The story of Sage Agastya going towards south is mentioned in Skanda Purana, Book II: Vaishnavakhanda, Section I: Venkatcala Mahatmya, Chapter 31. It was narrated by Sage Bharadvaja to Arjuna. This incident happened when all the Devas, Bhutas and other living beings went to see Lord Shiva marriage on Himalaya. Because of that, Earth became unbalanced, so Lord Shiva asked sage Agastya to go to south to balance the Earth.
- Formerly the Goddess, the daughter of Daksa, was subjected to insult by her father. After forsaking that body she became the daughter of the Snow-clad Mountain (Himalaya).
- The Mountain (Himalaya) was approached and requested by the Seven Sages. Hence he was ready to give his daughter in marriage to Mrtyunjaya (Siva).
- The Bull-emblemed Lord of the universe came to the residence of Himavan, named Osadhiprastha, in order to marry Sarvamangalā (Pārvatī).
- At his bidding all the living beings, both mobile and immobile, came there to rejoice in the felicity and prosperity of the Lord of Bhutas (goblins).
- The earth in the northern region became heavily burdened with their weight and caved into such an extent that it reached the nether worlds.
- The southern region became very light because there was no burden on it. Hence it went up, on seeing which everyone became frightened.
- On realising this change in the position of the earth, Mahesvara turned towards Agastya and said, “Come here, O highly intelligent one.” Then he spoke these words:
21-22. “Since all the Bhutas have come down here, the earth has become over-burdened by their weight. It has undergone a great alteration. Hence it behoves you, O highly intelligent one, to level up the earth. How can this be done by anyone other than you?
- Indeed you are born of my splendour. You are engaged in the protection of the Worlds. Hence, O my dear one, at my instance level up this earth.
24-26. You must not stay here among all those persons who have come down here eager to witness my marriage celebration. If you stay here, no one will be competent to set right the change in the level of the earth. Hence, O sinless one, you must go. Wherever you stay, I shall reveal unto you this form of mine resplendent in my marriage with the daughter of the Mountain.'
- After saying this Mahesvara embraced him and bade farewell to him. Saying “So be it', the sage bowed down to him and went in the direction of South.
- When Agastya, a tiger among sages, went to the southern region after crossing the Vindhya mountain, the earth became level.
Now, Sage Agastya going to south for breaking pride of Vindhya is described in Skanda Purana, Book IV: Kasi-khanda, Section I: Purvardha Mahatmya, Chapter 1-5. The story goes like this: Vindhya was growing his size and at one time, he became so large that he was obstructing the path of Sun. So, all became frightened. Then, Sage Agastya along his wife Lopamudra went there and ordered him to bow down until he again came here. So, Vindhya bow down in respect of Sage Agastya. And Agastya never went to North after that. So, Vindhya is still waiting for him.
I am providing some excerpt from chapter 5.
- The sage went ahead a few steps with sweat drops appearing on his forehead. By then, it appeared as though the ground shrank below with the fear, "I will be doomed for not rising up by way of revering him.'
- Seated as though in the vehicle of his penance, within half the period required for twinkling (of eyes), the sage saw in front of him the lofty Mountain who had blocked the path of the sky.
54-56. On seeing the sage standing before him along with his wife, the Mountain trembled. The sage who had destroyed Vatapi, the brother of Ilvala, appeared to be blazing like the fire at the time of the final annihilation with three fiery flames, one arising from the separation from Kasi and the other two from the power of penance and the wrath (of the sage). The Mountain became dwarf-like as though he was desirous of going deep into the earth. He said: "Let me be granted the favour of being commanded. I am your servant."
- O wise Vindhya, you are good and you know me factually (i.e. my prowess). Be short in stature till my return.
58. After saying this, the sage, the storehouse of austerities, made the southern quarter duly possessed of a guardian in the form of his footprints in the company of that chaste lady (in that direction).
59-60. When the excellent sage had gone, the trembling Mountain anxiously looked in that direction and thought: "If he has gone, well it is. I am reborn today as I have not been cursed by Agastya. There is no one blessed like me.'
- At that time, Aruna, conscious of the opportune moment, drove the horses. When the movement of the Sun was revived as before, the whole world derived great relief and normalcy.
- The Mountain remained as though suppressed by the great burden of the thought, "Perhaps the sage may return today, tomorrow or the day after.'
- The sage has not returned till today. Nor has the Mountain increased in size like the tree of wishful thinking of wicked people.