Final answer:
In 'The Time Machine', it is the Time Traveller who finds matches in the museum-like palace of green porcelain, not characters named Dudley and Filby.
Step-by-step explanation:
In H.G. Wells' novel The Time Machine, the protagonist, commonly referred to as the Time Traveller, is accompanied by characters named Dudley, Filby, and Weena during different parts of his journey. However, there seems to be a confusion in the question as the characters Dudley and Filby do not find anything in the museum; this event is not a part of the narrative. It is the Time Traveller himself who visits a palace of green porcelain, which could be considered a museum, where he finds matches which become significant later in the story. The Time Traveller uses these matches for light and for fire, which is critical in his interactions with the Morlocks, the antagonistic creatures of the future world he explores. Importantly, it should be noted that the Time Traveller is often alone in his explorations, or accompanied by Weena, one of the Eloi, but not by characters named Dudley and Filby during these events.