The point of first and second contact was a problem for those in the 18th and 19th Centuries, sent on expeditions around the world to measure the Transit of Venus, in order to refine the Earth/Sun distance. This distance was needed to calculate the size of the Solar System.

Seeing conditions, the 'Black Drop Effect' ( due to optics quality ), plus magnification and image brightness, can make spotting first and second contact difficult. White light gives a nice clean limb of the Sun to watch against. But is that the edge of the Sun? The Chromesphere is above the photosphere, is that where first contact is made? and is it the top of the spicules or the base of them?

These three Hydrogen Alpha pictures below are all from the same image, with the brightness and contrast adjusted up and down. In the first Mercury could still be partially across the limb. In the second, it could be second contact, and in the third, it is already fully onto the disc. So where is its exact position?

With the instrumentation of the 18th and 19th Centuries, it is amazing that they narrowed down the distance as accurately as they did.