add the missing day, and proclaim the chief days of the year--the shortest day, the longest day, and the equinox-days of equal halves of sunshine and darkness. In ancient China, if the State astronomer made a wrong calculation in predicting an eclipse he was decapitated. It is easy to understand how it became desirable to recognise more convenient divisions of the year than the four quarters marked by the solstices and the equinoxes. Various astronomical events were studied, and their regular recurrence ascertained, and they were used for this purpose. But the most obvious natural timekeeper to make use of, besides the sun, was the moon. The moon completes its cycle of change on the average in 29-1/2 days. It was used by every man to mark the passage of the year, and its periods from new moon to new moon were called, as in our language, "months" or "moons," and divided into quarters. It is, however, an awkward fact that twelve lunar months give 354 days, so that there are eleven days left over when the solar year is divided into lunar months. The attempt to invent and cause the adoption of a system which shall regularly mark out the year into the popular and universally recognised "moons," and yet shall not make the year itself, so built up, of a length which does not agree with the true year recorded by the return of the rising sun to exactly the same spot on the horizon after 365 days and a few hours, has been throughout all the history of civilised man, and even among prehistoric peoples, a matter of difficulty. It has led to the most varied and ingenious systems, entrusted to the most learned priests and state officers, and mostly so complicated as to break down in the working, until we come to the great clear-headed man Julius Caesar.