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The university is wonderful to him and he had always wanted to address to this "august body" of students and professors. What is the meaning of "august body"? I couldn't find it anywhere.
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"august" here is an adjective meaning "inspiring respect and admiration" (definition from COED, saving me thinking one up!). It's pronounced with the stress on the second syllable (unlike the month).

"body" means "group", "collection" (of students and professors).