«Fair administration of justice» is a reference to current criminal proceedings. (politics.stackexchange.com)
«In fair administration of justice no man can be judge in his own case,» the Court wrote in 1967, «however exalted his station, however righteous his motives, and irrespective of his race, color, politics, or religion. (educationnext.org)
Reginald Heber Smith, a leading lawyer in Boston, famously explained it this way: a failure to provide fair administration of the law «not only robs the poor of their only protection, but places in the hands of their oppressors the most powerful and ruthless weapon ever invented.» (nlada.org)