Testing time
Aditya Rishi

It takes a long time to become young. — Pablo Picasso

(Continued from last week)

THE clock that was like a jewel in the crown of St Peter's Church in Z`FCrich was officially put into use when it showed 6 o'clock, but it was soon realised that the hour-hand and minute-hand had been interchanged and attached to the wrong axes. Now, the minute-hand moved with a speed 12 times greater than the hour-hand (But these were not the correct hands). On the time given by the clock maker, when the clock was unveiled to the world, something remarkable happened: on the moment everyone looked at the clock, it showed exactly the right time.

When asked how he had done it, the clock maker said: "The problem was: if the clock started in the 6 o'clock position, then, what was the first moment that it showed the correct time again?" Watchmakers of Switzerland, who had all gathered there to witness the unveiling of the clock, still failed to understand how could such a moment be calculated, so, they turned to the clock maker for the answer.

The man who had saved Switzerland's reputation said: "I could say that the answer just dropped out of my head, but the truth is that it was a testing time for all of us, and I was not an exception. Time was short, so, the hands could not be put back into the right place. Like all of you, I, too, had given up. I looked up in despair at the clock and, for a moment, imagined it to be showing the correct time."

"It led me to the wild thought of putting up a correct clock beside the church clock, which gave me an idea. I imagined a second pair of hands turning together with the wrong pair of hands, but in the correct way. When the wrong pair is in the same position as the right pair, this means that the time shown is right. First, look at the hour-hands that are at 12. One turns with the correct speed, the other with a speed that is 12 times as small. These two hands come in the same position again when the slow hand has progressed x minutes. The fast hand, then, has progressed 60+x minutes. The time x that passed, then holds: (60+x)/12 = x, meaning that x = 5 5/11 minutes. The minutes-hands that start at 6 holds the same. The clock with interchanged hands, therefore, shows the correct time again at 5 5/11 minutes past 7."

The fame of the Z`FCrich clock and its maker spread across Europe and, soon, everyone wanted to wear watches made in Switzerland. Mathematical precision became the hallmark of Swiss watch industry which took off from here. The clock on top of the tower of St Peter's Church in Z`FCrich, with the diameter of its face measuring 8.7 m, is still the largest church clock in Europe. (Write at The Tribune or adityarishi99@yahoo.co.in)