After Nabuchodonosor, the kingdom fell to his son, whom I find called Euilmarodac in the Chronicles. He died in the twelfth year of his reign, and made room for his younger brother, who was called Balthasar. He, when in the fourteenth year he gave a public feast to his chief men and rulers, ordered the sacred vessels (which had been taken away by Nabuchodonosor from the temple at Jerusalem, yet had not been employed for any uses of the king, but were kept laid up in the treasury) to be brought forth.
And when all persons, both of the male and female sex, with his wives and concubines, were using these amid the luxury and licentiousness of a royal banquet, suddenly the king observed fingers writing upon the wall, and the letters were perceived to be formed into words. But no one could be found who was able to read the writing. The king, therefore, in perturbation called for the magi and the Chaldæans. When these simply muttered among themselves and answered nothing, the queen reminded the king that there was a certain Hebrew, Daniel by name, who had formerly revealed to Nabuchodonosor a dream containing a secret mystery, and had then, on account of his remarkable wisdom, been promoted to the highest honors.
Accordingly, he, being sent for, read and interpreted the writing, to the effect that, on account of the sin of the king, who had profaned vessels sacred to God, destruction impended over him, and that his kingdom was given to the Medes and Persians. And this presently took place. For, on the same night, Balthasar perished, and Darius, a Mede by nation, took possession of his kingdom. He again, finding that Daniel was held in the highest reputation, placed him at the head of the whole empire, in this following the judgment of the kings who had preceded him. For Nabuchodonosor had also set him over the kingdom, and Balthasar had presented him with a purple robe and a golden chain, while he also constituted him the third ruler in the kingdom.
Source: Sacred History (New Advent)