An optimistic Fitzhugh is packing for departure: Mark is working with a giant scientist, Andre, to perfect the "Delta Device" and give them the power source they need. It runs amuck, exposing the Earthlings and Andre to strange radiation. Andre's superior, Berger, is suspicious and tracks Andre back to the Spindrift, only to have it vanish before his eyes. Apparently the Earthlings and their ship have turned invisible.
Strange things begin to happen. Fitzhugh witnesses Steve "slow down" temporally, and then Barry and Chipper vanish. The Earthlings soon realize that some of the giants are invisible too (??). Kobick manages to capture Valerie, but she is invisible to Berger, who inadvertently lets her free. Meanwhile, trying to contact Andre, first Dan and then Steve vanish. Steve appears to be trapped in a hallucinatory landscape, and is attacked by distorted versions of Kobick, Berger, and Mark. Fitzhugh also disappears after turning the Delta Device back on, and manages to find Steve, and they then find Dan.
The effects of the radiation wear off, and Barry also snaps back to normal. Berger tries to have Andre arrested, but Andre counter-accuses him and Kobick, sick of the whole thing, believes Andre. The Earthlings get back to the Spindrift just in time to shut down the Delta Device Fitzhugh turned on, but it burns out and the group can't contact Andre again because Berger is still watching him.