“But the frog won’t jump in conformity to the conditions of the paradox.”

“Then you’ll have to make him, that’s all. I’ll give you two weeks to set up control conditions and determine the truth of this miserable puzzle. I want no more wrangling, month after month. I want this settled, once and for all.”

Hardy and Grote were silent.

“Well, Grote,” Hardy said at last, “let’s get it started.”

“We’ll need a net,” Grote said.

“A net and a jar.” Hardy sighed. “We might as well be at it as soon as possible.”

The “Frog Chamber,” as it got to be called, was quite a project. The University donated most of the basement to them, and Grote and Hardy set to work at once, carrying parts and materials downstairs. There wasn’t a soul who didn’t know about it before long. Most of the science majors were on Hardy’s side; they formed a Failure Club and denounced the frog’s efforts. In the philosophy and art departments there was some agitation for a Success Club, but nothing ever came of it.

Grote and Hardy worked feverishly on the project. They were absent from their classes more and more of the time, as the two weeks wore on. The Chamber itself grew and developed, resembling more and more a long section of sewer pipe running the length of the basement. One end of it disappeared into a maze of wires and tubes: at the other there was a door.

One day when Grote went downstairs there was Hardy already, peering into the tube.

“See here,” Grote said, “we agreed to keep hands off unless both of us were present.”

“I’m just looking inside. It’s dark in there.” Hardy grinned. “I hope the frog will be able to see.”

“Well, there’s only one way to go.”

Hardy lit his pipe. “What do you think of trying out a sample frog? I’m itching to see what happens.”

“It’s too soon.” Grote watched nervously as Hardy searched about for his jar. “Shouldn’t we wait a bit?”

“Can’t face reality, eh? Here, give me a hand.”

There was a sudden sound, a scraping at the door. They looked up. Pitner was standing there, looking curiously into the room, at the elongated Frog Chamber.

“What do you want?” Hardy said. “We’re very busy.”

“Are you going to try it out?” Pitner came into the room. “What are all the coils and relays for?”

“It’s very simple,” Grote said, beaming. “Something I worked out myself. This end here—”

“I’ll show him,” Hardy said. “You’ll only confuse him. Yes, we were about to run the first trial frog. You can stay, boy, if you want.” He opened the jar and took a damp frog from it. “As you can see, the big tube has an entrance and an exit. The frog goes in the entrance. Look inside the tube, boy. Go on.”

Pitner peered into the open end of the tube. He saw a long black tunnel. “What are the lines?”

“Measuring lines. Grote, turn it on.”

The machinery came on, humming softly. Hardy took the frog and dropped him into the tube. He swung the metal door shut and snapped it tight. “That’s so the frog won’t get out again, at this end.”

“How big a frog were you expecting?” Pitner said. “A full-grown man could get into that.”

“Now watch.” Hardy turned the gas cock up. “This end of the tube is warmed. The heat drives the frog up the tube. We’ll watch through the window.”

They looked into the tube. The frog was sitting quietly in a little heap, staring sadly ahead.

“Jump, you stupid frog,” Hardy said. He turned the gas up.

“Not so high, you maniac!” Grote shouted. “Do you want to stew him?”

“Look!” Pitner cried. “There he goes.”

The frog jumped. “Conduction carries the heat along the tube bottom,” Hardy explained. “He has to keep on jumping to get away from it. Watch him go.”

Suddenly Pitner gave a frightened rattle. “My God, Hardy. The frog has shrunk. He’s only half as big as he was.”

Hardy beamed. “That is the miracle. You see, at the far end of the tube there is a force field. The frog is compelled to jump towards it by the heat. The effect of the field is to reduce animal tissue to its proximity. The frog is made smaller the farther he goes.”

“Why?”

“It’s the only way the jumping span of the frog can be reduced. As the frog leaps he diminishes in size, and hence each leap is proportionally reduced. We have arranged it so that the diminution is the same as in Zeno’s paradox.”

“But where does it all end?”

“That,” Hardy said, “is the question to which we are devoted. At the far end of the tube there is a photon beam which the frog would pass through, if he ever got that far. If he could reach it, he would cut off the field.”

“He’ll reach it,” Grote muttered.

“No. He’ll get smaller and smaller, and jump shorter and shorter. To him, the tube will lengthen more and more, endlessly. He will never get there.”

They glared at each other. “Don’t be so sure,” Grote said.

They peered through the window into the tube. The frog had gone quite a distance up. He was almost invisible, now, a tiny speck no larger than a fly, moving imperceptibly along the tube. He became smaller. He was a pin point. He disappeared.

“Gosh,” Pitner said.

“Pitner, go away,” Hardy said. He rubbed his hands together. “Grote and I have things to discuss.”

He locked the door after the boy.

“All right,” Grote said. “You designed this tube. What became of the frog?”

“Why, he’s still hopping, somewhere in a sub-atomic world.”

“You’re a swindler. Some place along that tube the frog met with misfortune.”

“Well,” Hardy said. “If you think that, perhaps you should inspect the tube personally.”

“I believe I will. I may find a trap door.”

“Suit yourself,” Hardy said, grinning. He turned off the gas and opened the big metal door.

“Give me the flashlight,” Grote said. Hardy handed him the flashlight and he crawled into the tube, grunting. His voice echoed hollowly. “No tricks, now.”

Hardy watched him disappear. He bent down and looked into the end of the tube. Grote was half-way down, wheezing and struggling. “What’s the matter?” Hardy said.

“Too tight….”

“Oh?” Hardy’s grin broadened. He took his pipe from his mouth and set it on the table. “Well, maybe we can do something about that.”

He slammed the metal door shut. He hurried to the other end of the tube and snapped the switches. Tubes lit up, relays clicked into place.

Hardy folded his arms. “Start hopping, my dear frog,” he said. “Hop for all you’re worth.”

He went to the gas cock and turned it on.

It was very dark. Grote lay for a long time without moving. His mind was filled with drifting thoughts. What was the matter with Hardy? What was he up to? At last he pulled himself on to his elbows. His head cracked against the roof of the tube.

It began to get warm. “Hardy!” His voice thundered around him, loud and panicky. “Open the door. What’s going on?”

He tried to turn around in the tube, to reach the door, but he couldn’t budge. There was nothing to do but go forward. He began to crawl, muttering under his breath. “Just wait, Hardy. You and your jokes. I don’t see what you expect to—”

Suddenly the tube leaped. He fell, his chin banging against the metal. He blinked. The tube had grown; now there was more than enough room. And his clothing! His shirt and pants were like a tent around him.

“Oh, heavens,” Grote said in a tiny voice. He rose to his knees. Laboriously he turned around. He pulled himself back through the tube the way he had come, towards the metal door. He pushed against it, but nothing happened. It was now too large for him to force.

He sat for a long time. When the metal floor under him became too warm he crawled reluctantly along the tube to a cooler place. He curled himself up and stared dismally into the darkness. “What am I going to do,” he asked himself.

After a time a measure of courage returned to him. “I must think logically. I’ve already entered the force field once, therefore I’m reduced in size by one-half. I must be about three feet high. That makes the tube twice as long.”