Transits of Mercury and Venus across the face of the Sun are rare. The 20th century had 15 transits of Mercury and the 21st century will have 14, the two most recent occurring on 15 November 1999 and 7 May 2003. We report on our observations and analysis of a black-drop effect at the 1999 and 2003 transits of Mercury seen in high spatial resolution optical imaging with NASA’s Transition Region and Coronal Explorer (TRACE) spacecraft. We have separated the primary contributors to this effect, solar limb darkening and broadening due to the instrumental point spread function, for the 1999 event. The observations are important for understanding historical observations of transits of Venus, which in the 18th and 19th centuries were basic for the determination of the scale of the solar system. Our observations are in preparation for the 8 June 2004 transit of Venus, the first to occur since 1882. Only five transits of Venus have ever been seen – in 1639, 1761, 1769, 1874, and 1882. These events occur in pairs, whose members are separated by 8 years, with an interval between pairs of 105 or 122 years. Nobody alive has ever seen a transit of Venus.