the Moon in a telescopic view. The planet appears as a small and "full" disc when it is on the opposite side of the Sun (at superior conjunction). Venus shows a larger disc and "quarter phase" at its maximum elongations from the Sun, and appears its brightest in the night sky. The planet presents a much larger thin "crescent" in telescopic views as it passes along the near side between Earth and the Sun. Venus displays its largest size and "new phase" when it is between Earth and the Sun (at inferior conjunction). Its atmosphere is visible through telescopes by the halo of sunlight refracted around it. The phases are clearly visible in a 4" telescope. Daylight apparitions Naked-eye observations of Venus during daylight hours exist in several anecdotes and records. Astronomer Edmund Halley calculated its maximum naked eye brightness in 1716, when many Londoners were alarmed by its appearance in the daytime. French emperor Napoleon Bonaparte once witnessed a daytime apparition of the planet while at a reception in Luxembourg. Another historical daytime observation of the planet took place during the inauguration of the American president Abraham Lincoln in Washington, D.C., on 4March 1865. Although naked eye visibility of Venus's phases is disputed, records exist of observations of its crescent. Transits The Venusian orbit is slightly inclined relative to Earth's orbit; thus, when the planet passes between Earth and the Sun, it usually does not cross the face of the Sun. Transits of Venus occur when the planet's inferior conjunction coincides with its presence in the plane of Earth's orbit. Transits of Venus occur in cycles of with the current pattern of transits being pairs of transits separated by eight years, at intervals of about or —a pattern first discovered in 1639 by the English astronomer Jeremiah Horrocks. The latest pair was June 8, 2004 and June 5–6, 2012. The transit could be watched live from many online outlets or observed locally with the right equipment and conditions. The preceding pair of transits occurred in December 1874 and December 1882; the following pair will occur in December 2117 and December 2125. The 1874 transit is the subject of the oldest film known, the 1874 Passage de Venus. Historically, transits of Venus were important, because they allowed astronomers to determine the size of the astronomical unit, and hence the size of the Solar System as shown by Horrocks in 1639.