The "United Systems" are in the final testing stages of a space warp, a "tunnel in the sky" to instantly send a ship from one section of the galaxy to another. The Enterprise is hanging in space, waiting to retrieve the subject who will pass through the hole in space in a shuttle craft.

Four light years away, the shuttle enters the warp. And a safe distance off the Enterprise’s bow, the warp field exit comes alive, a flickering grid against space, phasing in and out, shifting through the primary color spectrum.

But something has gone wrong. The shuttle cannot escape the warp. The warp fades, seems on the brink of winking out of existence.

Spock, waiting in the transporter room in case of emergency, beams the pilot aboard, but the transporter goes wonky -- readings show that that there are several men in the beam. Finally, three different versions of the man materialize, one yellow, one red, one blue. They’re slightly out of phase. The three figures then step together and become one whole normally-colored man, Robert Jones.

As Jones steps off the transporter, he again "shatters" into his three separately-colored components again.

Jones is confined to Sick Bay, and soon Spock has an explanation. He is a "Protracted Man." Because he was removed from the warp field before it shut down he has been stretched along the fourth dimension--time. Thus he is splitting into three forms, each now about a half a second apart. As time passes the three forms will grow further and further apart. Any disturbance in the fabric of space and time, even a warp engine, might irrevocably split him totally apart.

Kirk is confronted by Jones’ brother, who is a crewman aboard the Enterprise. He demands to know how Kirk can help Robert.

On the bridge, Scotty reports that there is a matter/anti-matter drain on the ship’s engines. The drain is coming from Sick Bay. Robert Jones’ time protraction is drawing energy from whatever source is closest.

After a conference with his department heads, Kirk takes Scotty’s advice and shields Jones in a cabin lined with inch-thick collapsed steel foil. Perhaps this will stop him from drawing energy from the engines.

It does not. He draws even more power, unconsciously, right through the shields, drains the Enterprise dangerously low. They return him to Sick Bay. He is now a full second and a half out of sync and can no longer communicate with people in a normal time stream. His brother is very upset at this failure.

Spock suggests they totally shut the Enterprise down, all engines, all generators, everything. Scotty protests -- the ship would have no gravity, no life support, they’d be helpless, plus the shields that normally protect the Enterprise personnel from the radiations of space and stars would be gone. They’d die.

Kirk orders the ship to go to warp to get them away from a nearby star, lessen the radiation when they do shut down. Bad decision. The instant the ship goes into warp, Jones splits into dozens of separate components, and some go running about the ship. Kirk orders the Enterprise brought out of warp. Jones’ images regroup, but they are now three seconds out of phase because the ship’s warp engines interfered with his time protraction. This new protraction amount has drained the Enterprise’s power. They now must use final emergency power just to survive.

Crewman Jones yells at Kirk for what he has done to his brother, Kirk orders him to go to his quarters.

Robert Jones escapes. Spock comes up with a solution, tells Kirk to find Jones and bring him to the transporter room. Kirk orders a security team to find him. Though they cannot touch him, since he exists across a span of time, perhaps a phaser blast will stop him.

Crewman Jones confronts Kirk on the bridge. They argue. Finally Jones’ anger subsides, and he asks that he alone be allowed to bring his brother to the transporter room.

Crewman Jones’ voice is fed into a computer and is garbled in such a way that Robert Jones can understand him. Crewman Jones explains what must be done, then fires the phaser at the spread out images of his brother. They collapse into one being.

In the transporter room Spock explains how the transporter may be able to reintegrate the three components of Jones back into one time component. It will take all the power the ship has left. Every system is shut down except the transporter.

Spock carefully operates the transporter controls. . . and it works. Robert Jones, whole and normal, materializes on the transporter platform.

Later, Kirk congratulates Spock on his timely solution to the problem.

From the premise:

Spock almost winces, and perhaps he complains that he will never understand an Earthman’s concept of humor. "After all, there was a solution to the problem. It was just a matter of time."

Kirk gives him a look. "Mr. Spock, was that a joke you just told?"

"Who, me? Captain!"