OOC: Eep! Hold on a moment. I need to edit this post. And post faster

Okay, edited!

Ohhh. Abby nodded back to the professor. She had learned about Eratostenes before. Inventor of the leap day, discovered the earth's tilted axis... the list of things he was known for was a good length. The zenith. Yes, she had heard of that too. That was what was used in the Florence Cathedral, if she recalled correctly. To indicate the astronomical signs and time of the day. Gotchaa.

She raised her hand again. "Sir, the reason for this is because Syene is located on the Tropic of Cancer, the latitutde on the earth that represents the sun's path with the season changes," she said. "It also happens to be directly below the sun, which is why the gnomon would not cast a shadow in Syene. However, Alexandria is north of the Tropic of Cancer, meaning it would cast a shadow."

Abby listened as the professor went on about the distance between Syene and Alexandria. Oh, this one was good. Her hand went up again. "These number are important because Eratosthenes couldn't walk all the way around the earth to measure its distance," she said. "Instead, by using the distance between just Syene and Alexandria plus the difference between the zeniths at the two cities, he could conclude that the distance between Syene and Alexandria is one-fiftieth the total circumference of the earth. Then, he could just use ratios to find the total."

Trixie raised her hand to correct the younger student. She had mentioned this just a minute ago, had he not heard her. "The measurements could be used to calculate the circumfrence of the Earth. Although his measuremnets couldn't be completely accurate seeing as he was a little out at places and Alexandria isn't exactly south of Syene" she declared. "I know the measurements sir. His original estimate was 5000 stadia which in todays terms would be 800km." she smiled.

Chris raised his hand and lookde at the Professor. "Well I am not sure if this 'counter' actually used his feet to count or sometiye of ruler or what not, but regarless of his methods, it is pretty certain that he was not too accurate. Althought his efforts would get him something close to the actual number. But the reason he did this was to try and get the circumfrence of the Earth, but I have a question Professor I am not exactly sure how this small measurement could help get the whole circumfrenece of the planet." the Gryffindor was very curiosu about this guy they were learning about.

OOC: As usual, the other posts have been noted. :>

"It is, but even here, maths is necessary. I would hate to think of what would happen to your potions if you did not measure correctly."

"Not so much the light or the view, but... Miss Force, do you know?" The girl had an almost frighteningly excited grin on her face. Risu pointed at her.

"That he did, but I was looking for an exact explanation as to how. Very well." Risu indicated the picture that the quietly humming projector had thrown against the wall behind him.

"The importance is this: Eratosthenes knew the distance compared to a full circle. Which is to say, seven degrees. But he needed a figure to compare those seven degrees against - and that is why he made someone measure the distance between Syene and Alexandria."

He turned back to the class. "To cut a long story short, the king's step counter estimated the distance to be about 5000 stadia, or 835 kilometres. So... seven degrees corresponded to 5000 stadia in Eratosthenes' time. I will spare you the calculations," he smiled thinly at the girl who had spoken up earlier, "but the end result of those calculations was a circumference of the Earth of about 230 thousand stadia."


"You explained it very well," Risu said with a nod. "That's exactly what he did. Now, depending on how long you take one stadium to be, you get greatly differing results. But if you take the value a stadium had in Egypt at that time, about 160 metres, Eratosthenes calculated the circumference of the Earth to an accuracy of only a few percent. Our best estimate today is a little more than 40,000 kilometres at the equator. Eratosthenes arrived at 41,700 kilometres."

He spread out his hands. "Very impressive for an ancient living more than 2000 years ago, and very impressive for someone who used nothing more than a stick, some observations and a tiny bit of maths. Now..." He flicked his wand, and the projector turned off. "We're nearly done, but what were some of the limitations of Eratosthenes' method?"

Trixie raised her hand. "Do you mean how he can't be exactly right?" she asked. "Well for a start Syene isn't exactly on the Tropic of Cancer, but slightly North, and he used this in order to make his measurements. And as I mentioned just a minute ago, Alexandria isn't exactly south of Syene. The last is that the sun appears as a disk located at a finite distance from the earth instead of as a point source of light at an infinite distance" she siad sounding like a ravenclaw. Woah. "So therefore the distances weren't exactly reliable" she smiled. "But giving him credit, his measurements were extremely close to the actual measurements. Which as you said was pretty impressive for a guy of his era" she giggled.

"Some limitations were that overland distances weren't reliable because of the travel on the Nile river, they were also not completely accurate because of the locations were not exact as well, but an estimate," Selena tried.

Dang, he had a point. Math was pretty important, lucky for her, she sucked at it. But as soon as he put his latest question out, she was lost again.

Simon put up his hand. "the accuracy of his calculation was limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the earth instead of as a point source of light at an infinite distance. " He said before continuing. "The greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable." Simon hoped that he was right but wasn't sure.

Chris raised his hand to answer the Astonomu Professor's question, "Professor, a limitation of his method was that the angles like that can only be measure at about a quater of a degree and the distances that he covered on land were not reliable enough to make the equation work out correctly." the Gryffindor stated. It was too bad really, the man was a good thinker for the time at least.

Kel shook his head at his notes, which were pretty much a mess of numbers and words that Kel didn't exactly understand. Sure, he liked astronomy, but things like this confused him. He liked 'Which planet is this? Which planet is this?' much more. But of course, that would've been too easy, huh?

Limitations? He raised a hand. "It...took a lot of time, work, and effort?" he answered, not exactly sure if those things counted as limitations. But, hey, at least he tried.

Phyre listened to the correct answers and sighed, raising her hand to try again. "If any calculations had gone wrong, the entire measurement could be off," she said shakily. "Furthermore, if he had used a different amount as a stadia, then he would have been wrong, and yet credited to this day to be extremely accurate, as accurate as one could be with the technology available at the time. Because of the differing measurement systems and opinions within the same measuring system, his method, while perfected by himself, would not be able to be used by many others of his time. While it's not a limitation on Eratosthenes himself, it would effect his method."

Santi was surprised at how he actually liked it when a professor agreed with him. He'd never been one for participation before. But deciding to give it another go, he raised his hand. "That it can't be used for much else," he suggested. "Not to mention its lack of accuracy. Any error would multiply by fifty times due to scaling up." Santi sat back again. Okay, that was it. He was done talking... perhaps. He had no idea why, but this astronomy discussion made him want to input... why would that be?

Limitations, now. Abby thought for a moment. "Of course, there's the obvious one," she said. "By step counting, the distance he found between Syene and Alexandria couldn't be perfectly accurate." Now for the less obvious ones. "Also, Syene can't possibly be exactly on the Tropic of Cancer. That means that the distance between Syene and Alexandria is a little over or under one-fiftieth of the earth's circumference."

"I agree, but we are the ones who don't know how much a stadium was. Eratosthenes was certainly aware of the length of one, but that knowledge has been lost. But if we take his value of 5000 stadia for the distance between Alexandria and Syene, then we can get an approximation of how long he and his contemporaries thought a stadium was."


"You are all correct," Risu said, nodding, "although the exact positions of Syene and Alexandria were probably the smaller problem. As you've pointed out," he nodded in the direction of the Head Boy, "distance measurements on land were very unreliable. Nowadays, with satellites and aeroplanes, measuring the distance between two points on Earth is rather trivial. But in the time of Eratosthenes, a linear distance was extremely difficult to procure. But even so, Eratosthenes' estimate was valid for a very long time, and it's one of the most famous scientific experiments of the entire ancient world."

Risu chuckled. "It certainly did take a lot of time, but those were probably not limitations to Eratosthenes. He compiled a three-volume encyclopaedia on geography, and I would guess that that took him much longer than calculating the Earth's circumference. All he had to do was wait for the distance estimate between Alexandria and Syene."

He clapped his hands. "And with that, we shall conclude this lesson. Homework... is on the board." He flicked his wand over his shoulder, and writing appeared. "An essay on your evaluation of the scientific method, or, if you are artistically inclined, a detailed sketch and explanation of Eratosthenes' famous experiment." He dropped his wand on the desk. "Thank you all for coming. If you have any questions about the lesson or your homework, I'll be available in my office."

Risu began gathering his things.



Homework

Choose one:

Write a short essay discussing the merits and limitations of the scientific method. (3+ paragraphs)

Give a detailed explanation, including an original drawing, of Eratosthenes' calculations of the circumference of the Earth.

Homework can be handed in until 11.59pm GMT on Saturday, 29 May. This assignment is worth up to 15 points.

OOC: Make sure to read the submission guidelines carefully.

Chris nodded as the Professor agreed with the inconvience and unaccurateness of the way Eratosthenes caculated the land distances. Chris raised his hand to add something to that. "Professor wouldn't another factor to the inaccurateness of the measurement be the fact that if he was measure on the actual ground, he would have to factor out the amount of space that he measure going up hills and such correct?" the Head Boy said as he collected his things and scribbled down the homework assignment.

He hadn't need all these heavy encyclopaedias after all, then. Risu, trying to decide whether to carry them into his office again or just leave them in the classroom, looked up to see the Head Boy address him.

He nodded. "To be sure. A further thing to keep in mind is that, unlike a straight linear distance measurement, natural obstacles might have prevented the travelling counter to head directly for the other city. In other words, it's quite possible that he had to travel around things."

Chris nodded. "But if he had to go around around things wouldn't that add to the distance calculated?" he thought for a second. "Well I guess he could have measure the length of the Natural obsticle and then just subtract it." the Head Boy said thinking harder. But that was way back then and the lesson as over.

The Gryffindor did, however, notice that the Professor began to fuss with the large stack of rather Heavy looking encyclopeadias. "Professor Risu, would you like some help with those?" the Head Boy asked with a small smile.

Keeley inwardly jumped for joy. Yesssss!! The lesson was over!!! She quickly copied down the assignment quickly and packed away her things. Aaaand, now she could leave! She skipped out of the room cheerily, wondering where she would go. Outside, perhaps.

"That's certainly possible," Risu agreed. "In fact, I might go so far as to say that it's even likely that that's what happened. But I am not a geographer, nor a historian, so I couldn't tell you if any large obstacles between Alexandria and Syene even existed at that time. Travelling that distance was obviously a difficult affair, but it might not have been impeded by anything bigger than hilly grounds."

He thumped the encyclopaedias, raising a cloud of dust. "Thank you, but no, that's alright," he said with a slight smile. "I might just store them in the classroom. And I guess," he pointed at his wand, "I could also levitate them back. I keep forgetting I'm around witches and wizards again now. Could use magic freely if I needed to."

Class was over? Huh?

Turning her attention back to everyone, Evelyn sat there for a moment, looking at people who were leaving. Wait, they were leaving. Class really was over? Crap...

Looking down at her notebook, she saw there were pretty much no notes except little doodles of stars and dragons. Dangit! Closing her notebook, she stuffed it, gently, into her bag and stood up. Next time, she soooo was not going to be sitting next to the window. It was too distracting.

"Bye Professor." she mumbled as she walked passed him and to the door. Now, the long descent to, whatever class she had next. Or was it a break? If it was a break, than she was going to bed...

Oh, the lesson was over. Abby gathered her things, putting away her quill and ink back into her bag. Soo, she had liked Astronomy. Yup! A lot better than she had at Salem, at least. She scribbled down the homework, stuffed her parchment into a notebook, and slipped it into her bag before slinging it over her shoulder. The professor was nice too. "Thanks for the lesson, Professor Antares," she said with a smile as she walked out the door.

Amy scribbled down the homework in a planner, said packed up her stuff saying goodbye proffessor and walked out of the lesson , inwardly punching the sky becuase she could go out into the boiling sun

Selena quickly scribbled down the homework and grabbed her things stuffing them into her bag. Lessons were over and she had homework to do. Selena felt depressed. She needed chocolate. She popped one into her mouth and swallowed before waving at the teacher. "Till next time, Professor," Selena said before she left the classroom.

Sapphyre smiled as the class was summed up, and she stood, using her walking cane to navigate her was out of the classroom. At the door, she smiled slightly and turned back to the professor, who seemed to be having a conversation with another student. "Good day, Professor Antares. The lesson was great... even if I didn't understand till the end."

Maddie packed away her things neatly into her bag, and hefted it onto her shoulder
'Proffessor?' she said 'If I wanted to come back here later tonight, would that pass you gave me still work?' she asked