After receiving an outdated signal and going to investigate the crew of the Enterprise begins to shrink. As operating (or even reaching) the controls becomes more difficult, Spock calculates that they will soon shrink down to 1/16th of an inch.
They determine that they're being hit with rays of "spiral energy" from the volcanic planet sending the signal. Kirk beams down to investigate and discovers a. that the transporter has restored him to his proper size, since his parameters are stored in the buffers and b. the rays are coming from a city that's about knee-high. He beams back aboard to find his crew gone, and threatens the city to return them now or he'll blow them to bits.
The Mendant—the leader of the city—replies with Kirk's crew all in the background and explains that the shrink-ray was the best way he could think to get the ship's attention. He and the rest of his city descend from an old Earth colony originally called "Terra Ten" (corrupted now into Terratin) and that they are fine being tiny, but not being wiped out by a sharp uptick in volcanic activity. Kirk beams up the city and the Enterprise transports it to a more stable M-Class planet, for which he and his crew are named "honorary Terratins."
This episode provides examples of:
- Artistic Licence – Biology: The shrinkray works by making anything spiral-shaped compress as small as it possibly can. While this could affect spiral DNA molecules it doesn't explain how the trillions of non-spiral molecules in the human body (bone, muscle, etc...) are affected.
- Death World: The planet has turned into a volcanic hellhole, which is why the Terratins called for help.
- Dinky Drivers: The crew buys some time by improvising ways to operate the controls, but it's only a temporary stopgap.
- Distress Ball: Nurse Chapel somehow trips and falls into a fishtank several times taller than she is when she goes to get some medical supplies off a table.
- Incredible Shrinking Man: There is a lower limit to how far the crew will shrink, but it's far below the threshold where they'll be able to operate the ship (even by jumping up and down on buttons). They have to rig up ladders, rope made of string, and use a device for mending earbones on Sulu's leg after he falls the three feet from his console to the floor.
- Although a three-foot fall actually becomes less dangerous the smaller you are.
- Magic Pants: They went out of their way to say that the uniform cloth was made of an algae-based fiber to explain why it shrank proportionally with the wearer.
- Race Against the Clock: To find a solution before they become unable to work the controls.
- Shout-Out: To Gulliver's Travels. Kirk references it directly by calling the inhabitants Lilliputian.
- Shrink Ray: The planet's crystalline internal structure causes it to emit these all over its surface, shrinking down anything organic or spiral-shaped (like the ship's dilithium crystals).
