Part One: Foresight
There was a knock on the door. "C'mon in," Hagrid called to whoever was outside.
The door opened to reveal Albus Dumbledore, Headmaster of Hogwarts School of Witchcraft and Wizardry.
"Good afternoon, Hagrid," Dumbledore said pleasantly, stepping inside the large one-room hut.
"'Afternoon, Professor!" Hagrid replied, beaming as much as his blackened eye would permit. "Cuppa tea?" he offered.
Hagrid set two enormous tea cups on the round wooden table as Dumbledore sat down.
"That's quite a case of periorbital hematoma, Hagrid," Dumbledore said, smiling.
"Er, what?" Hagrid said confusedly, sloshing tea onto the table.
"Your eye," Dumbledore said, nodding at it politely and still smiling.
Hagrid set the kettle down, and touched his eye self-consciously, wincing as he did so. "Oh, well, er, this is from... I was out in the forest," he concluded.
"I see," Dumbledore said kindly, taking the closer tea cup and lifting it to his mouth.
Hagrid looked at him nervously and took his own cup, accidentally pouring half of it into his beard.
"I have a favor to ask of you, Hagrid," Dumbledore said, setting his cup down on its saucer.
"Anythin', Professor," Hagrid replied after draining the rest of his cup, into his mouth this time.
"You're still on good terms with the centaurs, correct?"
Hagrid nodded. "'Course I am. Wouldn' dream of ever doin' 'em any harm, an' I've helped a fair few of 'em outta tight spots before, so I've earned my respect with 'em."
"Good, good," Dumbledore said, not impatiently. "I would like you to go into the forest and request for them to meet with me at the edge of the forest when the sun's azimuth is at 264 degrees."
Once again, confusion spread across Hagrid's face. "The sun's... wha'?"
"The sun's azimuth," Dumbledore repeated.
"Meet you when the azi... thing is at two-hunnerd six'y-four degrees."
Dumbledore nodded. "They'll understand." He finished his tea and stood up. "Thank you for the tea, Hagrid, it was wonderful as usual. I shall return at five o'clock to meet with the centaurs." He smiled and walked out, patting Fang on the head as he went.
When the sun's azimuth reached 264 degrees, or precisely five o'clock, two centaurs emerged at the edge of the forest. One had red hair and a chestnut body; he stroked his beard in contemplation as he gazed squintingly at the sky, his red tail flicking gently. The other appeared to be somewhat younger, with white-blond hair, clear blue eyes, and a palomino body; he looked in the direction of Hagrid's hut, watching as Dumbledore strode towards them.
"Ronan, Firenze," Dumbledore said, nodding at each one in turn, "I thank you for venturing this far from the safety of the forest to speak with me."
Ronan nodded as he turned his gaze to Dumbledore. "Great changes are soon to come," he said in his melancholy voice, as though he had not heard what Dumbledore had said.
"Indeed they are," Dumbledore agreed; "I have an offer that I would like to propose to you."
"What kind of offer?" Firenze inquired, with a curious swish of his tail.
"I shall soon be needing to replace a member of my teaching staff, this very night, if I am correct. I am aware that you are well skilled in reading the motions of the planets, among other divinations."
"You are asking us to enter into your service?" Ronan asked, staring boldly at the wizard.
"I am asking you to confer your wisdom unto the students of Hogwarts, with no bounds placed upon your freedom."
Ronan considered this phrasing; he stroked his beard, musing over Dumbledore's proposal.
"I believe the others would disapprove," he said finally, in a morose voice. "Bane particularly would criticize acceptance of such an offer..."
Firenze took a step forward and addressed Dumbledore. "Bane has always stressed neutrality towards humans, but the heavens say that adhering adamantly to that stance will be our demise."
"Firenze," Ronan said in warning, intent to silence the younger centaur.
The palomino flicked his tail in irritation. "Do not deceive yourself, Ronan - you know what I speak is truth."
Ronan returned his gaze skyward.
Firenze turned back to Dumbledore. "I do not fear Bane's wrath, nor do I think you make this offer out of ill will. I trust Hagrid, and he places great faith in you, Albus Dumbledore. Therefore, I shall accept." He bowed slightly to Dumbledore.
Unbeknownst to the others, a third centaur stood in the nearby gloom of the forest, out of sight but within earshot. Upon hearing Firenze's agreement to serve at Hogwarts, he turned and cantered deeper into the forest.
Hearing the sound of hooves receding, Ronan turned and peered into the forest. He saw a flash of black hair and a chestnut brown body.
"Magorian," he said, and, with a glance at Firenze, he turned and galloped after the other centaur.
---"Oh, really, Professor McGonagall? And your authority for that statement is...?"
"That would be mine."
"Yours, Professor Dumbledore? I'm afraid you do not understand the position. I have here an Order of Dismissal signed by myself and the Minister of Magic. Under the terms of Educational Decree Number Twenty-three, the High Inquisitor of Hogwarts has the power to inspect, place upon probation, and sack any teacher she - that is to say, I - feel is not performing up to the standard required by the Ministry of Magic. I have decided that Professor Trelawney is not up to scratch. I have dismissed her."
"You are quite right, of course, Professor Umbridge. As High Inquisitor you have every right to dismiss my teachers. You do not, however, have the authority to send them away from the castle. I am afraid that the power to do that still resides with the headmaster, and it is my wish that Professor Trelawney continue to live at Hogwarts."
"No - no, I'll g-go, Dumbledore! I sh-shall l-leave Hogwarts and s-seek my fortune elsewhere -"
"No. It is my wish that you remain, Sibyll. Might I ask you to escort Sibyll back upstairs, Professor McGonagall?"
"Of course. Up you get, Sibyll..."
"And what are you going to do with her once I appoint a new Divination teacher who needs her lodgings?"
"Oh, that won't be a problem. You see, I have already found us a new Divination teacher, and he will prefer lodgings on the ground floor."
"You've found -? You've found? Might I remind you, Dumbledore, that under Educational Decree Twenty-two -"
"- the Ministry has the right to appoint a suitable candidate if - and only if - the headmaster is unable to find one. And I am happy to say that on this occasion I have succeeded. May I introduce you?"
Firenze trotted into the Great Hall to stand beside Dumbledore, alarming several students standing near the open doors. His tail flicked nervously as he looked around at the students.
---"This is Firenze. I think you'll find him suitable."---
Note: For those of you who were wondering, the sun's azimuth is a way of determining it's position in the sky (as far as I can tell at least...). I obtained the information from an online Sun Position Calculator using the latitude/longitude for London. So, it's about as accurate as I can get for spending approximately 10 minutes' worth of research on the subject. I assumed that centaurs would be more familiar of telling time according to the sun, as I'm pretty sure that they don't have watches. :) Thanks for reading!