A couple hundred years ago, astronomers realized that it was possible to use transits to determine the distances to the sun and planets. We knew their relative distances from the sun, but we could not easily put that in absolute terms. So astronomers developed a clever trick.
At different parts of the Earth, a transit begins at slightly different times because the observers are looking from slightly different angles. If you can time the start of the eclipse very accurately, and you know the distance between the two observers, you can calculate the exact distance to the planet.
Unfortunately, this didn't work. First, in the days prior to atomic clocks, GPS, and even radio, clocks were just not quite accurate enough to get a good measurement. Also, astronomers did not know about the now-infamous "black drop" effect. Astronomers decided to make timing measurements at the moment that Mercury or Venus was first fully inside the sun (because it is hard to be looking at just the right instant when the transit begins). But when explorers were watching transits, they noticed that the round planet and the round sun did not break cleanly, but a little thread of black connected them for some time after the planet was fully inside the sun.
The explanation of the black drop (which you can observe tomorrow if you have the right equipment!) is still unclear. It is probably due to a variety of things -- Earth's atmosphere, the atmosphere of Venus (when Venus transits), and imperfect instruments used for the observing. So, the measurements of the distance to the planets were not as accurate as was hoped.
These days, we measure the distance to the planets by radar -- we bounce a radar pulse off of the planet and see how long it takes to return. That's VERY accurate!
Tomorrow, we will talk about transits and modern science.