And pray for the life of the king, and of his sons - Even heathens believed that offerings made in their behalf to the God of the Jews would be available. And this principle has had considerable influence in certain states where there was even a form of religion established by the law, to induce them to tolerate other forms, that the state might have the benefit of their prayers.

That they may offer sacrifices of sweet savours unto the God of heaven,.... Such as will be acceptable to him, Genesis 8:21
and pray for the life of the king, and of his sons; prayer being wont to be made at the time of the morning and evening incense; and the Jews used to pray for other people besides themselves, and especially when desired, and particularly for kings and civil magistrates, to whom they were subject, see Jeremiah 29:7, the sons of Darius Hystaspis, for whose life, as well as his own, he would have prayer made, were, according to Herodotus (d), three by his first wife, the daughter of Gobryas, before he began to reign, the eldest of which was Artobazanes; which sons must be here meant, since this was towards the beginning of his reign; he had afterwards four more by Atossa the daughter of Cyrus, the eldest of which was Xerxes, who succeeded him: many of the Heathens had an high opinion of the God of the Jews, and of their prayers to him for them; even the Emperor Julian (e) styles him the best of all the gods, and desired the Jews to pray to him for the welfare of his kingdom; nor need it seem strange that Darius should desire the same, since he was a devout prince; his father Hystaspes is supposed by some to be the same that was one of the most famous among the Persian Magi, or ministers in sacred things; and Darius himself had so great a veneration for the men of that sacred order, that he commanded that it should be put upon his sepulchral monument, that he was master of the Magi (f); and by his familiarity with the priests of Egypt, and learning their divinity, had the honour, while alive, to have deity ascribed to him (g).
(d) Polymnia, sive, l. 7. c. 2. (e) Opera, par. 2. ep. 25. p. 153. (f) Porphyr. de abstinentia, l. 4, c. 16. (g) Diodor. Sic. l. 1. p. 85.

The end the king had in view in all this follows: "That they (the priests) may offer sacrifices well-pleasing to the God of heaven, and pray for the life of the king and of his sons." ניחוחין (comp. Daniel 2:46) are sacrifices agreeable to God, ניחוחין ריח (Leviticus 1:9, Leviticus 1:13, and elsewhere), i.e., sacrifices pleasing to God. Cyrus had commanded the rebuilding of the temple at Jerusalem, because he acknowledged the God of Israel to be the God of heaven, who had given him the kingdoms of the earth (Ezra 1:2). Darius was treading in his footsteps by also owning the God of the Jews as the God of heaven, and desiring that the blessing of this God might rest upon himself and his dynasty. Such an acknowledgment it was possible for the Persian kings to make without a renunciation of their polytheism. They could honour Jahve as a mighty, nay, as the mightiest God of heaven, without being unfaithful to the gods of their fathers; while the Jews could also, in the interest of their own welfare, pray and offer sacrifices in the temple of the Lord for the life of the king to whom God had caused them to be subject (comp. Jeremiah 29:7). Accordingly we find that in after times sacrifices were regularly offered for the king on appointed days: comp. 1 Macc. 7:33, 12:11; 2 Macc. 3:35, 13:23; Joseph. Antiq. xii. 2. 5, and elsewhere.