A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
4 Kings (2 Kings) 2:1
kg2 2:1ELIJAH DIVINES JORDAN. (Kg2 2:1-10)
when the Lord would take up Elijah--A revelation of this event had been made to the prophet; but, unknown to him, it had also been revealed to his disciples, and to Elisha in particular, who kept constantly beside him.
Gilgal--This Gilgal (Jiljil) was near Ebal and Gerizim; a school of the prophets was established there. At Beth-el there was also a school of the prophets, which Elijah had founded, notwithstanding that place was the headquarters of the calf-worship; and at Jericho there was another [Kg2 2:4]. In travelling to these places, which he had done through the impulse of the Spirit (Kg2 2:2, Kg2 2:4-6), Elijah wished to pay a farewell visit to these several institutions, which lay on his way to the place of ascension and, at the same time, from a feeling of humility and modesty, to be in solitude, where there would be no eye-witnesses of his glorification. All his efforts, however, to prevail on his attendant to remain behind, were fruitless. Elisha knew that the time was at hand, and at every place the sons of the prophets spoke to him of the approaching removal of his master. Their last stage was at the Jordan. They were followed at a distance by fifty scholars of the prophets, from Jericho, who were desirous, in honor of the great occasion, to witness the miraculous translation of the prophet. The revelation of this striking event to so many was a necessary part of the dispensation; for it was designed to be under the law, like that of Enoch in the patriarchal age, a visible proof of another state, and a type of the resurrection of Christ.
4 Kings (2 Kings) 2:3
kg2 2:3take away thy master from they head--an allusion to the custom of scholars sitting at the feet of their master, the latter being over their heads (Act 22:3).
4 Kings (2 Kings) 2:8
kg2 2:8Elijah took his mantle, and wrapped it together, and smote the waters--Like the rod of Moses, it had the divinely operating power of the Spirit.
4 Kings (2 Kings) 2:9
kg2 2:9Elijah said unto Elisha, Ask what I shall do for thee--trusting either that it would be in his power to bequeath it, or that God, at his entreaty, would grant it.
let a double portion of thy spirit be upon me--This request was not, as is commonly supposed, for the power of working miracles exceeding the magnitude and number of his master's, nor does it mean a higher endowment of the prophetic spirit; for Elisha was neither superior to, nor perhaps equally great with, his predecessor. But the phrase, "a double portion," was applied to the first-born [Deu 21:17], and therefore Elisha's request was, simply, to be heir to the prophetic office and gifts of his master.
4 Kings (2 Kings) 2:10
kg2 2:10Thou hast asked a hard thing--an extraordinary blessing which I cannot, and God only, can give. Nevertheless he, doubtless by the secret directions of the Spirit, proposed to Elisha a sign, the observation of which would keep him in the attitude of an anxious waiter, as well as suppliant for the favor.
4 Kings (2 Kings) 2:11
kg2 2:11HE IS TAKEN UP TO HEAVEN IN A CHARIOT OF FIRE. (Kg2 2:11-18)
behold, there appeared a chariot of fire, and horses of fire--some bright effulgence, which, in the eyes of the spectators, resembled those objects.
went up by a whirlwind--a tempest or storm wind accompanied with vivid flashes of fire, figuratively used for the divine judgments (Isa 29:6).
4 Kings (2 Kings) 2:12
kg2 2:12Elisha saw it, and he cried, My father--that is, spiritual father, as the pupils of the prophets are called their sons.
the chariot of Israel, and the horseman thereof--that is, that as earthly kingdoms are dependent for their defense and glory upon warlike preparations, there a single prophet had done more for the preservation and prosperity of Israel than all her chariots and horsemen.
took hold of his own clothes and rent them--in token of his grief for his loss.
4 Kings (2 Kings) 2:13
kg2 2:13He took up also the mantle of Elijah--The transference of this prophetic cloak was, to himself, a pledge of his being appointed successor, and it was an outward token to others of the spirit of Elijah resting upon him.
4 Kings (2 Kings) 2:14
kg2 2:14smote the waters--The waving of the mantle on the river, and the miraculous division of the waters consequent upon it, was an evidence that the Lord God of Elijah was with him, and as this miracle was witnessed by the scholars of the prophets from Jericho, they forthwith recognized the pre-eminence of Elisha, as now the prophet of Israel.
4 Kings (2 Kings) 2:16
kg2 2:16fifty strong men, let them go, we pray thee, and seek thy master--Though the young prophets from Jericho had seen Elijah's miraculous passage of the Jordan, they had not witnessed the ascension. They imagined that he might have been cast by the whirlwind on some mountain or valley; or, if he had actually been admitted into heaven, they expected that his body would still be remaining somewhere on earth. In compliance with their importunity, he gave them permission, but told them what the result would be.
4 Kings (2 Kings) 2:20
kg2 2:20ELISHA HEALS THE WATERS. (Kg2 2:19-25)
Bring me a new cruse, and put salt therein--The noxious qualities of the water could not be corrected by the infusion of salt--for, supposing the salt was possessed of such a property, a whole spring could not be purified by a dishful for a day, much less in all future time. The pouring in of the salt was a symbolic act with which Elisha accompanied the word of the Lord, by which the spring was healed [KEIL].
4 Kings (2 Kings) 2:23
kg2 2:23there came forth little children out of the city--that is, the idolatrous, or infidel young men of the place, who affecting to disbelieve the report of his master's translation, sarcastically urged him to follow in the glorious career.
bald head--an epithet of contempt in the East, applied to a person even with a bushy head of hair. The appalling judgment that befell them was God's interference to uphold his newly invested prophet.