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"intense interrogation by police," 1900, probably a reference to Third Degree of master mason in Freemasonry (1772), the conferring of which included an interrogation ceremony. Third degree as a measure of severity of burns (most severe) is attested from 1866, from French (1832); in American English, as a definition of the seriousness of a particular type of crime (the least serious type) it is recorded from 1865.
Long and harsh, even brutal, questioning, esp by the police: The Third Degree, A Detailed and Appalling Expose´ of Police Brutality/ He's giving me a third about some gun he says I had
[1900+; origin uncertain]