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After a long pause, Tupelo added: “I can’t either. To tell the truth, the structure of the System, with the Boylston shuttle, is completely beyond me. I can only guess.”

Whyte swiveled his eyes up from the desk at a moment when anger was the dominant feeling within him.

“And you call yourself a mathematician, Professor Tupelo!” he said.

Tupelo almost laughed aloud. The incongruous, the absolute foolishness of the situation, all but overwhelmed him. He smiled thinly, and said: “I’m no topologist. Really, Mr. Whyte, I’m a tyro in the field — not much better acquainted with it than you are. Mathematics is a big pasture. I happen to be an algebraist.”

His candor softened Whyte a little. “Well, then,” he ventured, “if you don’t understand it, maybe we should call in a topologist. Are there any in Boston?”

“Yes and no,” Tupelo answered. “The best in the world is at Tech.”

Whyte reached for the telephone. “What’s his name?” he asked. “I’ll call him.”

“Merritt Turnbull. He can’t be reached. I’ve tried for three days.”

“Is he out of town?” Whyte asked. “We’ll send for him— emergency.”

“I don’t know. Professor Turnbull is a bachelor. He lives alone at the Brattle Club. He has not been seen since the morning of the 4th.”

Whyte was uncommonly perceptive. “Was he on the train?” he asked tensely.

“I don’t know,” the mathematician replied. “What do you think?”

There was a long silence. Whyte looked alternately at Tupelo and at the glass object on the desk. “I don’t understand it,” he said finally. “We’ve looked everywhere on the System. There was no way for the train to get out.”

‘The train didn’t get out. It’s still on the System,” Tupelo said.

“Where?”

Tupelo shrugged. “The train has no real ‘where.’ The whole System is without real ‘whereness.’ It’s double-valued, or worse.”

“How can we find it?”

“I don’t think we can,” Tupelo said.

There was another long silence. Whyte broke it with a loud exclamation. He rose suddenly, and sent the Klein bottle flying across the room. “You are crazy, professor!” he shouted. Between midnight tonight and 6:00 A.M. tomorrow, we’ll get every train out of the tunnels. I’ll send in three hundred men, to comb every inch of the tracks — every inch of the one hundred eighty-three miles. We’ll find the train! Now, please excuse me.” He glared at Tupelo.

Tupelo left the office. He felt tired, completely exhausted. Mechanically, he walked along Washington Street toward the Essex Station. Halfway down the stairs, he stopped abruptly, looked around him slowly. Then he ascended again to the street and hailed a taxi. At home, he helped himself to a double shot. He fell into bed.

At 3:30 that afternoon he met his class in “Algebra of Fields and Rings.” After a quick supper at the Crimson Spa, he went to his apartment and spent the evening in a second attempt to analyze the connective properties of the System. The attempt was vain, but the mathematician came to a few important conclusions. At eleven o’clock he telephoned Whyte at Central Traffic.

“I think you might want to consult me during tonight’s search,” he said. “May I come down?”

The general manager was none too gracious about Tupelo’s offer of help. He indicated that the System would solve this little problem without any help from harebrained professors who thought that whole subway trains could jump off into the fourth dimension. Tupelo submitted to Whyte’s unkindness, then went to bed. At about 4:00 A.M. the telephone awakened him. His caller was a contrite Kelvin Whyte.

“Perhaps I was a bit hasty last night, professor,” he stammered. “You may be able to help us after all. Could you come down to the Milk Street Cross-Over?”

Tupelo agreed readily. He felt none of the satisfaction he had anticipated. He called a taxi, and in less than half an hour was at the prescribed station. At the foot of the stairs, on the upper level, he saw that the tunnel was brightly lighted, as during normal operation of the System. But the platforms were deserted except for a tight little knot of seven men near the far end. As he walked towards the group, he noticed that two were policemen. He observed a one-car train on the track beside the platform. The forward door was open, the car brightly lit, and empty. Whyte heard his footsteps and greeted him sheepishly.

“Thanks for coming down, professor,” he said, extending his hand. “Gentlemen, Dr. Roger Tupelo, of Harvard. Dr. Tupelo, Mr. Kennedy, our chief engineer; Mr. Wilson, representing the Mayor; Dr. Gannot, of Mercy Hospital.” Whyte did not bother to introduce the motorman and the two policemen.

“How do you do,” said Tupelo. “Any results, Mr. Whyte?”

The general manager exchanged embarrassed glances with his companions. “Well… yes, Dr. Tupelo,” he finally answered. “I think we do have some results, of a kind.”

“Has the train been seen?”

“Yes,” said Whyte. “That is, practically seen. At least, we know it’s somewhere in the tunnels.” The six others nodded their agreement.

Tupelo was not surprised to learn that the train was still on the System. After all, the System was closed.

“Would you mind telling me just what happened?” Tupelo insisted.

“I hit a red signal,” the motorman volunteered. “Just outside the Copley junction.”

“The tracks have been completely cleared of all trains,” Whyte explained, “except for this one. We’ve been riding it, all over the System, for four hours now. When Edmunds, here, hit a red light at the Copley junction, he stopped, of course. I thought the light must be defective, and told him to go ahead. But then we heard another train pass the junction.”

“Did you see it?” Tupelo asked.

“We couldn’t see it. The light is placed just behind a curve. But we all heard it. There’s no doubt the train went through the junction. And it must be Number 86, because our car was the only other one on the tracks.”

“What happened then?”

“Well, then the light changed to yellow, and Edmunds went ahead.”

“Did he follow the other train?”

“No. We couldn’t be sure which way it was going. We must have guessed wrong.”

“How long ago did this happen?”

“At 1:38, the first time—”

“Oh,” said Tupelo, “then it happened again later?”

“Yes. But not at the same spot, of course. We hit another red signal near South Station at 2:15. And then at 3:28—”

Tupelo interrupted the general manager. “Did you see the train at 2:15?”

“We didn’t even hear it, that time. Edmunds tried to catch it, but it must have turned off onto the Boylston shuttle.”

“What happened at 3.28?”

“Another red light. Near Park Street. We heard it up ahead of us.”

“But you didn’t see it?”

“No. There is a little slope beyond the light. But we all heard it. The only thing I don’t understand, Dr. Tupelo, is how that train could run the tracks for nearly five days without anybody seeing—”

Whyte’s words trailed off into silence, and his right hand went up in a peremptory gesture for quiet. In the distance, the low metallic thunder of a fast-rolling train swelled up suddenly into a sharp, shrill roar of wheels below. The platform vibrated perceptibly as the train passed.

“Now we’ve got it!” Whyte exclaimed. “Right past the men on the platform below!” He broke into a run towards the stairs to the lower level. All the others followed him, except Tupelo. He thought he knew what was going to happen. It did. Before Whyte reached the stairs, a policeman bounded up to the top.