Argelian law was the set of laws governing Argelius II.
Created by the Argelians, Argelian law also applied to non-Argelians while on the planet. To avoid a diplomatic incident, in 2267 Captain Kirk therefore agreed to have Montgomery Scott be processed under Argelian law, when Scott was accused of several murders.
While Prefect Jaris at one point stated "The law of Argelius is love", laws from before the Great Awakening were still in effect by 2267. According to them, the penalty for murder was death by slow torture. (TOS: "Wolf in the Fold")