Two hundred years before 2268, the Argelians experienced what they call the "Great Awakening". In this awakening, they united under an uniglobal government and created a legal system that was based on love. This government was headed by a Prefect. The seat of government was located in a chief city. Due to inefficiencies in their government, this planet hired people from other planets to fill administrative positions.
Prior to stardate 3619, Argelius II signed a treaty with the Federation wherein Starfleet could use this planet as a space port for their ships. Crews of these ships would take their shore leave on this planet. For male crew members, the Argelian women were one of the highlights.
In 2364, the location of Argelius II in relation to the Jewel stars was depicted on a Federation star chart stored in the library computer of the USS Enterprise-D. The planet Alpha Eridani II was on a direct alignment between Argelius II and Earth. (TOS: "Wolf in the Fold"; TNG: "Datalore", "Conspiracy", display graphic)
According to the The Worlds of the Federation, the star that Argelius II orbits is named Argelius B (apparently part of a binary star system with Argelius A), and the Argelians refer to their world as Nelphia.
According to Star Trek: Star Charts ("United Federation of Planets I & III"), Argelius II was also known as Iota Leonis II. In 2378, Argelius II was a Federation member. The Argelius System, also known as the Iota Leonis System, was a binary star system. Argelius A was a F-class star with a magnitude of +7, which was 1/10 as bright as Sol. Argelius B was a F-class star. The system was located in or near Federation space.
The star chart seen in "Datalore" and "Conspiracy" was taken from page 133 of the Star Trek Spaceflight Chronology, where it was explained as showing a part of Federation space in the 2140s, with the thin lines denoting routes of commercial tourist starliners.
According to the novel The Sorrows of Empire, the mirror universe Montgomery Scott was likewise accused of brutally murdering three women on Argelius II. However, Captain James T. Kirk ensured that the charges were dropped without an investigation taking place.