“I have been considering the matter,” she informed him, after a little while, around a mouthful, “and in all cases, where the angle is ninety degrees, as I suppose you meant to draw it, the length of the longest side must be a number which, multiplied by itself, is equal to the lengths of the two shorter sides, each multiplied by themselves, added.” She swallowed noisily, and licked her chops clean. “Quite an interesting little observation; how did you come to make it?”

“I never,” Temeraire muttered. “It is the Pythagorean theorem; everyone knows it who is educated. Laurence taught it me,” he added, by way of making himself even more miserable.

“Hmh,” the other dragon said, rather haughtily, and flew away.

But she reappeared at Temeraire’s cave the next morning, uninvited, and poked him awake with her nose, saying, “Perhaps you would be interested to learn that there is a formula which I have invented, which can invariably calculate the power of any sum; what does Pythagoras have to say to that.”

“You never invented it,” Temeraire said, irritable at having been woken up early, with so empty a day to be faced. “That is the binomial theorem, Yang Hui made it a very long time ago,” and he put his head under his wing and tried to lose himself again in sleep.

He thought that would be all, but four days later, while he lay by his lake, the strange dragon landed beside him bristling and announced in a furious rush, her words nearly tumbling over one another in the attempt to get them out, “There, I have just worked out something quite new: the prime number coming in a particular position, for instance the tenth prime, is always very near the value of that position, multiplied by the exponent one must put on the number p to get that same value—the number p,” she added, “being a very curious number, which I have also discovered, and named after myself—”

“Certainly not,” Temeraire said, rousing with comfortable contempt, when he had made sense of what she was talking about. “That is e, and you are talking of the natural logarithm, and as for the rest, about prime numbers, it is all nonsense; only consider the prime fifteen—” and then he paused, working out the value in his head.

“You see,” she said, triumphantly, and after working out another two dozen examples, Temeraire was forced to admit the irritating stranger might indeed be correct.

“And you needn’t tell me that this Pythagoras invented it first,” the other dragon added, chest puffed out hugely, “or Yang Hui, because I have inquired, and no-one has ever heard of either of them; they do not live in any of the coverts or breeding grounds, so you may keep your tricks. I thought as much; who ever heard of a dragon named anything like Yang Hui; nonsense.”

Temeraire was neither despondent nor tired enough, in the moment, to forget how dreadfully bored he was, and so he was less inclined to take offense. “He is not a dragon, either of them,” he said, “and they are both dead anyway, for years and years; Pythagoras was a Greek, and Yang Hui was from China.”

“Then how do you know they invented it?” she demanded, suspiciously.

“Laurence read it me,” Temeraire said. “Where did you learn any of it, if not out of books?”

“I worked it out myself,” the dragon said. “There is nothing much else to do, here.”

Her name was Perscitia. She was an experimental cross-breed of a Malachite Reaper and a light-weight Pascal’s Blue, who had come out rather larger, slower, and more nervous than the breeders had hoped; and her coloring was not ideal for any sort of camouflage: the body and wings mostly bright blue and streaked with shades of pale green, with widely scattered spines along her back. She was not very old, either, unlike most of the once-harnessed dragons in the breeding grounds: she had given up her captain. “Well,” Perscitia said, “I did not mind my captain, he showed me how to do equations, when I was small, but I do not see any use in going to war, and getting oneself shot at or clawed up, for no reason which anyone could explain to me. And, when I would not fight, he did not much want me anymore,” a statement airily delivered, but Perscitia avoided Temeraire’s eyes, making it.

“If you mean formation-fighting, I do not blame you; it is very tiresome,” Temeraire said. “They do not approve of me in China,” he added, to be sympathetic, “because I do fight: Celestials are not supposed to.”

“China must be a very fine place,” Perscitia said, wistfully, and Temeraire was by no means inclined to disagree; he thought sadly that if only Laurence had been willing, they might now be together in Peking, perhaps strolling in the gardens of the Summer Palace again; he had not had the chance to see it in autumn.

And then he paused, and abruptly raising his head he said, “You say you made inquiries: what do you mean by that? You cannot have gone out.”

“Of course not,” Perscitia said. “I gave Moncey half my dinner, and he went to Brecon for me and put the question out on the courier circuit; this morning he went again, and the word was in no-one had ever heard of anybody by those names.”

“Oh—” Temeraire said, his ruff rising, “oh, pray; who is Moncey? I will give him anything he likes, if only he can find out where Laurence is; he may have all my dinner, for a week.”

Moncey was a Winchester, who had slipped the leash and eeled right out the door of the barn where he had hatched, past a candidate he did not care for, and so made his escape from the Corps. He had been coaxed eventually into the breeding grounds, more by the promise of company than anything else, being a gregarious creature. Small and dark purplish, he looked like any other Winchester at a distance, and excited no comment if either seen abroad or absent from the daily feeding; and as long as his missed meals were properly compensated for, he was very willing to oblige.

“Hm, how about you give me one of those cows, the nice fat sort they save for you special, when you are mating,” Moncey said. “I would like to give Laculla a proper treat,” he added, exultingly.

“Highway robbery,” Perscitia said indignantly, but Temeraire did not care at all; he was learning in any case to hate the taste of the cows, when it meant yet another miserably awkward evening session, and nodded on the bargain.

“But no promises, mind,” Moncey cautioned. “I’ll put it about, no fears, but it’ll be as many as a few weeks to hear back, if you want it sorted out proper to all the coverts, and to Ireland, and even so maybe no-one will have heard anything.”

“There is sure to have been word,” Temeraire said, low, “if he is dead.”

THE BALL CAME in down through the ship’s bows and crashed recklessly the length of the lower deck, the drumroll of its passage preceding it with castanets of splinters raining against the walls for accompaniment. The young Marine guarding the brig had been trembling since the call to go to quarters had sounded above; a mingling, Laurence thought, of anxiety and the desire to be doing something, and the frustration at being kept at so useless and miserable a post: a sentiment he shared from his still more useless place within the cell. The ball seemed only to be rolling at a leisurely pace by the time it approached the brig, and offered a first opportunity; the Marine had put out his foot to stop it before Laurence could say a word.

He had seen much the same impulse have much the same result on other battlefields: the ball took off the better part of the foot and continued unperturbed into and through the metal grating, skewing the door off its top hinge and finally embedding itself two inches deep into the solid oak wall of the ship, there remaining. Laurence pushed the crazily swinging door open and climbed out of the brig, taking off his neckcloth to tie the Marine’s foot; the young man was staring amazed at the bloody stump, and needed a little coaxing to limp along to the orlop. “A clean shot; I am sure the rest will come off nicely,” Laurence said for comfort, and left him to the surgeons; the steady roar of cannon-fire was going on overhead.