SECTION 1. MEASUREMENT

The Tunnel

Astronomers have measured the distance of the Sun from the Earth; even the distance of the fixed stars. How did they do this? Not by strolling through outer space with a measuring rod. The distance of places that cannot be reached is calculated from the distance of places that can be reached. To measure the stars we get down to Earth; cosmological survey has a terrestial base.

We begin with a terrestial problem. Due to increasing population a certain city of ancient Greece found its water supply insufficient, so that water had to be channeled in from a source in the nearby mountains. And since, unfortunately, a large hill intervened, there was no alternative to tunneling. Working from both sides of the hill, the tunnelers met in the middle as planned. See Figure 1.1.

How did the planners determine the correct direction to ensure that the two crews would meet? How would you have planned the job? Remember that the Greeks could not use radio signal or telescope, for they had neither. Nevertheless they devised a method and actually succeeded in making their tunnels from both sides meet somewhere inside the hill. Think about it.

Of course, had not the source been on a higher level than the city, there would not have been gravity to make the water flow through this aqueduct. But, to better concentrate on the crux of the matter, let us neglect the complication due to difference of levels.