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The eight princesses
The eight princesses are the only ones who know where the time machine is hidden, and they'll reveal only to a space ace at an experience level of 8 or higher (7000 exp. pts. or more). All this high-tech knowledge hints at the fact that the princesses actually come from the future of Sosaria using the time machine.
There's one princess in each of the eight kings castles. First, knock out Gwino the jester: she'll drop a key (it does not appear in the menu). The guards will then attack the Stranger. Make your way to the castle prisons. [U]nlock one of the two cells. Note that Gwino's key may only open one of the two cells, at random; you may need to exit and re-enter each castle a few times before Gwino drops the key to the princess' cell.
When the princess is free, bring her to the castle entrance. Each princess will then reward the Stranger with 500 gold, food and experience. If the Stranger is a Space Ace and he's at level 8 or higher, the princess will also reveal the location of the time machine (it's always far to the north-west of the castle).
Here's why Mondain was nowhere to be found during the age of Lord British: he was slain 1000 years earlier! His followers made everyone believe he was still alive, but it's probably Exodus who kept spawning and controlling monsters for centuries (as revealed in Ultima 3).
After the time travel, the Stranger find himself in Mondain's fortress. [G]et the gem so to break it, then attack Mondain. Chase him when he turns into a bat and slain him. Congratulations: you cleared Ultima 1!