It will be of interest to sketch briefly of a few men succeeding Augustus. None of the early emperors was followed by his own son, but, according to to the Roman law of adoption, they all counted as Caesars. Nero was the last one to the connected with Augustus, even by adoption, though the emperors continued to call themselves Caesar and Augustus, throughout the existence of the empire.

Tiberius
Augustus was succeeded by his adopted step-son Tiberius, who for a time ruled with comparative mildness. But he was naturally jealous and cruel and these traits soon broke out into action. He had a bodyguard of 10,000 men which he could use in any way he chose. He usurped the right to put to death without trial. Every attempt against him was made high treason. A word could be construed to mean hostility, and was punished by the confiscation of property and death.
Tiberius became one of the most gloomy and vicious tyrants. He at length placed the government in the hands of Sejanus, commander of his bodyguard, and retired to Capreae, where he gave himself up to the most cruel and disgusting debaucheries.

Sajanus
Sejanus killed several members of the royal household at Rome and was found to be plotting for the throne. Tiberius was more than ever filled with terror and suspicion. A massacre followed in which hundreds of men, women, and children perished. But the world at last breathed freer when the profligate monster was slain by a member of his own household.
Caligula followed. Mild and generous at first, he soon became a veritable demon of cruelty and vice. He was especially fond of witnessing the tortures of human beings. He was wildly extravagant and quickly drained the public treasury. His conduct even exasperated is solders and after reigning but four years he was killed by two of his own bodyguard.
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Reference: Woman: Her Position, Influence and Achievement Throughout the Civilized World. Designed and Arranged by William C. King. Published in 1900 by The King-Richardson Co. Copyright 1903 The King-Richardson Co.