses the following words and phrases to describe the fog: "rubs its back upon the window-panes," "rubs its muzzle," "licked its tongue," "slipped by," "made a sudden leap," and "curled once about the house, and fell asleep." All of these details, put together, paint a pretty clear picture of cats. They rub their backs and muzzles on things, slip by as they walk, and before going to sleep, often do a circle or two before settling in.
So, the fog is compared to a cat, using detailed word-choices and clues. It is a unique and apt description, one that gives the fog a clear personality and life to it, instead of having it be an inanimate object. I hope that helped; good luck!
As was mentioned in the previous post, T.S. Eliot uses an extended metaphor that compares the fog to an alley cat throughout the poem "The Love Song of J. Alfred Prufrock." Eliot associates the movements of the fog with those of an alley cat, and indirectly compares the two because he does not use the word "cat" throughout the extended metaphor. Similar to fog, cats are silent, mysterious creatures that are able to inhabit places that other animals cannot. Eliot provides details which reveal that an alley cat is being indirectly compared to the fog by depicting how the fog
"rubs its back...rubs its muzzle...Licked its tongue...Lingered upon the pool...made a sudden leap...Curled once about the house" (15-25).
The movements of the fog mirror those of an alley cat. Cats often rub their backs, lick their tongues, and linger around drains. References to a muzzle, and the creature's leaping around the house, further reinforce the idea that Eliot is comparing fog to an alley cat. It is unusual to compare an animal to a weather element, and this displays T.S. Eliot's expertise in creating an atmosphere.