Reading Guide. The question now is: how to get to Lanka to confirm that Sita really is there? To encourage Hanuman to make the jump, Jambavan (leader of the bears who are allied with the monkeys) tells Hanuman the story of Hanuman's birth and the amazing powers that he possesses. As he makes the crossing, Hanuman encounters a fierce rakshasi who tries to devour him. You can read more about this rakshasi at Wikipedia.
Image: The illustration depicts the story from right to left; on the right, you can see Hanuman confronting the rakshasi, and then on the left you can see him bursting out from the inside.
Source. Myths of the Hindus and Buddhists by Sister Nivedita (1914). [500 words]
Then the monkeys grew more hopeful, but when they marched down to the shore and sat beside the heaving sea they were again downcast, and took counsel together sadly enough. Now one monkey said he could bound over twenty leagues, and another fifty, and one eighty, and one ninety, and Angada, son of Vali, could cross over a hundred, but his power would not avail for the return.
Then Jambavan addressed Hanuman, and recalled his birth and origin, how the wind-god had begotten him and his mother Anjana had borne him in the mountains, and when he was still a child he had thought the sun to be a fruit growing in the sky, and sprang easily three thousand leagues toward it; how Indra had cast a bolt at him, breaking his jaw; how the wind-god in anger began to destroy the heavens and earth, till Brahma pacified him and granted him the boon that his son should be invulnerable, and Indra gave him the boon of choosing his own death.
"And do thou, heroic monkey, prove thy prowess now and bound across the ocean," Jambavan said, "for we look on thee as our champion, and thou dost surpass all things in movement and in vehemence." Then Hanuman roused himself, and the monkey host rejoiced. Swelling with pride and might, he boasted of the deed he would accomplish.
Then he rushed up the mountain Mahendra, shaking it in his wrath and frightening every beast that lived in its woods and caves. Intent upon achieving a hard task, where no friend could help and no foe hindered, Hanuman stood with head uplifted like a bull and, praying to the sun, to the mountain wind, to the Self-create and to all beings, he set his heart in the work to be accomplished. He grew great and stood like a fire, with bristling hair, and roared like thunder, brandishing his tail; so he gathered energy of mind and body.
"I will discover Sita or bring Ravana away in chains," he thought, and therewith sprang up so that the very trees were dragged upward by his impetus and fell back again behind him. He hurtled through the air like a mountain, his flashing eyes like forest fires, his lifted tail like Shakra's banner. So Hanuman held his way across the ocean. Nor, when the friendly ocean lifted up Mount Mainaka, well wooded and full of fruits and roots, would Hanuman stay to rest, but, rising up, coursed through the air like Garuda himself.
Then a grim rakshasi rose from the sea and caught him by the shadow, and would devour him, but he dashed into her mouth and, growing exceeding great, burst away again, leaving her dead and broken. Then he perceived the farther shore, and thinking his huge form ill-fitted for a secret mission, he resumed his natural size and shape, and so alighted on the shore of Lanka, nor was he ever so little wearied or fatigued.