Chapter Eleven, ``A Prince In Bondage'', reveals that the Hidden City has not been destroyed by Kane's attack.
In fact, finding one of Kane's soldiers has infiltrated the city and opened the doors, the Scientist-General Huer is fast to shut the doors and trap some of Kane's ships, along with a little fist fight where everyone was trained for 1930s-style Western fighting until Rogers remembers he has a ray gun.
Rogers proposes at a war council that the only alternative now is going on the attack, with Saturn's help. But Saturn won't answer the phone; while Rogers thinks the phone might just be turned off, Huer is sure it's broken. Despite the risk of crashing yet again, Rogers sets off to investigate on what he says is only his third trip there; it seems like more. Rogers goes in one of Kane's captured ships, since why not, he's flown those more than he's flown Hidden City ships, and while he's spotted by Kane's forces they don't suspect a thing as he goes to Saturn rather than Kane's headquarters.
Buddy snuck aboard Rogers's ship, of course, and despite his obeying the serial adventure rule of hiding by being near an object and thinking he was hiding, Rogers notices. It turns out Saturn's quiet because what with Rogers having left them unattended for fifteen minutes Kane's man Laska captured Prince Tallen and are holding him hostage in trade for Saturn's alliance or at least neutrality. Rogers, no one to learn from experience, bullies his way into the High Council chamber while the guards deliver halfhearted looks of partial disapproval I guess, and demands the chance to explain why giving in to Kane's demands is wrong.
``Gentlemen, you're dealing with the vilest type of crime known to man: kidnapping.''
And here we maybe remember that oh, yeah, in the 1930s there was a kidnapping wave and it really did seem like the end of the world for as long as J Edgar Hoover figured he could tout the FBI as the cure for it. Otherwise, man, I could come up with a dozen viler crimes without even digging into the minor Law & Order reruns this week. But Rogers goes on to prove his point through ... a flashback.
Specifically, he talks of how when Prince Tallen was first sent to Earth, to negotiate with Kane. While in Kane's council chambers, Rogers and Buddy had broken in, held the leaders of Earth under ray gun, forced Kane to show the dynamo room where, Rogers intoned, mind-controlled zombie slaves were being worked, and then talked Tallen into leaping out the window with them (with the aid of an antigravity belt).
Truly this proves how a treaty with Kane would result only in betrayal of Saturn. I think it also proves that the serial was made with an allotment of maybe ten minutes for flashbacks in the later chapters and nobody was able to figure out flashbacks which were on point.
So while Rogers may argue stupidly, Saturn's High Council is just that much stupider, and they vote to keep the alliance with the Hidden City and go to war with Kane's forces. Kane's forces, overhead, begin bombing, indicating either they were listening in to the deliberations or they got lucky. Under bombardment some of those huge cylindrical columns that are always in these kinds of sets fall down very near Buster Crabbe and if you aren't careful this looks like he and Buddy have been hit and that's our cliffhanger.
Trivia: Thomas Watson's introduced his iconic ``THINK'' sign while he was working for National Cash Register; when he left for the Computing-Tabulating-Recording corporation in 1914, he took the icon with him. Source: The Maverick And His Machine: Thomas Waston Sr and the Making of IBM, Kevin Maney.
Currently Reading: Star Science Fiction Original #4, Editor Frederik Pohl. (Great Original Stories, it says, and one did indeed hit the all-time great lists.) So the introduction is Pohl talking about the looming population bomb and how if we don't do something Soon, ``Malthusian Law is about to be re-enacted'' and what to do? ``That's the kind of question the eight writers in this present volume ... are well equipped to answer.'' I'm not sure how Fritz Leibner's ``Space-Time For Springers'' answers the Malthusian Law problem, however. And even the Kornbluth entry is one that's not about how all those genetically inferior lunkheaded idiots keep out-breeding the smart people (``The Advent On Channel Twelve'', which is more about the perils of The Mickey Mouse Club).