Monsieur Peter Barbiaux is either a resident of or visitor to Mechanicsburg who is unfortunate enough to be inside the city walls and drinking a beverage at the moment that Klaus Wulfenbach drops in with his Take-Five Bomb. This or some other startling event causes Peter to drop his cup right as the Bomb is activated and the two of them are more or less frozen in time. (The fact that light still passes through the city, albeit in a red-shifted state, is an indication that time is not totally stopped.)
Two and a half years later, now-Baron Gilgamesh Wulfenbach and his minions have managed to extend tunnels of unfrozen time into the city as far as Peter's location. A surveyor's range pole has set up in front of the poor fellow, to which has been attached a piece of paper recording his name and various other bits of collected data. A gauge marker has also been attached, indicating the current level of the cup. Thus, the rate of fall of the cup gives the Empire's scientists some idea of how fast time is passing, by comparing to rate of fall during normal time.