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A truth assessor was a piece of technology employed by the Megara during trials. As the name implied, it determined the level of truth of a witness' statements. In other words, it was essentially a lie detector. It worked by means of a beam of energy which scanned the brain of an individual.
One of the key issues in the Fourth Doctor's trial was why the Doctor's first witness, Romana, was compelled to be attached to the truth assessor, while his second, Cessair of Diplos, was not. The Megara denied the Doctor's request on the grounds that she was not a direct witness to the events for which the Doctor was on trial. Because the Megarans were such strict interpreters of the Galactic Charter, this indicated that the Charter specified the circumstances under which the truth assessor could be used. (TV: The Stones of Blood)