I answer that, The grades of the angelic orders are assigned by Gregory (Hom. xxiv in Ev.) and Dionysius (Coel. Hier. vii), who agree as regards all except the "Principalities" and "Virtues." For Dionysius places the "Virtues" beneath the "Dominations," and above the "Powers"; the "Principalities" beneath the "Powers" and above the "Archangels." Gregory, however, places the "Principalities" between the "Dominations" and the "Powers"; and the "Virtues" between the "Powers" and the "Archangels." Each of these placings may claim authority from the words of the Apostle, who (Eph. 1:20,21) enumerates the middle orders, beginning from the lowest saying that "God set Him," i.e. Christ, "on His right hand in the heavenly places above all Principality and Power, and Virtue, and Dominion." Here he places "Virtues" between "Powers" and "Dominations," according to the placing of Dionysius. Writing however to the Colossians (1:16), numbering the same orders from the highest, he says: "Whether Thrones, or Dominations, or Principalities, or Powers, all things were created by Him and in Him." Here he places the "Principalities" between "Dominations" and "Powers," as does also Gregory.
Let us then first examine the reason for the ordering of Dionysius, in which we see, that, as said above (Article [1]), the highest hierarchy contemplates the ideas of things in God Himself; the second in the universal causes; and third in their application to particular effects. And because God is the end not only of the angelic ministrations, but also of the whole creation, it belongs to the first hierarchy to consider the end; to the middle one belongs the universal disposition of what is to be done; and to the last belongs the application of this disposition to the effect, which is the carrying out of the work; for it is clear that these three things exist in every kind of operation. So Dionysius, considering the properties of the orders as derived from their names, places in the first hierarchy those orders the names of which are taken from their relation to God, the "Seraphim," "Cherubim," and "Thrones"; and he places in the middle hierarchy those orders whose names denote a certain kind of common government or disposition---the "Dominations," "Virtues," and "Powers"; and he places in the third hierarchy the orders whose names denote the execution of the work, the "Principalities," "Angels," and "Archangels."
As regards the end, three things may be considered. For firstly we consider the end; then we acquire perfect knowledge of the end; thirdly, we fix our intention on the end; of which the second is an addition to the first, and the third an addition to both. And because God is the end of creatures, as the leader is the end of an army, as the Philosopher says (Metaph. xii, Did. xi, 10); so a somewhat similar order may be seen in human affairs. For there are some who enjoy the dignity of being able with familiarity to approach the king or leader; others in addition are privileged to know his secrets; and others above these ever abide with him, in a close union. According to this similitude, we can understand the disposition in the orders of the first hierarchy; for the "Thrones" are raised up so as to be the familiar recipients of God in themselves, in the sense of knowing immediately the types of things in Himself; and this is proper to the whole of the first hierarchy. The "Cherubim" know the Divine secrets supereminently; and the "Seraphim" excel in what is the supreme excellence of all, in being united to God Himself; and all this in such a manner that the whole of this hierarchy can be called the "Thrones"; as, from what is common to all the heavenly spirits together, they are all called "Angels."
As regards government, three things are comprised therein, the first of which is to appoint those things which are to be done, and this belongs to the "Dominations"; the second is to give the power of carrying out what is to be done, which belongs to the "Virtues"; the third is to order how what has been commanded or decided to be done can be carried out by others, which belongs to the "Powers."
The execution of the angelic ministrations consists in announcing Divine things. Now in the execution of any action there are beginners and leaders; as in singing, the precentors; and in war, generals and officers; this belongs to the "Principalities." There are others who simply execute what is to be done; and these are the "Angels." Others hold a middle place; and these are the "Archangels," as above explained.
This explanation of the orders is quite a reasonable one. For the highest in an inferior order always has affinity to the lowest in the higher order; as the lowest animals are near to the plants. Now the first order is that of the Divine Persons, which terminates in the Holy Ghost, Who is Love proceeding, with Whom the highest order of the first hierarchy has affinity, denominated as it is from the fire of love. The lowest order of the first hierarchy is that of the "Thrones," who in their own order are akin to the "Dominations"; for the "Thrones," according to Gregory (Hom. xxiv in Ev.), are so called "because through them God accomplishes His judgments," since they are enlightened by Him in a manner adapted to the immediate enlightening of the second hierarchy, to which belongs the disposition of the Divine ministrations. The order of the "Powers" is akin to the order of the "Principalities"; for as it belongs to the "Powers" to impose order on those subject to them, this ordering is plainly shown at once in the name of "Principalities," who, as presiding over the government of peoples and kingdoms (which occupies the first and principal place in the Divine ministrations), are the first in the execution thereof; "for the good of a nation is more divine than the good of one man" (Ethic. i, 2); and hence it is written, "The prince of the kingdom of the Persians resisted me" (Dan. 10:13).
The disposition of the orders which is mentioned by Gregory is also reasonable. For since the "Dominations" appoint and order what belongs to the Divine ministrations, the orders subject to them are arranged according to the disposition of those things in which the Divine ministrations are effected. Still, as Augustine says (De Trin. iii), "bodies are ruled in a certain order; the inferior by the superior; and all of them by the spiritual creature, and the bad spirit by the good spirit." So the first order after the "Dominations" is called that of "Principalities," who rule even over good spirits; then the "Powers," who coerce the evil spirits; even as evil-doers are coerced by earthly powers, as it is written (Rm. 13:3,4). After these come the "Virtues," which have power over corporeal nature in the working of miracles; after these are the "Angels" and the "Archangels," who announce to men either great things above reason, or small things within the purview of reason.