Ptolemy, to whom we are indebted for a great number of scientific statements in addition to his astronomical observations and those of Hipparchus which he has preserved to us, makes use of two important Epochs. The first is that of Nabonasser. The first year of his reign was in the year 747 B.C., and the month Thoth began on the 26th February in that year. Hence Nab. 1, Thoth 1 constitutes an Epoch equivalent to Feb. 26, 747 B.C. But this latter is the secular date and the astronomical is one less, namely, 746 B.C. The reason for this is that the secular date A.D. 1 passes directly to the year 1 B.C., when counting backwards, whereas the astronomical account makes A.D. 1 refer back to A.D. 0, and then to 1 B.C. Hence all dates _before_ the Christian Era are given in secular accounts as one year more than the astronomical. Now as to the Egyptian months used by Ptolemy. These were— 1. Thoth February. 2. Paophi March. 3. Athyr April. 4. Choiac May. 5. Tybi June. 6. Mechir July. 7. Phamenoth August. 8. Pharmuthi September. 9. Pachon October. 10. Payni November. 11. Epiphi December. 12. Mesori January. Each month contained thirty days, and there were five days at the end of the year which they called the Epagomene. The year began at noon on the first of Thoth. Another Epoch used by Ptolemy, and frequently referred to by the Greeks, is that of Calippus. The Calippic Period was invented by the man whose name it bears and dates to the year 330 B.C. It is a period of 76 years, which is four times 19, and was designed to bring the new and full moons to the same date of the solar year. The Olympiads were in use among the Greeks, and began in the year 776 B.C., on the 1st July (O.S.). Each Olympiad consists of four years, and in marking a date the number of the Olympiad and the year of that Olympiad are given. Thus the first of Calippus would fall in the third year of the 112th Olympiad. The astronomical years equivalent to these are, for the Olympiads 775 B.C., and for the Calippic Period 329 B.C. The Kali Yuga is an Indian Epoch which began at the New Moon of February 3102 B.C.—Feb. 5th. The Epoch of Salivahana in use among the Dravidians of India is the year A.D. 78. The Chinese Cycle of years began in the year 2696 B.C. (astronomical), at the New Moon of February, the Sun being then half-way between the Solstice and the Equinox.