Guest stars:

William Smithers        Capt. R. M. Merik (Mericus), dropped out of the Academy in his 5th year. failed a psychosimulator test, went into the merchant service.
Logan Ramsey            Claudius Marcus, Proconsul
Ian Wolfe               Septimus, ex senator, now a slave, follower of the Son
Rhodes Reason           Flavius Maximus, ex gladiator, slave, follower of the Son
Lois Jewell             Drusilla, female slave of C. Marcus
Bart LaRue              Announcer
Jack Perkins            Master of Game
William B. Harrison (not seen) last of the barbarians,  flight officer of the SS Beagle
Achilles, gladiator

Crew Appearances:
Kirk, Spock, McCoy
Checkov
Uhura
No Sulu
Scotty
 

Story:

Discovering the 6 year ago wreckage of starship Beagle(crew of 47), Kirk, Spock and McCoy beam down to planet 892-IV, to learn Beagle's Captain Merik has betrayed his crew, beaming them down to the planet's Roman style arena to fight to their deaths. Then, Merik adds Kirk and his crew to the list of combatants trying to force the crew to never leave the system and spread word of their remarkable planet.  Spock and McCoy must fight each other, and Kirk is sentenced to die. Scotty uses the power of the Enterprise to peacefully resue the landing party.

System 892 planet 4: earthlike in all ways plus parallel developement althought this 'earth' the Roman Empire never failed, Christianity was suppressed and only in their modern era did slaves hear of Christ's coming.  Analysis of the planet reveals smog, large cities, roadways, but no atomic power.

Hodgkin's Law of Parallel Planet Development

Cultural Quirks of 892-4:
Jupiter 8: a car
Nepturne bath salts
Mars Toothpaste
"Name the Winner" TV gladiator show

Foods: Garrot Rosted Sparrow
Roast Kid

Spock refers to WW III.

Spock usues neck pinch on prison guard and Flavius in the games.

Quotes:
"Once, just once, I would like to land someplace and say 'Behold, I am the arch angle Gabriel'". McCoy
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"Must you be so blasted honest?" McCoy
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In some parts of the galaxy I have seen forms of entertainment that make this look like a folk dance".Kirk
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"I'm trying to thank you, you pointed eared hobgobbin." McCoy.