The Elms, Wickshire, Cumbria
20 June 1015
My dearest cousin Armand,
No doubt you have been worried and disturbed by the news I've been sending you. You might even have enough affection for Brother Edward that you are distressed by his plight! I am sure I never observed such whilst you were here in Cumbria, but then I have been surprised to learn that I harbor considerable such affection myself.
Poor Edward's condition has been growing worse day by day. He seems to be in a fog, has nothing to say, does not respond to questions. He goes through the motions of his day, dressing, eating, driving to the Grimsbys, and so on; and perhaps he is more animated when he is with them, I do not know.
If you have been so troubled, you may set your heart at rest—or, if not at rest, you may rein in your heart's gallop to a gentle walk. We have determined what those hags have done, and we have plans in train to put an end to their wickedness.
You will recall from my last that the former Lieutenant Archer—and I have still not gotten a satisfactory answer from him about that—rode off at speed to find someone who might help. He returned yesterday morning with an older gentleman, a cheerful looking fellow in tweeds.
"Miss Montjoy, may I present to you Dr. Tillotson of Edenford University. He was my tutor during my brief time there, and I believe he can help us."
"Miss Montjoy," he said, taking my hand. "I am delighted to meet you. It is rare to find a woman who is inclined to the wizardly arts."
"Inclined but in no way proficient, Dr. Tillotson."
"We shall see! Now, as to your problem, I believe I know what has been done here. A most incompetent display, I may say, Miss Montjoy, quite leaving aside the wickedness. For I must tell you that it is quite out of court to include ordinary men and women in any magic geometry. Other wizards, sometimes, when collaborating on a major working, you know, but ordinary men and women, never."
"Is it against the law? Ought we to summon the Runners?" asked Blightwell, whom I had asked to join us.
"Against God's law, most certainly, Mr. Blightwell. But as for the King's law, the Royal College of Wizards has an…arrangement. We shall find out who assisted your neighbors in these endeavors, most assuredly, and put a stop to their antics."
I could not help but shiver at the chill in his tone—a shiver, but I must confess, a great deal of satisfaction as well.
"Now, Miss Montjoy, attend." And so saying, Dr. Tillotson took a notebook from his pocket and drew a diagram, which he handed over to me:
"This is the state of affairs during the first figure of your gallivant, yes? Wallace Hampton is partnered with Miss Grimsby, Edward Montjoy with Miss Willoughby, Lieutenant Pertwee with Miss Matilda Grimsby, and Edward Hargreaves with yourself."
"Yes, exactly so."
"At some moment, most likely just prior to the end of the figure and the changing of partners, the Misses Grimsby invoked the spell. That needn't mean that they are wizards, Miss Montjoy, only that they were given some means of triggering it."
"I never thought they were, Dr. Tillotson, for I have met them. Malicious, yes; incompetent, perhaps; cunning, certainly; intelligent, no."
"Quite. Now, what resulted from their efforts is what we might call a double unterminated partial Langston Transform." And then he looked at me expectantly. I tell you, my dear Armand, I have seldom felt so put upon the spot! Not even when—but doubtless you are tired of hearing about the duck pond.
But a Montjoy rises to the occasion.
"I see. Double, because repeated twice, one for each of the Grimsbys"
He nodded encouragingly.
I continued, "Partial, because power was only applied to some of the nodes. I am guessing that that would be the Grimsbys again."
"It is of all things likely, Miss Montjoy."
"Unterminated—" I began, and felt a chill strike me to my heart. "But that means that the magical power might run anywhere! One must always keep one's geometry properly terminated, Arcane Geometry is quite clear about that, though I had no idea what that might mean until just now. Are you then saying that the effect on Lieutenant Pertwee and Mr. Hampton was unplanned."
He smiled and nodded.
"And then, a Langston Transform—I do not quite recall, Dr. Tillotson, but I believe it involves moving some quality from one node to another."
"Well done, very well done, Miss Montjoy," he said, and then to Mr. Archer, "You were quite right to bring me, Archer. Quite right." Quickly, he drew another diagram and handed it to me. "And this is what eventuated."
"These numbers," I said, "4, 3, 2, 1—is that the amplitude of the magical power? So the power transferred from Agatha Grimsby to my brother Edward, and then to Jane as his previous partner, and thence to poor Mr. Hampton. And it decayed at each step…because the geometry was unterminated?"
"Indeed, Miss Montjoy. In a properly balanced geometry, the power flows to an equilibrium. Here it merely poured out until it was too diminished to have any further effect."
"And that would explain why Lieutenant Pertwee and Mr. Hampton were not as strongly affected."
"We are fortunate, Miss Montjoy, that our errant wizard did not apply more power to begin with, and that the pattern was to some extent self-terminating."
"Self-terminating—oh, I see. You mean that each foursome exchanged partners, rather than changing with yet more couples down the line." I shuddered. "But that would mean—"
"Yes, Miss Montjoy," said Lieutenant Archer. "In theory, all of the dancers might have been effected. The result could have been immeasurably worse, and much harder to fix."
"We are also fortunate the fellow did not terminate the geometry," said the professor. "If he had done the thing properly, I fear your brother's affections would be permanently affixed."
"How might it have been done properly?" I asked.
"You must tell me, Miss Montjoy."
I thought madly. "Suppose instead of a partial Langston, it had been a full Langston. I mean, suppose the wizard had applied the same magic force to my brother and to Mr. Hargreaves. That would balance the forces, leaving the new couples in equilibrium. And then it would take little power to to terminate it on each side. But that would also leave the Grimsby magically smitten as well, would it not?"
"Bravo, Miss Montjoy. Nearly correct all down the line. Without termination the arrangement would be what we call an unstable equilibrium; whether any power would pour out onto the other couple in each foursome would depend on the delicacy of the wizard's technique. I think we may take it that his technique is lacking in this regard. And the termination would be trickier than you might think, due to the inherent symmetries in the exchange of partners. But on the whole, quite so. There are also other methods, of course."
I blushed, Armand; I admit it.
"Well and good," said Blightwell, who am I afraid was growing impatient. "But how do we fix things. Must we throw another ball?"
"Oh, no, no, no, Mr. Blightwell," said Dr. Tillotson. "That would not serve at all."
"And why not? It worked for them!"
"I can't think of anything more likely to put their backs up," said Lieutenant Archer. "No, we have quite something different in mind. Dr. Tillotson has devised a spell that should serve, but we will need the aid of Miss Willoughby, Lieutenant Pertwee and Mr. Hampton. And yours as well, of course, Miss Montjoy. I have spoken with Pertwee already. With proper timing, we should be able to resolve matters before the Misses Grimsby know what has hit them."
And now I fear I must close, dear Armand, if Morphick is to get this to the post. Expect the best of news in my next!
Your increasingly hopeful cousin,