Duilio left the house before breakfast with the journal tucked under his arm. He caught a tram heading toward the parish of Massarelos and got off in time to head down Campo Alegre Street toward the Tavares boatyard. When Joaquim’s father had left the sea to pursue boatbuilding, Joaquim hadn’t chosen to enter the nascent family business, but his younger brother, Cristiano, had. Now twenty and just returned that summer from the university in Coimbra, Cristiano possessed a genius for engineering and mathematics that Duilio could only admire.

Through the large open doors on the side, he entered the shop where the smaller boats were constructed and was immediately surrounded by the aroma of fresh-sawn wood and resins mixed with a hint of cigarette smoke. Several workmen were currently assembling the ribs of a smallish boat, no more than thirty feet long. It was, to Duilio’s untrained eye, another of Cristiano’s fascinating experimental designs. Duilio spotted Joaquim’s younger brother standing above the pit where a boat was being assembled and called out his name. “Cristiano!”

The young man grinned widely and came around the pit to embrace Duilio. He resembled Joaquim very little, having a more angular face, like their father’s. “Cousin, it’s been too long. How is your mother?”

“She’s well,” Duilio assured him, “although not changed from the last time you saw her.”

“I’m sorry to hear that.” Frowning, Cristiano waved at the workmen to continue their tasks and then drew Duilio to one side toward the office. “I haven’t seen Joaquim in weeks. Tell him he needs to come for dinner.”

“I’ll nag him,” Duilio promised. “Although I must admit now that I’ve come here for reasons other than social, to drag you into our investigation.”

Cristiano opened the office door and gestured for Duilio to go in. A brown-haired English girl wearing dainty spectacles and an expensive tweed suit sat at one of the half-dozen wide drafting desks, a pencil behind one ear, scowling down at the page in front of her. Miss Atkinson was a scion of one of the British wine-trading families over on the Gaia shore, Duilio recalled, who’d come to work for the Tavares firm after leaving the university at Coimbra. She’d been the very first woman to study mathematics there. Although a couple of years older than Cristiano, her petite size made her seem younger.

Cristiano shut the office door. “Is this about the underwater houses?”

“Good guess,” Duilio said, glad he didn’t have to explain.

“Joaquim mentioned the investigation last time I saw him. Many of the same principles as submersible crafts or submarines,” the young man said, “and I’ve been studying those. So, how can I help?”

One of the nice things about Cristiano: he didn’t waste time. Duilio opened the journal, searching for the page that held the diagram in question. “My question is actually mathematical.”

“Miss Atkinson’s grasp is better than mine.” Cristiano gestured for the English girl to join them.

As Duilio hunted for the right page, Miss Atkinson rose and nearly tripped when her skirt was apparently caught under the leg of the stool. She jerked it free with one hand and came to join them, murmuring imprecations under her breath.

“According to this,” Duilio told them, “the houses have walls of cork, thinly covered with wood, which is why they’re still floating despite filling with water.”

“I told you those buoyancy charms were meaningless,” Cristiano said a bit smugly.

“I recall.” Duilio finally located the page near the back and stuck on a finger to hold the place. “This is secret, so you can’t say anything about it to anyone.”

The girl nodded dutifully, and Cristiano did likewise.

Duilio opened it out to the diagram. “Is this symbol in the middle something mathematical? Some bizarre formula? It has a plus sign in it.”

Cristiano and the girl exchanged a glance that appeared to condemn Duilio’s ignorance. “No, sir,” she said, “that’s not mathematical.”

“It’s more my field,” Cristiano offered. “Electrochemistry. That’s a schematic for a pile.”

“A pile?”

“A voltaic pile,” Cristiano said, “although it might mean a different form. The symbols aren’t standardized across Europe.” At Duilio’s blank look, he continued. “It’s a form of battery, a way to convert chemical energy to electrical energy using two disparate metals, usually silver and zinc, with saltwater as an electrolyte—”

Duilio held up his hand. “Wait. Chemical energy converts to electrical energy?”

“Yes,” Cristiano said patiently. “The two elements in each cell . . .”

“You’re just going to say more words I don’t understand. Let’s go back. This is a symbol for a battery. Two parts linked by seawater, right?”

“That’s one form,” Cristiano said. “It depends on your needs. Dry-cell batteries—”

Duilio held up his hand again. “What if it converted something like life force?”

Miss Atkinson’s brows rose. She cast a glance at Cristiano that plainly said Duilio was losing his grip on sanity. At his nod, she went back to her desk. Cristiano waited until she was out of earshot. “Are you serious?”

“Sadly enough, I am,” Duilio said quietly. “We think there’s one of these in each house. The middle ring is some form of necromancy. When the person touching the ring dies, their half of the diagram lights up. Two people die, it all lights up.”

Cristiano gazed at him disbelievingly. “This is part of those houses? Sitting underwater? Most of them have been there for months, Duilio. Any electrical charge would have dissipated long ago.”

“But this is magic, not electricity, so the rules wouldn’t be the same, would they?”

“I have no idea,” Cristiano said dryly. “We don’t study magic at Coimbra.”

Duilio closed his eyes, trying to figure out what was important here. “Each house had two people in it. Two elements in a cell, you said. So how many cells would they need to do something? If it were electricity, I mean.”

“Just one,” Cristiano said. “But more cells stacked together increase their power.”

“How many cells would you need if you were planning something big? If you already have twenty-six.”

Cristiano’s lips pursed. “I guess for style’s sake I would use thirty-two.”

Hadn’t Oriana's elderly friend said that the choice of two languages in the spell was a matter of style rather than content? “Why?”

Cristiano shrugged. “Twenty-eight is your next perfect number, thirty-four is your next magic number, but I would lean toward thirty-two. It’s a power of two, which works well with current.”

Duilio didn’t know what he meant by perfect number or magic number, but he did understand powers of two. “One last question. Say one of the cells was broken. Only halfway lit. What would happen then?”

“That cell would be useless. I would just try to bypass it,” Cristiano said. “It depends on how the cells are wired together, but if each is discrete, as those houses are, one cell should be easy to cut out.”

“And replaced by another?”

“I don’t see why not.”

“But that wouldn’t be tidy, would it?”

“No,” Cristiano said. “I would just replace the broken cell . . . or recharge it.”

Recharge. Which would mean finding Miss Paredes and sticking her back inside. Duilio closed the journal and stuffed it back into a pocket. He wasn’t about to let that happen.

* * *

Oriana had enjoyed a leisurely breakfast with Lady Ferreira and had just settled in the front sitting room to read to her when Mr. Ferreira strode in, the leather-bound journal in his hand. He gestured for Oriana to join him at the doorway. She excused herself to the lady, who nodded vaguely, and went to go speak to him.

“It’s a battery,” he said. “The whole thing is a battery.”

Oriana glanced back at Lady Ferreira to see if she’d overheard, but the lady’s attention had wandered. “What?”

“This symbol in the middle is a schematic for a voltaic pile, which takes one sort of energy and converts it to another. But the energy isn’t converted until the connection between the two halves is made by . . .” He closed his eyes. “Damn! I forgot what he called it.”

“Duilinho, watch your tongue,” his mother said softly from across the room.

He actually flushed at his mother’s mild rebuke. “My apologies, Miss Paredes. Cristiano was speaking of

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