The kings after Romulus were not known to be dynasts and no reference is made to the hereditary principle until after the fifth king Tarquinius Priscus. Consequently, some have assumed that the Tarquins and their attempt to institute a hereditary monarchy over this conjectured earlier elective monarchy resulted in the formation of the republic.. . .
. . . Whenever a Roman king died, Rome entered a period of interregnum (literally: between kings). Supreme power in the state would devolve to the Senate, which had the task of finding a new king. The Senate would assemble and appoint one of its own members as the interrex to serve for a period of five days with the sole purpose of nominating the next king of Rome. After the five-day period, the interrex would appoint (with the Senate's consent) another Senator for another five-day term. This process would continue until the election of a new king. Once the interrex found a suitable nominee for the kingship, he would bring the nominee before the Senate and the Senate would review him.[citation needed] If the Senate passed the nominee, the interrex would convene the Curiate Assembly and preside as its president during the election of the King.
Once a candidate was proposed to the Curiate Assembly, the people of Rome could either accept or reject the candidate-king.
The insignia of the king was twelve lictors wielding the fasces, a throne of a Curule chair, the purple Toga Picta, red shoes, and a white diadem around the head. Only the king could wear a purple toga.
Finally, on his latest album, Bob Dylan sings of the early Roman kings.