And, in fact, the version of the story arc called The Chase on my beloved BritBox has been cut to remove the sequence.
The setup is this: The Doctor has liberated a Time-Space Visualizer from The Space Museum. It allows (with some truly awful noises) the travelers to watch any moment in the future or the past. Ian wants to see Abraham Lincoln at Gettysburg, and is surprised that his wish is granted. Barbara wants only a view of Queen Elizabeth I's court, but gets to see Bacon, Shakespeare and the Queen herself discussing whether Falstaff was a slander of Sr John Oldcastle (spoiler: He was and the delighted Queen press for another play with Falstaff (also true). Then, the Beatles:
IAN: Well, Barbara, did you find out what you wanted to know?The whole first part of the episode has a "Rainy Sunday on the TARDIS" vibe that is quite charming; Vicki irritates the Doctor as he tries to get the Visualizer working; she then goes off to Ian, who is reading a science fiction anthology called Monsters From Outer Space, which he wryly describes to Vicli as "a bit far-fetched." She then drifts into the room she shares with Barbara:
BARBARA: I didn't really want to know anything. I just wanted to see Elizabeth's court. Did you see the way Shakespeare looked when he thought of Hamlet?
IAN: Yes, I did. I
(Vicki puts in her selection)
IAN: Well, where are we now?
ANNOUNCER [OC]: This is BBC One. The next programme is due to start in just under one minute.
BARBARA: Vicki, what year have you got on there?
DOCTOR: Come along, come.
IAN: You've got a television.
VICKI: I want to watch it.
HOST [on monitor]: Here singing their latest number one hit it's the fabulous wait for it. It's the fabulous Beatles!
VICKI: Yes! Fabulous!
BEATLES: I think I'm gonna be sad, I think it's today, yeah! The girl that's driving me mad, Is going away.
She's gotta ticket to ride, She's gotta ticket to ride. She's gotta ticket to ride, and she don't care. My baby don't care.
(Everyone is bopping and singing along until Barbara leans on the volume and they loose the picture)
IAN: Oh, Barbara.
DOCTOR: Now you've squashed my favourite Beatles!
IAN: Vicki, I had no idea you knew about the Beatles.
VICKI: Of course I know about them. I've been to their Memorial Theatre in Liverpool.
BARBARA: Well, what do you think of them, Vicki?
VICKI: Well, they're marvellous, but I didn't know they played classical music!
BARBARA: Classical music?
IAN: Get with it, Barbara. Get with it. Styles change, styles change.
VICKI: I am redundant around here.All of this is played for gentle comedy, and it's fun.
BARBARA: Oh, nonsense. Come and sit down and talk to me.
VICKI: I am a useless person.
(Vicki sits on the edge of a 'bed' which then tips her forward making her knock over whatever Barbara was using)
BARBARA: Oh, Vicki!
VICKI: Oh, what was it?
BARBARA: Oh, it was a dress for you.
After they watch their "shows," though, and land on a sandy wreck of a planet, the travelers get one on the house: Daleks. Daleks, I might add, searching all of time and space for the TARDIS:
Barbara tries to turn off the visualiser, but gets a signal instead)Of course, Ian and Vicki have gotten lost already.
DALEK [OC]: The Supreme Dalek is ready to receive your report!
DALEK [on monitor]: The report is ready.
BARBARA: Doctor! Doctor, come quickly!
DOCTOR [OC]: Yes, all right, my dear, all right, all right. What is it now? Gracious me, can't I even relax for five
(The Doctor enters)
DOCTOR: The Daleks!
BLACK: Give your report.
DALEK: Our time machine has been completed.
BLACK: The operation will proceed at once. The movement scanners have located the enemy time machine, Tardis.
DALEKS: Tardis! Tardis! Tardis! Tardis! Tardis!
BARBARA: Doctor, he said the Tardis. And look, on their screen, that's us.
DOCTOR: What is more important, he referred to the Tardis as the enemy time machine.
The first three episodes consist of the setup, and three vignettes. The first vignette, set on the dry, sandy planet Aridius (I see what you did, there--), is the least interesting. Not entirely without interest, mind, just the least interesting, in that the Aridians are cowards who agree to turn team TARDIS, whom they have rescued, over to the Daleks rather than face the Vengeance of the Daleks (sorry!) The mire-beasts plaguing the Aridians break through a cavern wall like the Kool Aid pitcher (and both with all the finesse of Chris Christie, but I digress), in the struggle, the travelers escape, regaining the TARDIS.
The second vignette is a comic little bit in New York, in 1966 (The Chase aired from May 22-June 26, 1965, so still in the future, albeit not much). We're on the Empire State Building Observation Deck, where the TARDIS materializes in front of a confused young Alabaman, Morton Dill, played by Peter Purves. (We'll meet again!)
Finally, the TARDIS lands on, and thus dooms, the Mary Celeste.
The vignettes are interesting--a mix of comic and straight Doctor Who styles. So, on Aridius, with the mercifully not yet seen mire beasts pursuing them, Ian and Vicki exchange insults:
[Chamber]The American accents in the Empire State Building vignette are nothing short of atrocious, and Dill is played by Purves as a grinning ass, but most of the comedy works, and the Mary Celeste sequence combines some good comedy with a creepy finish. Still, unlike some of Terry Nation's other episodes, the thing moves along at a brisk, enjoyable pace, and never gets dull.
IAN: Don't just stand there and scream, you little fool. Run!
(But there's another one in their path)
VICKI: Oh, don't just standing there gaping, you nit! Come on, back!
(Ian throws a rock at it)
A couple firsts, in this story--the first, primitive effect at showing the TARDIS traveling through the vortex (or whatever that effect os meant to be), and the Dalek's similar ship in hot pursuit.
Also, the TARDIS crew are now the nemesis of the Daleks, their "greatest enemy."
The myth of the Oncoming Storm, it seems, has begun.
EDITED TO ADD: I meant to include, but failed to, the delightfully insane, but rather nifty, jazzy incidental music that captures the jaunty feel of these first three episodes. Terry Nation has given us his most fun script to date, and the production team has gone for it.