Kervis hauled Tervis to his feet. “Look here,” he said, dragging Tervis toward the north-facing window. “Bet you can see Allaskar from there!”

Tervis shook off his brother’s grasp and pulled away from the window. Meralda motioned him toward her. “Hold this, if you will,” she said, thrusting her instrument bag into the boy’s arms.

Tervis nodded. “Yes, ma’am.”

“Oh,” said Kervis, his face pressed to the glass. “Oh,” he said again, softly.

Meralda joined him at the window.

Tirlin lay sprawled below. The Lamp River wound shimmering from the east, passed beneath the bridge, and lost itself amid the walls and rooftops and spires of the college. The park wall and its dancing gargoyles were invisible, swallowed whole by the distance. The old oaks, tiny now, stood swaying in a ring. Meralda felt she was flying, looking down on the heads of giants.

Kervis gasped and started. A bright green passenger dirigible flew into view, fans straining, climbing steeply and bearing west. But before it turned and was lost beyond the window frame, Meralda was sure she saw the flash of a lady’s white-gloved hand through a brass-worked salon porthole.

Kervis rapped the glass with his knuckles. “How thick is this, ma’am?” he asked, stepping back. “And how do they clean it?”

Meralda smiled. “The glass is nearly four feet thick,” she said. “And, believe it or not, once a year a Phendelit chimney sweep named Mad Hansa hangs on a line from an airship and polishes all the glass from outside.”

Kervis’ jaw dropped. “Mad Hansa,” he said.

Meralda nodded. “It’s an all day affair,” she said. “The park fills with people who come to watch.” Meralda shrugged. “Especially after the year Mad Hansa hired an apprentice. Too bad about him, really.”

Kervis swallowed and stepped away from the window. “Now then,” said Meralda. “Work to do.” She pulled back her sleeves and brushed a damp lock of hair out of her eyes. “Tervis, my bag. Please stand back and be silent.”

“Yes, ma’am,” said the Bellringers. Tervis came to stand before her, hefting her bag out at arm’s length before him.

Meralda thanked him, reached inside, and pulled out a small black cloth bag clasped with an intricate silver catch.

Tervis’ eyes bulged. Meralda released the catch, opened the bag, and pulled out a silver ball attached to a fine silver chain. A hole pierced the bottom of the ball. Meralda shook the bag until a short piece of sharpened white chalk fell into her hand. She then pushed the chalk into the hole in the ball.

Meralda grasped the far end of the chain and let the ball hang free. With her arm above her head, the ball hung just above the floor.

Meralda took a deep breath and whispered a word.

The first few windings of Meralda’s spell unlatched and flailed about. Meralda let go of the chain, and before it could fall the spell caught hold, suspending chain and ball in the empty air below the ceiling.

Tervis grinned in sudden wonder, and some of the fear left his eyes. Kervis bit back a squeak of amazement.

With another word, Meralda stilled the ball’s small oscillations.

“Stand back, if you will,” she said, to Tervis.

Tervis made great backward-shuffling strides to the far edge of the flat. Meralda squinted, said a word and made a gesture. The ball and chain sailed to rest in the center of the flat.

Meralda followed. She kneeled before the ball and chain, fumbled in her skirt pocket, and withdrew her short, battered retaining wand. The wand was warm, and at her touch it gave off a hum like the buzzing of a single angry honeybee.

Tufts of pocket lint clung to the wand. Meralda rubbed the lint off with her skirt, took the wand in both hands, and unlatched the rest of the seeking spell with a long rhythmic word.

The spell discharged with a crackle and a flash, draining Meralda’s retaining wand with a sound like frying bacon.

“Look!” said Kervis, as the ball began to dart about, swinging to and fro as if testing the air for scents.

“Hush,” said Tervis.

The silver ball strained at the chain, pulling it taut until the chalk tip touched the floor. Then the ball swung to the north, pulling the chain with it at a slight angle and drawing a short straight line upon the floor.

Meralda clapped her hands, and caught the chain as it went limp and fell. “That’s all,” she said. “We’re nearly done.”

“What now?” asked Kervis, as Meralda wound the chain loosely around her left hand.

“I use a ruler,” said Meralda. “I measure the length of the line on the floor. I use this to calculate the height of the flat.”

Kervis tilted his head.

“A ruler?” he said.

“A ruler,” replied Meralda. “Tervis?”

Tervis trotted to her, bag in hand. She reached inside, found the folding Eryan ruler in its pouch by the copper-bound Loman jars, and pulled it out.

Kervis frowned. Meralda smiled. “I need to anchor my shadow moving spell to a spot here in the flat,” she said. “And to do that, I have to know exactly how high off the ground the spot is.”

Tervis frowned. “Couldn’t someone measure the steps, and then count them?” he said. “Ma’am?”

Meralda unfolded the ruler, kneeled, and laid the flat edge against the chalk mark. “Very good, Tervis,” she said, squinting at the tiny marks on the ruler’s edge. “That was, in fact, the first recorded method by which the Tower’s height was surveyed. And it was a good estimate. But to move the Tower’s shadow will require more than just good estimates.”

Kervis stepped close, but leaped away when he saw his shadow fall over Meralda’s ruler. “Pardon, ma’am,” he said, scratching his head beneath his helmet, “but how does that little scratch on the floor tell you how tall the Tower is?”

Meralda put her nose nearly to the floor, decided on a figure, and used the chalk from the ball to scribble the numbers on the floor.

“Mathematics,” she said, rising. “The biggest part of magic. Not the stuff of epic legends, I know, but the stuff of magic nonetheless.”

“Mathematics?” asked Tervis, wrinkling his nose. “You mean two-and-two and take away four, that sort of thing?”

“That very sort of thing,” said Meralda, grinning at the thought of old Master Blimmett’s sputtering, should he ever hear his High Mathematica studies dubbed a “two-and-two and take away four sort of thing”.

Tervis stared down at the mark on the floor.

“The process is called trigonometry,” said Meralda. “I caused the ball to be attracted to the Historical Society marker by the park gates. It pulled the chain away from the vertical by that much.” She pointed to the scribbles on the floor with the tip of her boot.

“And since I know the exact distance from the center of the Tower to the Society marker, and since I know the length of the chain and the angle of deflection, I can calculate the exact height of a point just below the ceiling of the Wizard’s Flat.”

“As you say, ma’am,” said Tervis. Then he grinned. “Magic!”

Meralda folded her ruler. “Magic,” she said, putting away her gear.

The half-open door to the stair beckoned. Meralda dropped her bag and tied it shut.

“Time to go, gentlemen,” she said. Tervis mopped his brow. Kervis, who had been dashing from window to window, trotted back to join Meralda and Tervis before the door.

“It’s downhill, this time,” Kervis said. “Shall I go first again, ma’am?”

Meralda lit her magelamp with a word and motioned Kervis toward the door.

“Last one down is a Vonat,” he said, before slipping out into the dark.

Meralda followed. Tervis came after, and though his hand shook when Meralda handed him the key he managed to lock the door without fumbling.

Meralda pocketed the key, bade Kervis to wait until she set the magelamp’s twin beams wider and brighter, and then brushed back her hair.

A line from a Phendelit play crept whispering into Meralda’s mind. “We climb now the walls of the cold dark night,” said the hero, at the base of the stair that wound down to the Pale Gate. “No sun now to warm us, no light for our feet. Just darkness and silence and down to defeat.”