when Herschel recommended them, the astronomical day began at noon. The astronomical day had begun at noon ever since Ptolemy chose to begin the days for his astronomical observations at noon. He chose noon because the transit of the Sun across the observer's meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset, which vary by several hours. Midnight was not even considered because it could not be accurately determined using water clocks. Nevertheless, he double-dated most nighttime observations with both Egyptian days beginning at sunrise and Babylonian days beginning at sunset. Medieval Muslim astronomers used days beginning at sunset, so astronomical days beginning at noon did produce a single date for an entire night. Later medieval European astronomers used Roman days beginning at midnight so astronomical days beginning at noon also allow observations during an entire night to use a single date. When all astronomers decided to start their astronomical days at midnight to conform to the beginning of the civil day, on , it was decided to keep Julian days continuous with previous practice, beginning at noon. During this period, usage of Julian day numbers as a neutral intermediary when converting a date in one calendar into a date in another calendar also occurred. An isolated use was by Ebenezer Burgess in his 1860 translation of the Surya Siddhanta wherein he stated that the beginning of the Kali Yuga era occurred at midnight at the meridian of Ujjain at the end of the 588,465th day and the beginning of the 588,466th day (civil reckoning) of the Julian Period, or between or . Robert Schram was notable beginning with his 1882 Hilfstafeln für Chronologie. Here he used about 5,370 "days of the Julian Period". He greatly expanded his usage of Julian days in his 1908 Kalendariographische und Chronologische Tafeln containing over 530,000 Julian days, one for the zeroth day of every month over thousands of years in many calendars. He included over 25,000 negative Julian days, given in a positive form by adding 10,000,000 to each. He called them "day of the Julian Period", "Julian day", or simply "day" in his discussion, but no name was used in the tables. Continuing this tradition, in his book "Mapping Time: The Calendar and Its History" British physics educator and programmer Edward Graham Richards uses Julian day numbers to convert dates from one calendar into another