Yang and Verbiest should each use their mathematical skills to determine the answers and that "The Heavens would be the judge". The contest was held at the Bureau of Astronomy in the presence of senior-ranking government ministers and officials from the observatory. Unlike Yang, Verbiest had access to the latest updates on the Rudolphine Tables, and was assisted by telescopes for observation. He succeeded in all three tests, and was immediately installed as Head of the Mathematical Board and Director of the Observatory. Out of consideration for him, the exiled Jesuits were authorized to return to their missions. Meanwhile, Yang was sentenced to the same death he had planned for his Jesuit rival, but the sentence was reduced to exile and he died en route to his native home. Initial projects The 1670 calendar included an extra month unnecessarily, added to hide other errors and to bring the lunar months in line with the solar year. Verbiest suggested the errors should be corrected, including removing the extra month. This was an audacious move, as the calendar had been approved by the emperor himself. Fearing the emperor's response, the observatory officials begged him to withdraw this request, but he responded: "It is not within my power to make the heavens agree with your calendar. The extra month must be taken out." Much to their surprise, the emperor after studying the research, agreed, and it was done. After this, Verbiest and the emperor formed a real friendship, with the Jesuit teaching him geometry, philosophy and music. He was frequently invited to the palace and to accompany the Emperor on his expeditions throughout the empire. He translated the first six books of Euclid into Manchu and took every opportunity to introduce Christianity. In response, the Emperor elevated him to the highest grade of the mandarinate and granted permission for him to preach Christianity anywhere in the empire. Verbiest undertook many projects, including the construction of an aqueduct, the casting of 132 cannons for the imperial army – far superior to any previous Chinese weapons – and the design of a new gun carriage. He created star charts for the Kangxi Emperor in order to tell the time at night. Other inventions included a steam engine to propel ships. Instruments for Beijing Observatory Having resolved the issues surrounding the calendar, Verbiest went on to compose a table of all solar and lunar eclipses for