The air both day and night felt like breathing through a dishrag.' What language technique is used in this sentence?

Simile.

Explanation:

Figurative languages are those literary techniques used by writers to provide more color in their writings. These techniques allow the writers to provide more in-depth meaning or image to their works by using numerous mechanisms such as hyperbole, simile, metaphor, personification, etc among others.

The statement "the air both day and night felt like breathing through a dishrag" from the novel Cold Mountain by Charles Frazier is a simile. It compares two unlike things, in this case, the air and breathing through a dishrag.  

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king hrothgar despair over the inability to defeat grendel