13th June, afternoon: The first lines on the map

Three points in a line made sure of the line's being straight, Cotton knew that - if he lined the rear sight up with the foresight and both were in line with the target, it made a straight line and that was the path the bullet took when he pulled the trigger, so it made sense that the same thing was true when drawing a line on a piece of paper.

He looked around. "I'll go, sir... unless Rottlaender wants to?" The younger Rifleman would probably get there before he could - Cotton wasn't sure he could muster the energy to run everywhere the way the younger lad did.

Freddie became wide-eyed for a moment. He hadn't been able to follow the Captain's explanations and was rather uncertain what had been asked of the men before.

"You mean, hold the Stange on the stone there?"

When Captain Torrington nodded and repeated, "Hold the pole upright on that rock, yes, until I tell you otherwise.", he nodded eagerly and snatched the brightly painted wooden stick from the Captain's hand. Before anybody could say anything, he had turned and was already galloping off towards the small rising.

Edward exhaled and watched his batman run over the short grass. "I'm getting old!", he complained to no-one in particular, then waved one of the guardsmen to follow him and keep his eyes open.

When Rottländer had taken his position, standing as upright as the pole and concentrating so much on holding it straight that his brow was heavily furrowed, Edward took the alidate again. Placing the centre over their previous cross, aiming the instrument towards the pole and marking out that line on the paper as well took only a minute. Then he took the board with the paper down and showed it around.

"There! The second side of our triangle. Now we need to take the equipment over to the other peg to complete it. Pye, you already had your moment of glory, but would someone else care to try to place the tripod and level the table? Cotton, how about you?"

"Everything alright here?"

Padstowe sauntered up to the group, having spotted the surveying equipment in the company of his friend Vickery, an unfamiliar Engineers officer and a lot of confused Guardsmen and Riflemen.

Edward looked up to see an unknown officer come towards them. He wasn't quite sure what regiment the uniform indicated, but he could see that the man wore the insignia of a captain. He touched his hat politely and answered:

"Yes, quite well, thank you, Sir. We're undertaking a little survey."

Padstowe glanced at the rifleman currently wrestling with the tripod and resited the urge to raise his eyebrows.

"And training up a few fresh sappers by the looks of things," he commented. He was not sure of the Engineer's humour, but he knew that Vickery would take the comment in the spirit it was meant.

"Don't snatch," he began, addressing Rottländer. Too late. He managed not to roll his eyes. "If you're getting old, I feel positively ancient," he said to Torrington with a smile, and turned as Padstowe came to join them.

"May I introduce Captain Padstowe, of the 50th Foot, currently acting as an Exploring Officer?" he said. "Captain Torrington, of the Royal Engineers." He wasn't quite sure whether Torrington preferred to use his title in the Service, or not, and decided that decision was best left to Torrington himself.

Padstowe smiled and held out his hand to Torrington, grateful to Vickery for the introduction.

"A pleasure, captain."

Edward shook hands, not smiling, but with more animation than he would have shown in London. He loved his occupation, and even though he kept it well in check, doing the practical work held the same appeal as a new toy had for a boy.

"Likewise, captain. I'm more than glad to meet a man who I hope can give me some information about the landscape here."

Some commotion made him turn, but it was only a soldier who had learned that holding fingers between the legs of the tripod while collapsing it wasn't exactly wise. Rottländer was still standing some distance away, patiently - or at least not yet openly fidgety - holding the rod. He turned to Captain Padstow again.

"It's their first day of training, but I hope they will do better than sappers. Although I believe blowing up things would be quite to the liking of some."

Padstowe mentally marked Torrington down as a rather serious fellow, but he did not seem unpleasant. A little preoccupied with work, perhaps, but he was correct in highlighting their professional interest in each other.

"Most of what I gather goes back to Scovell, but you are welcome to peruse my observations on the terrain. I have recently returned from patrolling to the north-east of here."

"I would hope my men would have rather more... finesse... than to want to blow up everything in sight, Captain," Vickery said, with an eyebrow quirked.

"The good Captain here is teaching us how to draw maps, Captain," Vickery said, turning back to Padstowe. "Perhaps you would care to join the lesson? Or at least, join me in observing it."

"I should be glad to - that is, if Captain Torrington does not object?"

"Certainly not, Sir. It would be my pleasure."

The warmth in Edward's voice made this more than just a polite answer. He detailed another two guardsmen to hold a rod right atop the peg they were standing next to, then led the two officers over to where the soldiers by now had managed to deploy the plain table. He checked it over and nodded. Probably they would take less care once they saw the task as routine, but right now, the surface was perfectly aligned. He hooked the U-shaped plumb around his drawing board again, matching the end with the other cross on the baseline, and balanced it over the table until the plumb was centred over the peg. Then he set it down.

"The end of the baseline I drew on the paper is now centred over the peg, but it is still pointing a bit in the wrong direction. To correct this, I will lay the alidate along the line and take a back-sighting. In other words, I will look through it and turn the board until I have aimed it at the rod on the other peg. This part is a bit difficult, because the cross, the point on the map that represents this peg, must of course stay right above the peg itself."

The engineer demonstrated what he had tried to explain, holding the alidate on the board and turning it until the crosshair of the instrument was neatly in the middle of the rod and the plumb above the peg. He was a bit out of practice, having worked with a theodolite mostly in the last year, but still he thought he had done this quite neatly, without too much awkward rearranging.

"Now, I do just what I have done on the other side, lay the alidate over the end of the line, aim it at Rottlaender's peg ... mark the endpoints ... draw a line through them ... and here it is. Our first, small part of a map. Where the lines cross, that small rising is - only of course, the map has smaller scale, so it is only about ..."

He checked the distance with his long steel ruler.

"... 39 inches. We have defined that one inch on the map represents a yard on the ground, so Rottlaender should be 39 yards, or 117 feet away. Measure it, if you like, and take a look at the map. I won't lift it up, because we would have to realign it for the next step again then, but I think you're all tall enough to see anyway."

He stepped back from the table to give the soldiers some room to look at it, but also to remove himself from the proceedings now. They would probably be much more willing to have a proper look at things when there was no officer peering over their shoulders. With a wry smile, he explained to Padstowe:

"Even if they manage to make the whole thing topple over, there isn't much that they can wreck. Measuring things with an alidate has come out of fashion, as it often lacks precision, but it is perfect for explaining the principles, if you don't want to expose your precious theodolite to experiments. And of course it is much more understandable if one can see actual lines on a paper instead of just numbers."

Pye remained standing close to the devices and observed quietly. He stole a glance at the newly arrived officer sometimes, then averted his gaze again to see what the men had managed to do or what Torrington had explained and showed them. He inched closer to have a better look, still struggling to grasp the whole concept. It was complicated but he tried to make it less so in his head.

Even that was easier said than done. He persisted stubbornly however. If the officer believed them able to grasp this concept he could atleast attempt to. He glanced at Freddie and grinned.

The young German grinned back, balancing his rod on the assigned stone. He had no idea what they were doing, but it was certainly better than the usual drills. He only hoped Pye had understood what the Captain had tried to explain.

((OOC - resurrecting this thread because it's fun, dammit!))

Vickery retired to the sidelines with Padstowe, still close enough to see what the Engineer and his helpers were doing, but not so close that the Captains' presence would distract them.

Cotton had been carefully adjusting the set of the table, as Pye had earlier, until it was exactly level, when he stood back and looked at the Engineer.

Torrington checked it and nodded approvingly.

"Very good! Now we just repeat what we have done before - take a backsighting to the last position we were in to align our map ..." He did just that. "And then to the other rod ... making another triangle."

He pointed to the new collection of lines.

"And that is all the secret of map-making ... well, not quite, but the better part of it. If you have two points you know, and can get the directions to a third from both points, you know where that third one is, too. Angles always are the same on paper as in the landscape, and all measurements of length are reduced by the same ratio on paper. That means if something is a hundred times as long in nature as it is on the map, and the map is properly made, all other things on the map are a hundred times as long in nature as well. If you remember these three rules, you have mastered nearly all the mathematics involved."

He looked at his 'students', then at Vickery and Padstowe, waiting for questions.

"So... it's all just triangles, sir?" Cotton rubbed at his ear, trying to picture exactly how triangles worked when trying to put in hills or rivers, and couldn't. "So... how d'you put in a stream or summat, sir? D'you make a triangle for every bend or summat, to make it look right?"

Edward nodded.

"Yes, exactly. Whenever some line isn't straight, it is divided into smaller parts which are closer to the shape of the original. And each of the parts form one side of a triangle."

He searched for an analogy:

"Hm, it's really connecting dots on paper. If you have just two dots on it, and you connect them with a straight line, it is the distance as the crow flies, but not the line of the river."

He made a quick sketch in his pocket book to demonstrate.

"If you add a third point here, it is already better, but still not very much like the curve of the river. But add a few more, and you can come pretty close. At some point, you can even paint in the rest by hand, smoothing the lines a bit."

He drew a base line on the concave side of the 'river'.

"And if we choose the points well, we need only to put the measuring instrument in place at two points. Here and here, with a fixed distance between these two points."

He lightly marked out the triangles.

"Oh.... so..." Pye was contemplating the explanations. "....I think I understand." He said sheepishly. He was not sure and he would certainly not want to be told to present his newly gained knowledge. He didn't even know to work with numbers too well or how to write them down.

"That's how you know how long we have ter walk ter get t' places too?" He asked.