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Fenner nervously glanced around the small agora that was formed by the crossing of the streets, waiting for his contact, when he noticed a figure walking along Gate street, a dark spot barely discernable against the lesser darkness that surrounded him. He paused at the corner diametrically opposite from Fenner, and then crossed quickly. When he came near, Fenner saw that he was Gadlin, and relaxed somewhat. Gadlin made the sign, which Fenner returned.
"This way," Fenner whispered, and together they swiftly made their way to Fenner's house. It was a single-room affair, like every other dwelling in the quarter. Fenner lit a lamp, saw that the door and window were sure, and then gestured towards the fireplace. Removing one of the mantle stones, he revealed a cavity which was stuffed with papers. These he took out and spread before Gadlin.
"It came to me while I was working on the problem of degrees of change in higher spaces," Fenner said, a bit of eagerness creeping into his voice. "It occurred to me then that a certain class of functions was similar to its change, but altered in a consistent way. I sought at once to reverse the alteration in a particular case, to find the accumulation of the function, and finding success, I was able to generalize the solution to the whole class I was working with." He turned a final sheet over. "And there's the formula there," he said with some pride.
"This is quite good," the visitor said when he had reviewed the leaves. "It is truly one of the Lost Formulae, burned in what they call the Great Cleansing. The others will certainly be glad to know it has been re-discovered. Now let me show you something." He drew a bundle of papers from under his outer robe, and waiting until Fenner had gathered and stored his, laid them out. "Another of the Brotherhood discovered it recently. It is a process by which most functions can be broken down into a sum of simpler functions of one variable, each factored by the changes of that function."
Fenner looked as the papers. "This looks useful. Might I have a copy?"
"You may keep this one," Gadlin said. "But I will need a copy of what you have there."
"Certainly," Fenner said. He got some blank sheets from under another stone by the hearth, and began copying his formulae. Gadlin waited, and accepted the papers from Fenner when he was done. They shook hands and Gadlin left.
Gadlin went up Gate street for a hundred paces, then turned down an alley, entering into the mazeway of sidestreets in that part of the city, and continued until he had gone perhaps five hundred meters. He came to Penitence Street, crossed, and then ducked into the shadows of an alley on the other side, looking back to see if he had been followed. He saw no sign of Fenner, or anyone else, and so continued down the alley to where it came out on Palace Street, crossed it into another alley, and at the dead end of that alley, knocked on one of the doors, quietly. He was let in.
"What do you have to report?" asked the one who admitted him, when he had made the door fast.
"Fenner is a bright fellow," Gadlin said, laying Fenner's papers before his superior. "He was able to find the integral of the dampened sinusoid on his own; these papers have his formulae, in his own hand. I have supplied him with Taylor's expansion."
"Good," said his superior. He examined the sheets and nodded in satisfaction. "Fenner shows exceptional promise. Any idea how long he was working before we came across him?"
"It must have been years," Gadlin said. "He doesn't appear to have any family."
"No family?"
Gadlin shook his head. "I've asked. Both parents and all of his brothers and sisters are dead. I don't think he's ever been married, either."
"I think Corvan has a lady—a widow—under observation. She's about the same age."
"Shall I arrange for them to meet?"
"Not just the two of them," Labey said. "It needs to look like it was their idea. A group meeting of the Brotherhood would serve our purposes better."